Peridynamics(PD)is an effective method for simulating the spontaneous initiation and propagation of tensile cracks in materials.However,it faces great challenges in simulating compression-shear cracking of geomaterial...Peridynamics(PD)is an effective method for simulating the spontaneous initiation and propagation of tensile cracks in materials.However,it faces great challenges in simulating compression-shear cracking of geomaterials due to the lack of efficient contact-friction models.This paper introduces an original contact-friction model that leverages twin mesh and potential function principles within PD to model rock cracking under tensile and compressive stresses.The contact detection algorithm,based on space segmentation axis-aligned bounding box(AABB)tree data structure,is used to address the significant challenge of highly efficient contact detection in compression and shear problems.In this method,the twin mesh and potential function are utilized to quantify contact detection and contact degree,as well as friction behavior.This is in contrast to the distance and circular contact area model,which lacks physical significance in the classical PD method.As demonstrated by the tests on specimens containing cracks,the proposed model can capture 8 types of secondary fractures,reduce the contact detection error by about 29%e56%,and increase the contact retrieval efficiency by over 1600 times compared to the classic PD models.This significantly enhances the capability of PD to simulate the initiation,expansion,and coalescence of intricate compression-shear cracks.展开更多
Peridynamics(PD)is an emerging method that establishes a theoretical framework based on non-local theory to describe material mechanical behavior with spatial integral equations.It gives a unified expression of the me...Peridynamics(PD)is an emerging method that establishes a theoretical framework based on non-local theory to describe material mechanical behavior with spatial integral equations.It gives a unified expression of the me-dium including state transformation and characterization in different scales.It is showing great potential for evaluating the complicated mechanical behaviors of brittle solids.In the past two decades,peridynamics has been showing its great potential and advantages in modeling crackings of brittle materials although there are many challenges.The present paper summarizes firstly the theoretical framework and advantages of peridy-namics for modeling fracturing.It introduces then the theoretical improvements to address challenges of peri-dynamics in modeling brittle solid crackings including the release of Poisson ratio limit,different fracture criteria,contact-friction models,coupled constitutive models,and computing accuracy.Afterward,the extension of peridynamics is introduced to the coupled modeling with the other methods such as finite element method,phase field method,and particle-like method before its applications in static and dynamic cracking as well as those under impacts.Meanwhile,some contents that require further exploration are briefly summarized.Finally,the blind spots and future development of peridynamics are analyzed and discussed for the deformation and fracturing modeling of brittle geomaterials.展开更多
Fracture in ductile materials often occurs in conjunction with plastic deformation.However,in the bond-based peridynamic(BB-PD)theory,the classic mechanical stress is not defined inherently.This makes it difficult to ...Fracture in ductile materials often occurs in conjunction with plastic deformation.However,in the bond-based peridynamic(BB-PD)theory,the classic mechanical stress is not defined inherently.This makes it difficult to describe plasticity directly using the classical plastic theory.To address the above issue,a unified bond-based peridynamics model was proposed as an effective tool to solve elastoplastic fracture problems.Compared to the existing models,the proposed model directly describes the elastoplastic theory at the bond level without the need for additional calculation means.The results obtained in the context of this model are shown to be consistent with FEM results in regard to force-displacement curves,displacement fields,stress fields,and plastic deformation regions.The model exhibits good capability of capturing crack propagation in ductile material failure problems.展开更多
The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic...The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.展开更多
In this paper,the degradation of mechanical properties of engineering cementitious composites(ECCs)at elevated temperatures and the failure of fiber are considered.A failure model under coupled thermo-mechanical loads...In this paper,the degradation of mechanical properties of engineering cementitious composites(ECCs)at elevated temperatures and the failure of fiber are considered.A failure model under coupled thermo-mechanical loads for ECC is developed based on bond-based peridynamics.A semi-discrete model is constructed to describe fiber–matrix interactions and simulate thermal failure in ECC.The peridynamic differential operator(PDDO)is utilized for non-local modeling of thermal fluid flow and heat transfer.A multi-rate explicit time integration method is adopted to address thermo-mechanical coupling over different time scales.Model validation is achieved through simulating transient heat transfer in a homogeneous plate,with results aligning with analytical solutions.The damage behavior of a heated ECC plate in a borehole and under a fire scenario is analyzed,providing insights for enhancing fire resistance and high-temperature performance of ECC materials and structures.展开更多
In this study,a numerical method was developed based on peridynamics to determine the ice loads for a ship navigating in level ice.Convergence analysis of threedimensional ice specimen with tensile and compression loa...In this study,a numerical method was developed based on peridynamics to determine the ice loads for a ship navigating in level ice.Convergence analysis of threedimensional ice specimen with tensile and compression loading are carried out first.The effects of ice thickness,sailing speed,and ice properties on the mean ice loads were also investigated.It is observed that the ice fragments resulting from the icebreaking process will interact with one another as well as with the water and ship hull.The ice fragments may rotate,collide,or slide along the ship hull,and these ice fragments will eventually drift away from the ship.The key characteristics of the icebreaking process can be obtained using the peridynamic model such as the dynamic generation of cracks in the ice sheet,propagation and accumulation of ice fragments,as well as collision,rotation,and sliding of the ice fragments along the ship hull.The simulation results obtained for the ice loads and icebreaking process were validated against those determined from the Lindqvist empirical formula and there is good agreement between the results.展开更多
In this study,we propose the first unified implementation strategy for peridynamics in commercial finite element method(FEM)software packages based on their application programming interface using the peridynamics-bas...In this study,we propose the first unified implementation strategy for peridynamics in commercial finite element method(FEM)software packages based on their application programming interface using the peridynamics-based finite element method(PeriFEM).Using ANSYS and ABAQUS as examples,we present the numerical results and implementation details of PeriFEM in commercial FEM software.PeriFEM is a reformulation of the traditional FEM for solving peridynamic equations numerically.It is considered that the non-local features of peridynamics yet possesses the same computational framework as the traditional FEM.Therefore,this implementation benefits from the consistent computational frameworks of both PeriFEM and the traditional FEM.An implicit algorithm is used for both ANSYS and ABAQUS;however,different convergence criteria are adopted owing to their unique features.In ANSYS,APDL enables users to conveniently obtain broken-bond information from UPFs;thus,the convergence criterion is chosen as no new broken bond.In ABAQUS,obtaining broken-bond information is not convenient for users;thus,the default convergence criterion is used in ABAQUS.The codes integrated into ANSYS and ABAQUS are both verified through benchmark examples,and the computational convergence and costs are compared.The results show that,for some specific examples,ABAQUS is more efficient,whereas the convergence criterion adopted in ANSYS is more robust.Finally,3D examples are presented to demonstrate the ability of the proposed approach to deal with complex engineering problems.展开更多
A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspire...A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method.展开更多
In the ice-covered oceanic region,the collision between sea ice and offshore structures will occur,causing the crushing failure of ice and the vibration of structures.The vibration can result in fatigue damage of stru...In the ice-covered oceanic region,the collision between sea ice and offshore structures will occur,causing the crushing failure of ice and the vibration of structures.The vibration can result in fatigue damage of structure and even endanger the crews’health.It is no doubt that this ice-structure interaction has been noted with great interest by the academic community for a long time and numerous studies have been done through theoretical analysis,experimental statistics and numerical simulation.In this paper,the bond-based Peridynamics method is applied to simulate the interaction between sea ice and wide vertical structures,where sea ice is modeled as elastic-plastic material,with a certain yield condition and failure criterion.Oscillation equation of single-degree-of-freedom is considered to investigate the vibration features of the structure during the interaction process.The damage of ice,ice forces and vibration responses of structure in the duration are obtained through numerical simulation.A parametric investigation is undertaken to identify the key parameters,such as ice thickness,the diameter of structure and relative velocity that trigger the ice crushing,ice forces and vibration responses of the structure.Results indicate that all three parameters have a positive correlation with the overall level of ice force and vibration displacement.Besides,a velocity coefficient is proposed to predict the vibration displacement based on its relation with ice speed.展开更多
While the present structural integrity evaluation method is based on the philosophy of assumed similitude, Fatigue and Damage Tolerance(F&DT) evaluations for next generation of air-vehicles require high-fidelity p...While the present structural integrity evaluation method is based on the philosophy of assumed similitude, Fatigue and Damage Tolerance(F&DT) evaluations for next generation of air-vehicles require high-fidelity physical models within cyberspace. To serve the needs of F&DT evaluation in digital twin paradigm, a fatigue damage-cumulative model within peridynamic framework is proposed in this paper. Based on the concept of fatigue element block and damage accumulation law in form of Coffin-Manson relationship, the proposed model applies to both fatigue crack initiation and fatigue crack growth;fatigue crack growth rates under constant-amplitude and simple variable-amplitude block loading cases can be well predicted for three common structural materials without inputs of Paris law parameters. Additionally, the proposed model can also be easily extended to a probabilistic version;for verification, multiple-site-damage problems are simulated and the statistic nature of fatigue process in experiments can be well captured. In the end, main features of the proposed model are summarized, and distinctions from the other models are discussed. There may be a potential for the peridynamic damage-cumulative model proposed in this work to numerically predict fatigue problems in digital twin paradigm for future generations of aerospace vehicles.展开更多
The ablation of ultra-high-temperature ceramics(UTHCs)is a complex physicochemical process including mechanical behavior,temperature effect,and chemical reactions.In order to realize the structural optimization and fu...The ablation of ultra-high-temperature ceramics(UTHCs)is a complex physicochemical process including mechanical behavior,temperature effect,and chemical reactions.In order to realize the structural optimization and functional design of ultra-high temperature ceramics,a coupled thermo-chemo-mechanical bond-based peridynamics(PD)model is proposed based on the ZrB_(2) ceramics oxidation kinetics model and coupled thermomechanical bond-based peridynamics.Compared with the traditional coupled thermo-mechanical model,the proposedmodel considers the influenceof chemical reactionprocessonthe ablation resistanceof ceramicmaterials.In order to verify the reliability of the proposed model,the thermo-mechanical coupling model,damage model and oxidation kinetic model are established respectively to investigate the applicability of the proposedmodel proposed in dealing with thermo-mechanical coupling,crack propagation,and chemical reaction,and the results show that the model is reliable.Finally,the coupled thermo-mechanical model and coupled thermo-chemo-mechanical model are used to simulate the crack propagation process of the plate under the thermal shock load,and the results show that the oxide layer plays a good role in preventing heat transfer and protecting the internal materials.Based on the PD fully coupled thermo-mechanical model,this paper innovatively introduces the oxidation kinetic model to analyze the influence of parameter changes caused by oxide layer growth and chemical growth strain on the thermal protection ability of ceramics.The proposed model provides an effective simulation technology for the structural design of UTHCs.展开更多
In this paper,a peridynamics-based finite element method(PeriFEM)is proposed for the quasi-static fracture analysis,which is of the consistent computational framework with the classical finite element method(FEM).Firs...In this paper,a peridynamics-based finite element method(PeriFEM)is proposed for the quasi-static fracture analysis,which is of the consistent computational framework with the classical finite element method(FEM).First,the integral domain of peridynamics is reconstructed,and a new type of element called peridynamic element(PE)is defined.Although PEs are generated by the continuous elements(CEs)of classical FEM,they do not affect each other.Then,spatial discretization is performed based on PEs and CEs,and the linear equations about nodal displacement are established according to the principle of minimum potential energy.Besides,cracks are characterized as degradation of the mechanical properties of PEs.Finally,the validity of the proposed method is demonstrated through numerical examples.展开更多
In the benchmark problems of peridynamics,there are some eccentric results,for example,singularity of uniaxial tension and anomalous dispersion of wave.The reasons to give rise to these results are investigated.We cal...In the benchmark problems of peridynamics,there are some eccentric results,for example,singularity of uniaxial tension and anomalous dispersion of wave.The reasons to give rise to these results are investigated.We calculated local tension and wave of an infinite rod after adding a divergence of local stress in the peridynamic motion equation.The acquired results verify that the singularity in the peridynamic solution of local tension problem and anomalous dispersion of peridynamic wave are all eliminated.Therefore,the anomalous features of some peridynamic solutions likely stem from the lack of local stress characterizing contact interactions.展开更多
We present a novel refinement approach in peridynamics(PD).The proposed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains(with no intersections)to the ...We present a novel refinement approach in peridynamics(PD).The proposed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains(with no intersections)to the nodes of the refinement zone.We will show that no ghost forces are needed when changing the horizon sizes in both subdomains.The approach is applied to both bond-based and state-based peridynamics and verified for a simple wave propagation refinement problem illustrating the efficiency of the method.展开更多
Digital image correlation(DIC)measurement technique and peridynamics(PD)method have been applied in specific fields extensively owing to their respective advantages in obtaining full-field deformation and local failur...Digital image correlation(DIC)measurement technique and peridynamics(PD)method have been applied in specific fields extensively owing to their respective advantages in obtaining full-field deformation and local failure of loaded materials and structures.This study provides a simple way to couple DIC measurements with PD simulations,which can circumvent the difficulties of DIC in dealing with discontinuous deformations.Taking the failure analysis of a compact tension specimen of aluminum alloy and a static three-point bending concrete beam as examples,the DIC experimental system firstly measures the full-field displacements,and then the PD simulation is applied on potential damage regions determined according to the correlation coefficients,to track the micro-crack evolution and macro-crack propagation.As results,the coupled DIC and PD approach can effectively measure the full-field displacement and the localized damage accumulation and crack propagation.展开更多
Molecular dynamics(MD)has served as a powerful tool for designing materials with reduced reliance on laboratory testing.However,the use of MD directly to treat the deformation and failure of materials at the mesoscale...Molecular dynamics(MD)has served as a powerful tool for designing materials with reduced reliance on laboratory testing.However,the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach.In this work,we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets.Firstly,we develop a novel coarse-graining method,to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets.Inspired by the weighted essentially non-oscillatory(WENO)scheme,the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil,then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities.Then,based on the coarse-grained MD data,a two-phase optimizationbased learning approach is proposed to infer the optimal peridynamics model with damage criterion.In the first phase,we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties.Then,in the second phase,the material damage criterion is learnt as a smoothed step function from the data with fractures.As a result,a peridynamics surrogate is obtained.As a continuum model,our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training,and hence allows for substantial reductions in computational cost compared with MD.We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene.Our tests show that the proposed data-driven model is robust and generalizable,in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.展开更多
The numerical simulation results utilizing the Peridynamics(PD)method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japane...The numerical simulation results utilizing the Peridynamics(PD)method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japanese prototype lining test.The load structure model takes into account the cracking process and distribution of the lining segment under the influence of local bias pressure and lining thickness.In addition,the influence of preset cracks and lining section formon the crack propagation of the concrete lining model is studied.This study evaluates the stability and sustainability of tunnel structure by the Peridynamics method,which provides a reference for the analysis of the causes of lining cracks,and also lays a foundation for the prevention,reinforcement and repair of tunnel lining cracks.展开更多
This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of model...This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of modeling the PD unit cell(UC)of continuous fiber-reinforced composite is presented.Periodic boundary conditions are derived and implemented through the Lagrange multiplier method.A matrix-dominated approach for modeling the interphase properties between dissimilar materials is proposed.The periodicity and continuity assumptions are employed to determine the stress and strain fields,as well as the effective elastic properties.The PD-UCs of square and hexagonal packs as well as the 0/90 laminate microstructure are modeled and compared with the analytical,numerical and experimental results from the literature.Good agreement of predicted effective properties can be observed.Unlike other PD homogenization approaches,the effective material properties can be directly and individually obtained from simple loading conditions.展开更多
In this paper,a semi-discrete model based on peridynamics(PD)for engineered cementitious composites(ECCs)is applied to simulate the fracture behavior of functionally graded ECC(FGECC)beams.This is a new application of...In this paper,a semi-discrete model based on peridynamics(PD)for engineered cementitious composites(ECCs)is applied to simulate the fracture behavior of functionally graded ECC(FGECC)beams.This is a new application of PD in ECC.Prior to simulating the crack behavior,the convergence of the PD model for ECC is discussed and the appropriate horizon size 5 and nonlocal ratio m are obtained,i.e.,S=1.6 mm and m=4.In addition,when the bond strain exceeds the elastic limit,a damage variable is introduced into the model,and the model is validated using a simple numerical algorithm.Finally,the dynamic fracture behavior of a two-dimensional FGECC beam under four-point bending is investigated,and the effect of the initial crack location on the fracture behavior is analyzed.Simulation results show that the initial crack location can affect the crack propagation pattern,thereby enabling one to understand the dynamic fracture behavior of ECC structures and guide the engineering practice.展开更多
Peridynamics(PD)is a widely used theory to simulate discontinuities,but its application in real-world structural problems is somewhat limited due to the relatively low-efficiency.The numerical substructure method(NSM)...Peridynamics(PD)is a widely used theory to simulate discontinuities,but its application in real-world structural problems is somewhat limited due to the relatively low-efficiency.The numerical substructure method(NSM)presented by the authors and co-workers provides an efficient approach for modeling structures with local nonlinearities,which is usually restricted in problems of continuum mechanics.In this paper,an approach is presented to couple the PD theory with the NSM for modeling structures with local discontinuities,taking advantage of the powerful capability of the PD for discontinuities simulation and high computational efficiency of the NSM.The structure is simulated using liner elastic finite element(FE)model while the local cracking regions are isolated and simulated using a PD substructure model.A force corrector calculated from the PD model is applied on the FE model to consider the effect of discontinuities.The PD is integrated in the substructure model using interface elements with embedded PD nodes.The equations of motions of both the NSM system and the PD substructure are solved using the central difference method.Three examples of two-dimensional(2D)concrete cantilever beams under the concentrated force are investigated to verify the proposed coupling approach.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.52278333)the China Scholarship Council(CSC)and the Science and Technology Department of Liaoning Province(Grant No.2024JH2/102500069).
文摘Peridynamics(PD)is an effective method for simulating the spontaneous initiation and propagation of tensile cracks in materials.However,it faces great challenges in simulating compression-shear cracking of geomaterials due to the lack of efficient contact-friction models.This paper introduces an original contact-friction model that leverages twin mesh and potential function principles within PD to model rock cracking under tensile and compressive stresses.The contact detection algorithm,based on space segmentation axis-aligned bounding box(AABB)tree data structure,is used to address the significant challenge of highly efficient contact detection in compression and shear problems.In this method,the twin mesh and potential function are utilized to quantify contact detection and contact degree,as well as friction behavior.This is in contrast to the distance and circular contact area model,which lacks physical significance in the classical PD method.As demonstrated by the tests on specimens containing cracks,the proposed model can capture 8 types of secondary fractures,reduce the contact detection error by about 29%e56%,and increase the contact retrieval efficiency by over 1600 times compared to the classic PD models.This significantly enhances the capability of PD to simulate the initiation,expansion,and coalescence of intricate compression-shear cracks.
基金supported by the National Natural Science Foundation of China(NO.52278333).
文摘Peridynamics(PD)is an emerging method that establishes a theoretical framework based on non-local theory to describe material mechanical behavior with spatial integral equations.It gives a unified expression of the me-dium including state transformation and characterization in different scales.It is showing great potential for evaluating the complicated mechanical behaviors of brittle solids.In the past two decades,peridynamics has been showing its great potential and advantages in modeling crackings of brittle materials although there are many challenges.The present paper summarizes firstly the theoretical framework and advantages of peridy-namics for modeling fracturing.It introduces then the theoretical improvements to address challenges of peri-dynamics in modeling brittle solid crackings including the release of Poisson ratio limit,different fracture criteria,contact-friction models,coupled constitutive models,and computing accuracy.Afterward,the extension of peridynamics is introduced to the coupled modeling with the other methods such as finite element method,phase field method,and particle-like method before its applications in static and dynamic cracking as well as those under impacts.Meanwhile,some contents that require further exploration are briefly summarized.Finally,the blind spots and future development of peridynamics are analyzed and discussed for the deformation and fracturing modeling of brittle geomaterials.
基金The corresponding author Lisheng Liu acknowledges the support from the National Natural Science Foundation of China(No.11972267)The corresponding author Xin Lai acknowledges the support from the National Natural Science Foundation of China(No.11802214).
文摘Fracture in ductile materials often occurs in conjunction with plastic deformation.However,in the bond-based peridynamic(BB-PD)theory,the classic mechanical stress is not defined inherently.This makes it difficult to describe plasticity directly using the classical plastic theory.To address the above issue,a unified bond-based peridynamics model was proposed as an effective tool to solve elastoplastic fracture problems.Compared to the existing models,the proposed model directly describes the elastoplastic theory at the bond level without the need for additional calculation means.The results obtained in the context of this model are shown to be consistent with FEM results in regard to force-displacement curves,displacement fields,stress fields,and plastic deformation regions.The model exhibits good capability of capturing crack propagation in ductile material failure problems.
基金supported by the National Key R&D Program of China(2020YFA0710500).
文摘The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.
基金supported by National Natural Science Foundation of China(Grant Numbers 11872339,11472248).
文摘In this paper,the degradation of mechanical properties of engineering cementitious composites(ECCs)at elevated temperatures and the failure of fiber are considered.A failure model under coupled thermo-mechanical loads for ECC is developed based on bond-based peridynamics.A semi-discrete model is constructed to describe fiber–matrix interactions and simulate thermal failure in ECC.The peridynamic differential operator(PDDO)is utilized for non-local modeling of thermal fluid flow and heat transfer.A multi-rate explicit time integration method is adopted to address thermo-mechanical coupling over different time scales.Model validation is achieved through simulating transient heat transfer in a homogeneous plate,with results aligning with analytical solutions.The damage behavior of a heated ECC plate in a borehole and under a fire scenario is analyzed,providing insights for enhancing fire resistance and high-temperature performance of ECC materials and structures.
基金This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement(Grant No.2017YFE0111400)the National Key R&D Program Strategic International Science and Technology Innovation Cooperation Key Specialities(Grant No.2016YFE0202700)+3 种基金the National Natural Science Foundation of China(Grant Nos.51579054 and 51639004)the Ministry of Industry and Information Technology’s High-tech Ship Research Project(Grant No.2017-614)Mr.Renwei Liu is supported by a two-year visiting student fellowship in University of California,Berkeley from Chinese Scholar Council(Grant No.201706680104)this support is gratefully acknowledged.The authors also graciously acknowledge Professor Shaofan Li of University of California,Berkeley and Fei Han of Dalian University of Technology for their guidance and fruitful discussion regarding this work.
文摘In this study,a numerical method was developed based on peridynamics to determine the ice loads for a ship navigating in level ice.Convergence analysis of threedimensional ice specimen with tensile and compression loading are carried out first.The effects of ice thickness,sailing speed,and ice properties on the mean ice loads were also investigated.It is observed that the ice fragments resulting from the icebreaking process will interact with one another as well as with the water and ship hull.The ice fragments may rotate,collide,or slide along the ship hull,and these ice fragments will eventually drift away from the ship.The key characteristics of the icebreaking process can be obtained using the peridynamic model such as the dynamic generation of cracks in the ice sheet,propagation and accumulation of ice fragments,as well as collision,rotation,and sliding of the ice fragments along the ship hull.The simulation results obtained for the ice loads and icebreaking process were validated against those determined from the Lindqvist empirical formula and there is good agreement between the results.
基金the financial support received from the National Natural Science Foundation of China(12272082,11872016)the National Key Laboratory of Shock Wave and Detonation Physics(JCKYS2021212003).
文摘In this study,we propose the first unified implementation strategy for peridynamics in commercial finite element method(FEM)software packages based on their application programming interface using the peridynamics-based finite element method(PeriFEM).Using ANSYS and ABAQUS as examples,we present the numerical results and implementation details of PeriFEM in commercial FEM software.PeriFEM is a reformulation of the traditional FEM for solving peridynamic equations numerically.It is considered that the non-local features of peridynamics yet possesses the same computational framework as the traditional FEM.Therefore,this implementation benefits from the consistent computational frameworks of both PeriFEM and the traditional FEM.An implicit algorithm is used for both ANSYS and ABAQUS;however,different convergence criteria are adopted owing to their unique features.In ANSYS,APDL enables users to conveniently obtain broken-bond information from UPFs;thus,the convergence criterion is chosen as no new broken bond.In ABAQUS,obtaining broken-bond information is not convenient for users;thus,the default convergence criterion is used in ABAQUS.The codes integrated into ANSYS and ABAQUS are both verified through benchmark examples,and the computational convergence and costs are compared.The results show that,for some specific examples,ABAQUS is more efficient,whereas the convergence criterion adopted in ANSYS is more robust.Finally,3D examples are presented to demonstrate the ability of the proposed approach to deal with complex engineering problems.
基金The authors acknowledge the supports from the ERC-CoG(Computational Modeling and Design of Lithium-ion Batteries(COMBAT)),RISE-BESTOFRAC and National Science Foundation of China(51474157).
文摘A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method.
基金This work is supported financially by the National Key R&D Program of China[2018YFC1406000,2016YFE0202700]Supported by the National Natural Science Foundation of China(NSFC)[Grant Nos.51809061,51639004]+1 种基金Supported by the Natural Science Foundation of Heilongjiang Province of China[LC2018021]Supported by the Fundamental Research Funds for the Central Universities[HEUCFM180111].
文摘In the ice-covered oceanic region,the collision between sea ice and offshore structures will occur,causing the crushing failure of ice and the vibration of structures.The vibration can result in fatigue damage of structure and even endanger the crews’health.It is no doubt that this ice-structure interaction has been noted with great interest by the academic community for a long time and numerous studies have been done through theoretical analysis,experimental statistics and numerical simulation.In this paper,the bond-based Peridynamics method is applied to simulate the interaction between sea ice and wide vertical structures,where sea ice is modeled as elastic-plastic material,with a certain yield condition and failure criterion.Oscillation equation of single-degree-of-freedom is considered to investigate the vibration features of the structure during the interaction process.The damage of ice,ice forces and vibration responses of structure in the duration are obtained through numerical simulation.A parametric investigation is undertaken to identify the key parameters,such as ice thickness,the diameter of structure and relative velocity that trigger the ice crushing,ice forces and vibration responses of the structure.Results indicate that all three parameters have a positive correlation with the overall level of ice force and vibration displacement.Besides,a velocity coefficient is proposed to predict the vibration displacement based on its relation with ice speed.
基金supported by the National Natural Science Foundation of China (No. 11672012)。
文摘While the present structural integrity evaluation method is based on the philosophy of assumed similitude, Fatigue and Damage Tolerance(F&DT) evaluations for next generation of air-vehicles require high-fidelity physical models within cyberspace. To serve the needs of F&DT evaluation in digital twin paradigm, a fatigue damage-cumulative model within peridynamic framework is proposed in this paper. Based on the concept of fatigue element block and damage accumulation law in form of Coffin-Manson relationship, the proposed model applies to both fatigue crack initiation and fatigue crack growth;fatigue crack growth rates under constant-amplitude and simple variable-amplitude block loading cases can be well predicted for three common structural materials without inputs of Paris law parameters. Additionally, the proposed model can also be easily extended to a probabilistic version;for verification, multiple-site-damage problems are simulated and the statistic nature of fatigue process in experiments can be well captured. In the end, main features of the proposed model are summarized, and distinctions from the other models are discussed. There may be a potential for the peridynamic damage-cumulative model proposed in this work to numerically predict fatigue problems in digital twin paradigm for future generations of aerospace vehicles.
基金support from the National Natural Science Foun-dation of China(11972267).
文摘The ablation of ultra-high-temperature ceramics(UTHCs)is a complex physicochemical process including mechanical behavior,temperature effect,and chemical reactions.In order to realize the structural optimization and functional design of ultra-high temperature ceramics,a coupled thermo-chemo-mechanical bond-based peridynamics(PD)model is proposed based on the ZrB_(2) ceramics oxidation kinetics model and coupled thermomechanical bond-based peridynamics.Compared with the traditional coupled thermo-mechanical model,the proposedmodel considers the influenceof chemical reactionprocessonthe ablation resistanceof ceramicmaterials.In order to verify the reliability of the proposed model,the thermo-mechanical coupling model,damage model and oxidation kinetic model are established respectively to investigate the applicability of the proposedmodel proposed in dealing with thermo-mechanical coupling,crack propagation,and chemical reaction,and the results show that the model is reliable.Finally,the coupled thermo-mechanical model and coupled thermo-chemo-mechanical model are used to simulate the crack propagation process of the plate under the thermal shock load,and the results show that the oxide layer plays a good role in preventing heat transfer and protecting the internal materials.Based on the PD fully coupled thermo-mechanical model,this paper innovatively introduces the oxidation kinetic model to analyze the influence of parameter changes caused by oxide layer growth and chemical growth strain on the thermal protection ability of ceramics.The proposed model provides an effective simulation technology for the structural design of UTHCs.
基金The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China(11872016)Fundamental Research Funds for the Central Universities(DUT20RC(5)005,DUT20LAB203)the Key Research and Development Project of Liaoning Province(2020JH2/10500003).
文摘In this paper,a peridynamics-based finite element method(PeriFEM)is proposed for the quasi-static fracture analysis,which is of the consistent computational framework with the classical finite element method(FEM).First,the integral domain of peridynamics is reconstructed,and a new type of element called peridynamic element(PE)is defined.Although PEs are generated by the continuous elements(CEs)of classical FEM,they do not affect each other.Then,spatial discretization is performed based on PEs and CEs,and the linear equations about nodal displacement are established according to the principle of minimum potential energy.Besides,cracks are characterized as degradation of the mechanical properties of PEs.Finally,the validity of the proposed method is demonstrated through numerical examples.
基金The support of the National Nature Science Foundation of China through the Grant No.11672129 is gratefully acknowledged.
文摘In the benchmark problems of peridynamics,there are some eccentric results,for example,singularity of uniaxial tension and anomalous dispersion of wave.The reasons to give rise to these results are investigated.We calculated local tension and wave of an infinite rod after adding a divergence of local stress in the peridynamic motion equation.The acquired results verify that the singularity in the peridynamic solution of local tension problem and anomalous dispersion of peridynamic wave are all eliminated.Therefore,the anomalous features of some peridynamic solutions likely stem from the lack of local stress characterizing contact interactions.
文摘We present a novel refinement approach in peridynamics(PD).The proposed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains(with no intersections)to the nodes of the refinement zone.We will show that no ghost forces are needed when changing the horizon sizes in both subdomains.The approach is applied to both bond-based and state-based peridynamics and verified for a simple wave propagation refinement problem illustrating the efficiency of the method.
基金the National Natural Science Foundation of China(Nos.11932006,11672101)the National Key Research&Development Program of China(Nos.2018YFC0406703,2017YFC1502603)+1 种基金the China Postdoctoral Science Foundation(2019M651667)The author Tianyi Li gratefully acknowledges the financial support from China Scholarship Council(No.201906710076).
文摘Digital image correlation(DIC)measurement technique and peridynamics(PD)method have been applied in specific fields extensively owing to their respective advantages in obtaining full-field deformation and local failure of loaded materials and structures.This study provides a simple way to couple DIC measurements with PD simulations,which can circumvent the difficulties of DIC in dealing with discontinuous deformations.Taking the failure analysis of a compact tension specimen of aluminum alloy and a static three-point bending concrete beam as examples,the DIC experimental system firstly measures the full-field displacements,and then the PD simulation is applied on potential damage regions determined according to the correlation coefficients,to track the micro-crack evolution and macro-crack propagation.As results,the coupled DIC and PD approach can effectively measure the full-field displacement and the localized damage accumulation and crack propagation.
基金the projects support by the National Science Foundation(No.DMS-1753031)the Air Force Office of Scientific Research(No.FA9550-22-1-0197)+3 种基金partially supported by the National Science Foundation(No.2019035)the support of the Sandia National Laboratories(SNL)Laboratory-directed Research and Development Programthe U.S.Department of Energy(DOE)Office of Advanced Scientific Computing Research(ASCR)under the Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems(PhILMs)project。
文摘Molecular dynamics(MD)has served as a powerful tool for designing materials with reduced reliance on laboratory testing.However,the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach.In this work,we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets.Firstly,we develop a novel coarse-graining method,to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets.Inspired by the weighted essentially non-oscillatory(WENO)scheme,the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil,then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities.Then,based on the coarse-grained MD data,a two-phase optimizationbased learning approach is proposed to infer the optimal peridynamics model with damage criterion.In the first phase,we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties.Then,in the second phase,the material damage criterion is learnt as a smoothed step function from the data with fractures.As a result,a peridynamics surrogate is obtained.As a continuum model,our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training,and hence allows for substantial reductions in computational cost compared with MD.We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene.Our tests show that the proposed data-driven model is robust and generalizable,in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.
基金supported by the National Natural Science Foundation of China (52079128).
文摘The numerical simulation results utilizing the Peridynamics(PD)method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japanese prototype lining test.The load structure model takes into account the cracking process and distribution of the lining segment under the influence of local bias pressure and lining thickness.In addition,the influence of preset cracks and lining section formon the crack propagation of the concrete lining model is studied.This study evaluates the stability and sustainability of tunnel structure by the Peridynamics method,which provides a reference for the analysis of the causes of lining cracks,and also lays a foundation for the prevention,reinforcement and repair of tunnel lining cracks.
基金This work is supported by the National Natural Science Foundation of China under Grant Nos.1190219711972234 and is sponsored by Shanghai Sailing Program under Contract No.19YF1421700.
文摘This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of modeling the PD unit cell(UC)of continuous fiber-reinforced composite is presented.Periodic boundary conditions are derived and implemented through the Lagrange multiplier method.A matrix-dominated approach for modeling the interphase properties between dissimilar materials is proposed.The periodicity and continuity assumptions are employed to determine the stress and strain fields,as well as the effective elastic properties.The PD-UCs of square and hexagonal packs as well as the 0/90 laminate microstructure are modeled and compared with the analytical,numerical and experimental results from the literature.Good agreement of predicted effective properties can be observed.Unlike other PD homogenization approaches,the effective material properties can be directly and individually obtained from simple loading conditions.
基金the Natural Science Foundation of China(Nos.11872339,11472248)the Natural Science Foundation of Henan Province(No.182300410221).
文摘In this paper,a semi-discrete model based on peridynamics(PD)for engineered cementitious composites(ECCs)is applied to simulate the fracture behavior of functionally graded ECC(FGECC)beams.This is a new application of PD in ECC.Prior to simulating the crack behavior,the convergence of the PD model for ECC is discussed and the appropriate horizon size 5 and nonlocal ratio m are obtained,i.e.,S=1.6 mm and m=4.In addition,when the bond strain exceeds the elastic limit,a damage variable is introduced into the model,and the model is validated using a simple numerical algorithm.Finally,the dynamic fracture behavior of a two-dimensional FGECC beam under four-point bending is investigated,and the effect of the initial crack location on the fracture behavior is analyzed.Simulation results show that the initial crack location can affect the crack propagation pattern,thereby enabling one to understand the dynamic fracture behavior of ECC structures and guide the engineering practice.
基金Financial support by the National Key Research and Development program of China under Grant No.2016YFC0701106the National Natural Science Foundation of China under grants No.51578473the program of China Scholarship Council(CSC,No.201606060083)are gratefully acknowledged.
文摘Peridynamics(PD)is a widely used theory to simulate discontinuities,but its application in real-world structural problems is somewhat limited due to the relatively low-efficiency.The numerical substructure method(NSM)presented by the authors and co-workers provides an efficient approach for modeling structures with local nonlinearities,which is usually restricted in problems of continuum mechanics.In this paper,an approach is presented to couple the PD theory with the NSM for modeling structures with local discontinuities,taking advantage of the powerful capability of the PD for discontinuities simulation and high computational efficiency of the NSM.The structure is simulated using liner elastic finite element(FE)model while the local cracking regions are isolated and simulated using a PD substructure model.A force corrector calculated from the PD model is applied on the FE model to consider the effect of discontinuities.The PD is integrated in the substructure model using interface elements with embedded PD nodes.The equations of motions of both the NSM system and the PD substructure are solved using the central difference method.Three examples of two-dimensional(2D)concrete cantilever beams under the concentrated force are investigated to verify the proposed coupling approach.
