For the solution of peridynamic equations of motion,a meshless approach is typically used instead of utilizing semi-analytical or mesh-based approaches.In contrast,the literature has limited analytical solutions.This ...For the solution of peridynamic equations of motion,a meshless approach is typically used instead of utilizing semi-analytical or mesh-based approaches.In contrast,the literature has limited analytical solutions.This study develops a novel analytical solution for one-dimensional peridynamic models,considering the effect of damping.After demonstrating the details of the analytical solution,various demonstration problems are presented.First,the free vibration of a damped system is considered for under-damped and critically damped conditions.Peridynamic solutions and results from the classical theory are compared against each other,and excellent agreement is observed between the two approaches.Next,forced vibration analyses of undamped and damped conditions are performed.In addition,the effect of horizon size is investigated.It is shown that for smaller horizon sizes,peridynamic results agree well with classical results,whereas results from these two approaches deviate from each other as the horizon size increases.展开更多
As a critical component of pulse solid rocket motors(SRMs),the soft pulse separation device(PSD)is vital in enabling multi-pulse propulsion and has become a breakthrough in SRM engineering applications.To investigate ...As a critical component of pulse solid rocket motors(SRMs),the soft pulse separation device(PSD)is vital in enabling multi-pulse propulsion and has become a breakthrough in SRM engineering applications.To investigate the opening performance of the PSD,an axial PSD incorporating a star-shaped prefabricated defect was designed.The opening process was simulated using peridynamics,yielding the strain field distribution and the corresponding failure mode.A single-opening verification test was conducted.The simulation results showed good agreement with the experimental data,demonstrating the reliability of the peridynamic modeling approach.Furthermore,the effects of the prefabricated defect shape and depth on the opening performance of the PSD were analyzed through simulation.The research results indicate that the established constitutive model and failure criteria based on peridynamics can reasonably predict the failure location and the opening pressure of the soft PSD.Under the impact loading,the weak zone of the soft PSD firstly ruptures,and the damaged area gradually propagates along with the prefabricated defect,eventually leading to complete separation.A smaller prefabricated defect depth or a wider prefabricated defect distribution can cause a reduction in opening pressure.These research results provide valuable guidance for the preliminary design and optimization of PSDs in pulse solid rocket motors.展开更多
This paper introduces a bond-based peridynamics(BB-PD)algorithm for crack identification,integrating the Delaunay triangulation method to accurately identify the structural characteristics of threedimensional(3D)crack...This paper introduces a bond-based peridynamics(BB-PD)algorithm for crack identification,integrating the Delaunay triangulation method to accurately identify the structural characteristics of threedimensional(3D)cracks in rocks.A bond-based crack quantification standard is proposed to analyze the evolution of cracks of various sizes.A multi-attribute peridynamic model,developed using a multilayer algorithm,was employed to simulate the fracturing process of sandstone disks and semi-disks under varying temperatures,with the model calibrated and validated against experimental results.The simulation results show that temperature induces nonlinear degradation in the tensile strength and fracture toughness of sandstone,with 500℃ identified as the threshold temperature.Thermal cracks exhibit varying degrees of influence on Mode I cracks across different temperature ranges.Thermal damage significantly promotes the initiation and propagation of Mode I cracks in sandstone,thereby reducing its tensile strength and fracture toughness.Under applied loads,crack propagation in sandstone predominantly occurs during the failure stage,characterized by the rapid growth of longer cracks and a slow increase or reduction in shorter cracks.展开更多
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
The peridynamic motion equation was investigated once again.The origin of incompatibility between boundary conditions and peridynamics was analyzed.In order to eliminate this incompatibility,we proposed a new peridyna...The peridynamic motion equation was investigated once again.The origin of incompatibility between boundary conditions and peridynamics was analyzed.In order to eliminate this incompatibility,we proposed a new peridynamic motion equation in which the effects of boundary traction and boundary displacement constraint were introduced.The new peridynamic motion equation is invariant under the transformations of rigid translation and rotation.Meanwhile,it also satisfies the requirements of total linear and angular momentum equilibrium.By this motion equation,three kinds of boundary value problems containing the displacement boundary condition,the traction boundary condition and mixed boundary condition are characterized in peridynamics.As examples,we calculated static tension and longitudinal vibration of a finite rod.The acquired solutions exhibit obvious nonlocal features,and the vibration has the dispersion similar to one dimensional atom chain vibration.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 establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models.We consider state-based peridynamic models where the force at a material point is due to bo...We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models.We consider state-based peridynamic models where the force at a material point is due to both the strain between two points and the change in volume inside the domain of the nonlocal interaction.The pairwise interactions between points are mediated by a bond potential of multi-well type while multi-point interactions are associated with the volume change mediated by a hydrostatic strain potential.The hydrostatic potential can either be a quadratic function,delivering a linear force–strain relation,or a multi-well type that can be associated with the material degradation and cavitation.We first show the well-posedness of the peridynamic formulation and that peridynamic evolutions exist in the Sobolev space H2.We show that the finite element approximations converge to the H2 solutions uniformly as measured in the mean square norm.For linear continuous fi nite elements,the convergence rate is shown to be Ct Δt+Csh2/ε2,where𝜖is the size of the horizon,his the mesh size,and Δt is the size of the time step.The constants Ct and Cs are independent of Δt and h and may depend on ε through the norm of the exact solution.We demonstrate the stability of the semi-discrete approximation.The stability of the fully discrete approximation is shown for the linearized peridynamic force.We present numerical simulations with the dynamic crack propagation that support the theoretical convergence rate.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 new bond-based peridynamic model is proposed to describe the dynamic properties of ceramics under impact loading.Ceramic materials show pseudo-plastic behavior under certain compressive loadings with h...In this study,a new bond-based peridynamic model is proposed to describe the dynamic properties of ceramics under impact loading.Ceramic materials show pseudo-plastic behavior under certain compressive loadings with high strain-rate,while the characteristic brittleness of the material dominates when it is subjected to tensile loading.In this model,brittle response under tension,softening plasticity under compression and strain-rate effect of ceramics are considered,which makes it possible to accurately capture the overall dynamic process of ceramics.This enables the investigation of the fracture mechanism for ceramic materials,during ballistic impact,in more detail.Furthermore,a bond-force updating algorithm is introduced to perform the numerical simulation and solve the derived equations.The proposed model is then used to analyze the dynamic response of ceramics tiles under impact loading to assess its validity.The results of damage development in ceramic materials are calculated and compared with the experimental results.The simulation results are consistent with the experiments,which indicates that the proposed rate-dependent peridynamic model has the capability to describe damage propagation in ceramics with good accuracy.Finally,based on a comparison between simulation and experimental results,it can be concluded that the damage results are in better agreement with experimental results than non-ordinary state-based peridynamic method.展开更多
De-icing technology has become an increasingly important subject in numerous applications in recent years.However,the direct numerical modeling and simulation the physical process of thermomechanical deicing is limite...De-icing technology has become an increasingly important subject in numerous applications in recent years.However,the direct numerical modeling and simulation the physical process of thermomechanical deicing is limited.This work is focusing on developing a numerical model and tool to direct simulate the de-icing process in the framework of the coupled thermo-mechanical peridynamics theory.Here,we adopted the fully coupled thermo-mechanical bond-based peridynamics(TM-BB-PD)method for modeling and simulation of de-icing.Within the framework of TM-BB-PD,the ice constitutive model is established by considering the influence of the temperature difference between two material points,and a modified failure criteria is proposed,which takes into account temperature effect to predict the damage of quasi-brittle ice material.Moreover,thermal boundary condition is used to simulate the thermal load in the de-icing process.By comparing with the experimental results and the previous reported finite element modeling,our numerical model shows good agreement with the previous predictions.Based on the numerical results,we find that the developed method can not only predict crack initiation and propagation in the ice,but also predict the temperature distribution and heat conduction during the de-icing process.Furthermore,the influence of the temperature for the ice crack growth pattern is discussed accordingly.In conclusion,the coupled thermal-mechanical peridynamics formulation with modified failure criterion is capable of providing a modeling tool for engineering applications of de-icing technology.展开更多
The peridynamic correspondence model provides a general formulation to incorporate the classical local model and,therefore,helps to solve mechanical problems with discontinuities easily.But it suffers from zero-energy...The peridynamic correspondence model provides a general formulation to incorporate the classical local model and,therefore,helps to solve mechanical problems with discontinuities easily.But it suffers from zero-energy mode instability in numerical implementation due to the approximation of deformation gradient tensor.To suppress zero-energy modes,previous stabilized methods were generally more based on adding a supplemental force state derived from bond-based peridynamic theory,which requires a bond-based peridynamic micro-modulus.In this work,we present an improved stabilized method where the stabilization force state is derived directly from the peridynamic correspondence model.Hence,the bond-based peridynamic micro-modulus is abandoned.This improved method needs no extra constant to control the magnitude of stabilization force state and it is suitable for either isotropic or anisotropic materials.Several examples are presented to demonstrate its performance in simulating crack propagation,and numerical results show its efficiency and effectiveness.展开更多
In this study,a peridynamic fiber-reinforced concrete model is developed based on the bond-based peridynamic model with rotation effect(BBPDR).The fibers are modelled by a semi-discrete method and distributed with ran...In this study,a peridynamic fiber-reinforced concrete model is developed based on the bond-based peridynamic model with rotation effect(BBPDR).The fibers are modelled by a semi-discrete method and distributed with random locations and angles in the concrete specimen,since the fiber content is low,and its scale is smaller than the concrete matrix.The interactions between fibers and concrete matrix are investigated by the improvement of the bond’s strength and stiffness.Also,the frictional effect between the fibers and the concrete matrix is considered,which is divided into static friction and slip friction.To validate the proposed model,several examples are simulated,including the tensile test and the three-point bending beam test.And the numerical results of the proposed model are compared with the experiments and other numerical models.The comparisons show that the proposed model is capable of simulating the fracture behavior of the fiber-reinforced concrete.After adding the fibers,the tensile strength,bending strength,and toughness of the fiber-reinforced concrete specimens are improved.Besides,the fibers distribution has an impact on the crack path,especially in the three-point bending beam test.展开更多
In the present work,a state-based peridynamics with adaptive particle refinement is proposed to simulate water ice crater formation due to impact loads.A modified Drucker-Prager constitutive model was adopted to model...In the present work,a state-based peridynamics with adaptive particle refinement is proposed to simulate water ice crater formation due to impact loads.A modified Drucker-Prager constitutive model was adopted to model ice and was implemented in the state-based peridynamic equations to analyze the elastic-plastic deformation of ice.In simulations,we use the fracture toughness failure criterion in peridynamics to simulate the quasi-brittle failure of ice.An adaptive particle refinement method in peridynamics was proposed to improve computational efficiency.The results obtained using the peridynamic model were compared with the experiments in previous literatures.It was found that the peridynamic simulation results and the experiments matched well except for some minor differences discussed,and the state-based peridynamic model has shown the specific predictive capacity to capture the detailed crater features of the ice.展开更多
Strain hardening and strain rate play an important role in dynamic deformation and failure problems such as high-velocity impact cases.In this paper,a non-ordinary state-based peridynamic model for failure and damage ...Strain hardening and strain rate play an important role in dynamic deformation and failure problems such as high-velocity impact cases.In this paper,a non-ordinary state-based peridynamic model for failure and damage of concrete materials subjected to impacting condition is proposed,taking the advantages of both damage model and nonlocal peridynamic method.The Holmquist-Johnson-Cook(HJC)model describing the mechanical character and damage of concrete materials under large strain,high strain rate and high hydrostatic pressure was reformulated in the framework of non-ordinary statebased peridynamic theory,and the corresponding numerical approach was developed.The proposed model and numerical approach were validated through simulating typical impacting examples and comparing the results with available experimental observations and results in literature.展开更多
In the research,the dynamic fracture failure problem of functionally graded materials(FGMs)containing two pre-cracks was analyzed using a bond-based Peridynamic(PD)method numerical model.The two convergence of decreas...In the research,the dynamic fracture failure problem of functionally graded materials(FGMs)containing two pre-cracks was analyzed using a bond-based Peridynamic(PD)method numerical model.The two convergence of decreasing the area of PD horizon(δ-convergence)and uniform mesh refinement(m-convergence)were studied.The effects of both crack position and distance between two cracks on crack propagation pattern in FGMs plate under tensile loads are studied.Furthermore,the effects of different gradient patterns on the dynamic propagation of cracks in FGMs are also investigated.The simulate results suggest that the cracks positions and the distance between them can significantly influence the dynamic propagation of crack in FGMs.Gradient mode also has a certain effect on crack propagation,but the effect of specific gradient variation patterns on dynamic propagation of crack is finite.展开更多
In this work,a bond-based peridynamics(PD)model was built to analyze the dynamic fracture of shale material.Both the the convergence studies and the result of dynamic crack propagation were presented.As well-known,cra...In this work,a bond-based peridynamics(PD)model was built to analyze the dynamic fracture of shale material.Both the the convergence studies and the result of dynamic crack propagation were presented.As well-known,crack propagation,aggregation,and bifurcation play an critical role in the failure analysis of brittle materials such as shale.The dynamic crack propagation and branching analysis of shale by using the PD method were discussed.Firstly,the valid and accuracy of the PD model for the rock materials was verified by comparing with the existed numerical results.Secondly,we discussed the convergence both with uniform grid refinement(m-convergence)and decreasing the peridynamics horizon(δ-convergence).Then the shale material with two pre-crack under uniaxial compression using the present PD model were discussed,and the influence of the different angle of flaws on the behavior of crack propagation was also analyzed.The results shows that both the loading conditions and the angle of flaws can influences the crack propagation in shale.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
The nonlocal peridynamic theory has been proven to be a promising method for the material failure and damage analyses in solid mechanics. Based upon the integro- differential equations, peridynamics enables predicting...The nonlocal peridynamic theory has been proven to be a promising method for the material failure and damage analyses in solid mechanics. Based upon the integro- differential equations, peridynamics enables predicting the complex fracture phenomena such as spontaneous crack nucleation and crack branching, curving, and arrest. In this paper, the bond-based peridynamic approach is used to study the impact damage in a beam with an offset notch, which is widely used to investigate the mixed I-II crack propagation in brittle materials. The predictions from the peridynamic analysis agree well with available experimental observations. The numerical results show that the dynamic fracture behaviors of the beam under the impact load, such as crack initiation, curving, and branching, rely on the location of the offset notch and the impact speed of the drop hammer.展开更多
In this paper,the quasi-static large deformation,wrinkling and fracture behaviors of bimodular structures and membranes are studied with an implicit bond-based peridynamic computational framework.Firstly,the constant ...In this paper,the quasi-static large deformation,wrinkling and fracture behaviors of bimodular structures and membranes are studied with an implicit bond-based peridynamic computational framework.Firstly,the constant and tangential stiffness matrices of the implicit peridynamic formulations for the nonlinear problems are derived,respectively.The former is con structed from the linearization of the bond strain on the basis of the geometric approximation while the latter is established according to the linearization of the pairwise force by using first-order Taylor’s expansion.Then,a bimodular material model in peridynamics is developed,in which the tensile or compressive behavior of the material at each point is conveniently described by the tensile or compressive states of the bonds in its neighborhood.Moreover,the bimodular material model is extended to deal with the wrinkling and fracture problems of membranes by setting the compressive micro-modulus to be zero.In addition,the incremental-iterative algorithm is adopted to obtain the convergent solutions of the nonlinear problems.Finally,several representative numerical examples are presented and the results demonstrate the accuracy and efficiency of the proposed method for the large deformation,wrinkling and fracture analyses of bimodular structures and membranes.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
文摘For the solution of peridynamic equations of motion,a meshless approach is typically used instead of utilizing semi-analytical or mesh-based approaches.In contrast,the literature has limited analytical solutions.This study develops a novel analytical solution for one-dimensional peridynamic models,considering the effect of damping.After demonstrating the details of the analytical solution,various demonstration problems are presented.First,the free vibration of a damped system is considered for under-damped and critically damped conditions.Peridynamic solutions and results from the classical theory are compared against each other,and excellent agreement is observed between the two approaches.Next,forced vibration analyses of undamped and damped conditions are performed.In addition,the effect of horizon size is investigated.It is shown that for smaller horizon sizes,peridynamic results agree well with classical results,whereas results from these two approaches deviate from each other as the horizon size increases.
基金supported by the National Natural Science Foundation of China(No.12202011)the Youth Research fund of Shanghai Academy of Spaceflight Technology(KJW-KT-QNKYJJ-2022-25)China Postdoctoral Science Foundation(Nos.2024T170009,2022M710190).
文摘As a critical component of pulse solid rocket motors(SRMs),the soft pulse separation device(PSD)is vital in enabling multi-pulse propulsion and has become a breakthrough in SRM engineering applications.To investigate the opening performance of the PSD,an axial PSD incorporating a star-shaped prefabricated defect was designed.The opening process was simulated using peridynamics,yielding the strain field distribution and the corresponding failure mode.A single-opening verification test was conducted.The simulation results showed good agreement with the experimental data,demonstrating the reliability of the peridynamic modeling approach.Furthermore,the effects of the prefabricated defect shape and depth on the opening performance of the PSD were analyzed through simulation.The research results indicate that the established constitutive model and failure criteria based on peridynamics can reasonably predict the failure location and the opening pressure of the soft PSD.Under the impact loading,the weak zone of the soft PSD firstly ruptures,and the damaged area gradually propagates along with the prefabricated defect,eventually leading to complete separation.A smaller prefabricated defect depth or a wider prefabricated defect distribution can cause a reduction in opening pressure.These research results provide valuable guidance for the preliminary design and optimization of PSDs in pulse solid rocket motors.
基金financially supported by the National Natural Science Foundation of China(Grant No.42077231).
文摘This paper introduces a bond-based peridynamics(BB-PD)algorithm for crack identification,integrating the Delaunay triangulation method to accurately identify the structural characteristics of threedimensional(3D)cracks in rocks.A bond-based crack quantification standard is proposed to analyze the evolution of cracks of various sizes.A multi-attribute peridynamic model,developed using a multilayer algorithm,was employed to simulate the fracturing process of sandstone disks and semi-disks under varying temperatures,with the model calibrated and validated against experimental results.The simulation results show that temperature induces nonlinear degradation in the tensile strength and fracture toughness of sandstone,with 500℃ identified as the threshold temperature.Thermal cracks exhibit varying degrees of influence on Mode I cracks across different temperature ranges.Thermal damage significantly promotes the initiation and propagation of Mode I cracks in sandstone,thereby reducing its tensile strength and fracture toughness.Under applied loads,crack propagation in sandstone predominantly occurs during the failure stage,characterized by the rapid growth of longer cracks and a slow increase or reduction in shorter cracks.
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This work was supported by the National Natural Science Foundation of China(Grant 11672129)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics,MCMS-I-0218G01).
文摘The peridynamic motion equation was investigated once again.The origin of incompatibility between boundary conditions and peridynamics was analyzed.In order to eliminate this incompatibility,we proposed a new peridynamic motion equation in which the effects of boundary traction and boundary displacement constraint were introduced.The new peridynamic motion equation is invariant under the transformations of rigid translation and rotation.Meanwhile,it also satisfies the requirements of total linear and angular momentum equilibrium.By this motion equation,three kinds of boundary value problems containing the displacement boundary condition,the traction boundary condition and mixed boundary condition are characterized in peridynamics.As examples,we calculated static tension and longitudinal vibration of a finite rod.The acquired solutions exhibit obvious nonlocal features,and the vibration has the dispersion similar to one dimensional atom chain vibration.
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 establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models.We consider state-based peridynamic models where the force at a material point is due to both the strain between two points and the change in volume inside the domain of the nonlocal interaction.The pairwise interactions between points are mediated by a bond potential of multi-well type while multi-point interactions are associated with the volume change mediated by a hydrostatic strain potential.The hydrostatic potential can either be a quadratic function,delivering a linear force–strain relation,or a multi-well type that can be associated with the material degradation and cavitation.We first show the well-posedness of the peridynamic formulation and that peridynamic evolutions exist in the Sobolev space H2.We show that the finite element approximations converge to the H2 solutions uniformly as measured in the mean square norm.For linear continuous fi nite elements,the convergence rate is shown to be Ct Δt+Csh2/ε2,where𝜖is the size of the horizon,his the mesh size,and Δt is the size of the time step.The constants Ct and Cs are independent of Δt and h and may depend on ε through the norm of the exact solution.We demonstrate the stability of the semi-discrete approximation.The stability of the fully discrete approximation is shown for the linearized peridynamic force.We present numerical simulations with the dynamic crack propagation that support the theoretical convergence rate.
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supported by the National Natural Science Foundation of China(Nos.11972267 and 11802214)the Fundamental Research Funds for the Central Universities(WUT:2018IB006 and WUT:2019IVB042).
文摘In this study,a new bond-based peridynamic model is proposed to describe the dynamic properties of ceramics under impact loading.Ceramic materials show pseudo-plastic behavior under certain compressive loadings with high strain-rate,while the characteristic brittleness of the material dominates when it is subjected to tensile loading.In this model,brittle response under tension,softening plasticity under compression and strain-rate effect of ceramics are considered,which makes it possible to accurately capture the overall dynamic process of ceramics.This enables the investigation of the fracture mechanism for ceramic materials,during ballistic impact,in more detail.Furthermore,a bond-force updating algorithm is introduced to perform the numerical simulation and solve the derived equations.The proposed model is then used to analyze the dynamic response of ceramics tiles under impact loading to assess its validity.The results of damage development in ceramic materials are calculated and compared with the experimental results.The simulation results are consistent with the experiments,which indicates that the proposed rate-dependent peridynamic model has the capability to describe damage propagation in ceramics with good accuracy.Finally,based on a comparison between simulation and experimental results,it can be concluded that the damage results are in better agreement with experimental results than non-ordinary state-based peridynamic method.
基金the University of California at Berkeley.Ms.Y.Song gratefully acknowledges the financial support from the Chinese Scholar Council(CSC Grant No.201706680094).
文摘De-icing technology has become an increasingly important subject in numerous applications in recent years.However,the direct numerical modeling and simulation the physical process of thermomechanical deicing is limited.This work is focusing on developing a numerical model and tool to direct simulate the de-icing process in the framework of the coupled thermo-mechanical peridynamics theory.Here,we adopted the fully coupled thermo-mechanical bond-based peridynamics(TM-BB-PD)method for modeling and simulation of de-icing.Within the framework of TM-BB-PD,the ice constitutive model is established by considering the influence of the temperature difference between two material points,and a modified failure criteria is proposed,which takes into account temperature effect to predict the damage of quasi-brittle ice material.Moreover,thermal boundary condition is used to simulate the thermal load in the de-icing process.By comparing with the experimental results and the previous reported finite element modeling,our numerical model shows good agreement with the previous predictions.Based on the numerical results,we find that the developed method can not only predict crack initiation and propagation in the ice,but also predict the temperature distribution and heat conduction during the de-icing process.Furthermore,the influence of the temperature for the ice crack growth pattern is discussed accordingly.In conclusion,the coupled thermal-mechanical peridynamics formulation with modified failure criterion is capable of providing a modeling tool for engineering applications of de-icing technology.
基金This work was supported by the National Natural Science Foundation of China(Grants 11472196,11172216 and 11772237).
文摘The peridynamic correspondence model provides a general formulation to incorporate the classical local model and,therefore,helps to solve mechanical problems with discontinuities easily.But it suffers from zero-energy mode instability in numerical implementation due to the approximation of deformation gradient tensor.To suppress zero-energy modes,previous stabilized methods were generally more based on adding a supplemental force state derived from bond-based peridynamic theory,which requires a bond-based peridynamic micro-modulus.In this work,we present an improved stabilized method where the stabilization force state is derived directly from the peridynamic correspondence model.Hence,the bond-based peridynamic micro-modulus is abandoned.This improved method needs no extra constant to control the magnitude of stabilization force state and it is suitable for either isotropic or anisotropic materials.Several examples are presented to demonstrate its performance in simulating crack propagation,and numerical results show its efficiency and effectiveness.
基金The authors are pleased to acknowledge the support by the National Natural Science Foundation of China through contract/Grant Nos.11772237,11472196 and 11172216to acknowledge the open funds of the State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology)through contract/Grant No.GZ19110.
文摘In this study,a peridynamic fiber-reinforced concrete model is developed based on the bond-based peridynamic model with rotation effect(BBPDR).The fibers are modelled by a semi-discrete method and distributed with random locations and angles in the concrete specimen,since the fiber content is low,and its scale is smaller than the concrete matrix.The interactions between fibers and concrete matrix are investigated by the improvement of the bond’s strength and stiffness.Also,the frictional effect between the fibers and the concrete matrix is considered,which is divided into static friction and slip friction.To validate the proposed model,several examples are simulated,including the tensile test and the three-point bending beam test.And the numerical results of the proposed model are compared with the experiments and other numerical models.The comparisons show that the proposed model is capable of simulating the fracture behavior of the fiber-reinforced concrete.After adding the fibers,the tensile strength,bending strength,and toughness of the fiber-reinforced concrete specimens are improved.Besides,the fibers distribution has an impact on the crack path,especially in the three-point bending beam test.
文摘In the present work,a state-based peridynamics with adaptive particle refinement is proposed to simulate water ice crater formation due to impact loads.A modified Drucker-Prager constitutive model was adopted to model ice and was implemented in the state-based peridynamic equations to analyze the elastic-plastic deformation of ice.In simulations,we use the fracture toughness failure criterion in peridynamics to simulate the quasi-brittle failure of ice.An adaptive particle refinement method in peridynamics was proposed to improve computational efficiency.The results obtained using the peridynamic model were compared with the experiments in previous literatures.It was found that the peridynamic simulation results and the experiments matched well except for some minor differences discussed,and the state-based peridynamic model has shown the specific predictive capacity to capture the detailed crater features of the ice.
基金The authors acknowledge the support from the National Key R&D Program of China(No.2018YFC0406703)National Natural Science Foundation of China(No.51679077)the Fundamental Research Funds for the Central Universities in China(No.2015B18314,2017B13014).
文摘Strain hardening and strain rate play an important role in dynamic deformation and failure problems such as high-velocity impact cases.In this paper,a non-ordinary state-based peridynamic model for failure and damage of concrete materials subjected to impacting condition is proposed,taking the advantages of both damage model and nonlocal peridynamic method.The Holmquist-Johnson-Cook(HJC)model describing the mechanical character and damage of concrete materials under large strain,high strain rate and high hydrostatic pressure was reformulated in the framework of non-ordinary statebased peridynamic theory,and the corresponding numerical approach was developed.The proposed model and numerical approach were validated through simulating typical impacting examples and comparing the results with available experimental observations and results in literature.
基金the Natural Science Foundation of China(Nos.11472248,11872339)the Natural Science Foundation of Henan Province(No.182300410221).
文摘In the research,the dynamic fracture failure problem of functionally graded materials(FGMs)containing two pre-cracks was analyzed using a bond-based Peridynamic(PD)method numerical model.The two convergence of decreasing the area of PD horizon(δ-convergence)and uniform mesh refinement(m-convergence)were studied.The effects of both crack position and distance between two cracks on crack propagation pattern in FGMs plate under tensile loads are studied.Furthermore,the effects of different gradient patterns on the dynamic propagation of cracks in FGMs are also investigated.The simulate results suggest that the cracks positions and the distance between them can significantly influence the dynamic propagation of crack in FGMs.Gradient mode also has a certain effect on crack propagation,but the effect of specific gradient variation patterns on dynamic propagation of crack is finite.
基金This work was supported by the Natural Science Foundation of China(Nos.11472248,51708510,11872339)the Natural Science Foundation of Henan Province(No.182300410221).
文摘In this work,a bond-based peridynamics(PD)model was built to analyze the dynamic fracture of shale material.Both the the convergence studies and the result of dynamic crack propagation were presented.As well-known,crack propagation,aggregation,and bifurcation play an critical role in the failure analysis of brittle materials such as shale.The dynamic crack propagation and branching analysis of shale by using the PD method were discussed.Firstly,the valid and accuracy of the PD model for the rock materials was verified by comparing with the existed numerical results.Secondly,we discussed the convergence both with uniform grid refinement(m-convergence)and decreasing the peridynamics horizon(δ-convergence).Then the shale material with two pre-crack under uniaxial compression using the present PD model were discussed,and the influence of the different angle of flaws on the behavior of crack propagation was also analyzed.The results shows that both the loading conditions and the angle of flaws can influences the crack propagation in shale.
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Project supported by the Natural Science Foundation of Jiangsu Province(No.BK20140789)the Fundamental Research Funds for the Central Universities(No.30915118826)
文摘The nonlocal peridynamic theory has been proven to be a promising method for the material failure and damage analyses in solid mechanics. Based upon the integro- differential equations, peridynamics enables predicting the complex fracture phenomena such as spontaneous crack nucleation and crack branching, curving, and arrest. In this paper, the bond-based peridynamic approach is used to study the impact damage in a beam with an offset notch, which is widely used to investigate the mixed I-II crack propagation in brittle materials. The predictions from the peridynamic analysis agree well with available experimental observations. The numerical results show that the dynamic fracture behaviors of the beam under the impact load, such as crack initiation, curving, and branching, rely on the location of the offset notch and the impact speed of the drop hammer.
基金The work was supported by the National Natural Science Foundation of China(Grants 11672062,11772082,and 11672063)the 111 Project(Grant B08014)the Fundamental Research Funds for the Central Universities.
文摘In this paper,the quasi-static large deformation,wrinkling and fracture behaviors of bimodular structures and membranes are studied with an implicit bond-based peridynamic computational framework.Firstly,the constant and tangential stiffness matrices of the implicit peridynamic formulations for the nonlinear problems are derived,respectively.The former is con structed from the linearization of the bond strain on the basis of the geometric approximation while the latter is established according to the linearization of the pairwise force by using first-order Taylor’s expansion.Then,a bimodular material model in peridynamics is developed,in which the tensile or compressive behavior of the material at each point is conveniently described by the tensile or compressive states of the bonds in its neighborhood.Moreover,the bimodular material model is extended to deal with the wrinkling and fracture problems of membranes by setting the compressive micro-modulus to be zero.In addition,the incremental-iterative algorithm is adopted to obtain the convergent solutions of the nonlinear problems.Finally,several representative numerical examples are presented and the results demonstrate the accuracy and efficiency of the proposed method for the large deformation,wrinkling and fracture analyses of bimodular structures and membranes.
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.
