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
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
Thermal damage and thermal fracture of rocks are two important indicators in geothermal mining projects.This paper investigates the effects of heating and water-cooling on granite specimens at various temperatures.The...Thermal damage and thermal fracture of rocks are two important indicators in geothermal mining projects.This paper investigates the effects of heating and water-cooling on granite specimens at various temperatures.The laboratory uniaxial compression experiments were also conducted.Then,a coupled thermo-mechanical ordinary state-based peridynamic(OSB-PD)model and corresponding numerical scheme were developed to simulate the damage of rocks after the heating and cooling processes,and the change of crack evolution process was predicted.The results demonstrate that elevated heating temperatures exacerbate the thermal damage to the specimens,resulting in a decrease in peak strength and an increase in ductility of granite.The escalating occurrence of thermal-induced cracks significantly affects the crack evolution process during the loading phase.The numerical results accurately reproduce the damage and fracture characteristics of the granite under different final heating temperatures(FHTs),which are consistent with the test results in terms of strength,crack evolution process,and failure mode.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
This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic...This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic differential operator(PDDO),eliminating the need for calibration procedures.The model employs a multi-rate explicit time integration scheme to handle varying time scales in multi-physics systems.Through simulations conducted on granite and ceramic materials,this model demonstrates its effectiveness.It successfully simulates thermal damage behavior in granite arising from incompatible mineral expansion and accurately calculates thermal crack propagation in ceramic slabs during quenching.To account for material heterogeneity,the model utilizes the Shuffle algorithm andWeibull distribution,yielding results that align with numerical simulations and experimental observations.This coupled thermomechanical model shows great promise for analyzing intricate thermomechanical phenomena in brittle materials.展开更多
Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t...Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.展开更多
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
The surrounding rock of roadways exhibits intricate characteristics of discontinuity and heterogeneity.To address these complexities,this study employs non-local Peridynamics(PD)theory and reconstructs the kernel func...The surrounding rock of roadways exhibits intricate characteristics of discontinuity and heterogeneity.To address these complexities,this study employs non-local Peridynamics(PD)theory and reconstructs the kernel function to represent accurately the spatial decline of long-range force.Additionally,modifications to the traditional bondbased PD model are made.By considering the micro-structure of coal-rock materials within a uniform discrete model,heterogeneity characterized by bond random pre-breaking is introduced.This approach facilitates the proposal of a novel model capable of handling the random distribution characteristics of material heterogeneity,rendering the PD model suitable for analyzing the deformation and failure of heterogeneous layered coal-rock mass structures.The established numerical model and simulation method,termed the sub-homogeneous PD model,not only incorporates the support effect but also captures accurately the random heterogeneous micro-structure of roadway surrounding rock.The simulation results obtained using this model show good agreement with field measurements from the Fucun coal mine,effectively validating the model’s capability in accurately reproducing the deformation and failure mode of surrounding rock under bolt-supported(anchor cable).The proposed subhomogeneous PD model presents a valuable and effective simulation tool for studying the deformation and failure of roadway surrounding rock in coal mines,offering new insights and potential advancements.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
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 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
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 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
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
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funded by the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX22_0613)the National Natural Science Foundation of China(Grant Nos.41831278 and 51878249).
文摘Thermal damage and thermal fracture of rocks are two important indicators in geothermal mining projects.This paper investigates the effects of heating and water-cooling on granite specimens at various temperatures.The laboratory uniaxial compression experiments were also conducted.Then,a coupled thermo-mechanical ordinary state-based peridynamic(OSB-PD)model and corresponding numerical scheme were developed to simulate the damage of rocks after the heating and cooling processes,and the change of crack evolution process was predicted.The results demonstrate that elevated heating temperatures exacerbate the thermal damage to the specimens,resulting in a decrease in peak strength and an increase in ductility of granite.The escalating occurrence of thermal-induced cracks significantly affects the crack evolution process during the loading phase.The numerical results accurately reproduce the damage and fracture characteristics of the granite under different final heating temperatures(FHTs),which are consistent with the test results in terms of strength,crack evolution process,and failure mode.
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supported by the University Natural Science Foundation of Jiangsu Province(Grant No.23KJB130004)the National Natural Science Foundation of China(Grant Nos.11932006,U1934206,12172121,12002118).
文摘This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic differential operator(PDDO),eliminating the need for calibration procedures.The model employs a multi-rate explicit time integration scheme to handle varying time scales in multi-physics systems.Through simulations conducted on granite and ceramic materials,this model demonstrates its effectiveness.It successfully simulates thermal damage behavior in granite arising from incompatible mineral expansion and accurately calculates thermal crack propagation in ceramic slabs during quenching.To account for material heterogeneity,the model utilizes the Shuffle algorithm andWeibull distribution,yielding results that align with numerical simulations and experimental observations.This coupled thermomechanical model shows great promise for analyzing intricate thermomechanical phenomena in brittle materials.
基金This work was financially supported by the Key Science and Technology Project of Longmen Laboratory(No.LMYLKT-001)Innovation and Entrepreneurship Training Program for College Students of Henan Province(No.202310464050)。
文摘Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
基金supported by the National Natural Science Foundation of China(Nos.12302264,52104004,12072170,and 12202225)the Natural Science Foundation of Shandong Province(No.ZR2021QA042)Special Fund for Taishan Scholar Project(No.Tsqn202211180).
文摘The surrounding rock of roadways exhibits intricate characteristics of discontinuity and heterogeneity.To address these complexities,this study employs non-local Peridynamics(PD)theory and reconstructs the kernel function to represent accurately the spatial decline of long-range force.Additionally,modifications to the traditional bondbased PD model are made.By considering the micro-structure of coal-rock materials within a uniform discrete model,heterogeneity characterized by bond random pre-breaking is introduced.This approach facilitates the proposal of a novel model capable of handling the random distribution characteristics of material heterogeneity,rendering the PD model suitable for analyzing the deformation and failure of heterogeneous layered coal-rock mass structures.The established numerical model and simulation method,termed the sub-homogeneous PD model,not only incorporates the support effect but also captures accurately the random heterogeneous micro-structure of roadway surrounding rock.The simulation results obtained using this model show good agreement with field measurements from the Fucun coal mine,effectively validating the model’s capability in accurately reproducing the deformation and failure mode of surrounding rock under bolt-supported(anchor cable).The proposed subhomogeneous PD model presents a valuable and effective simulation tool for studying the deformation and failure of roadway surrounding rock in coal mines,offering new insights and potential advancements.
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 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.
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 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.
