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 non-ordinary state-based peridynamic(NOSB PD)model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics.In the present work,we first develop an NOSB PD model...The non-ordinary state-based peridynamic(NOSB PD)model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics.In the present work,we first develop an NOSB PD model corresponding to the Johnson–Holmquist II(JH-2)constitutive damage model,which can describe the severe damage of concrete under intense impact compression.Besides,the numerical oscillation problem of the NOSB PD caused by zero-energy mode is analyzed and hence a bond-associated non-ordinary state-based peridynamic(BA-NOSB PD)model is adopted to remove the oscillation.Then,the elastic deformation of a three-dimensional bar is analyzed to verify the capability of BA-NOSB PD in eliminating the numerical oscillation.Furthermore,concrete spalling caused by the interaction of incident compression wave and reflected tension wave is simulated.The dynamic tensile fracture process of concrete multiple spalling is accurately reproduced for several examples according to the spalling number and spalling thickness analysis,illustrating the approach can well simulate and analyze the concrete spalling discontinuities.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 this study,a new state-based peridynamic formulation is developed for functionally graded Euler-Bernoulli beams.The equation of motion is developed by using Lagrange’s equation and Taylor series.Both axial and tra...In this study,a new state-based peridynamic formulation is developed for functionally graded Euler-Bernoulli beams.The equation of motion is developed by using Lagrange’s equation and Taylor series.Both axial and transverse displacements are taken into account as degrees of freedom.Four different boundary conditions are considered including pinned support-roller support,pinned support-pinned support,clamped-clamped and clamped-free.Peridynamic results are compared against finite element analysis results for transverse and axial deformations and a very good agreement is observed for all different types of boundary conditions.展开更多
In process industries,the characteristics of industrial activities focus on the integrality and continuity of production process,which can contribute to excavating the appropriate features for industrial anomaly detec...In process industries,the characteristics of industrial activities focus on the integrality and continuity of production process,which can contribute to excavating the appropriate features for industrial anomaly detection.From this perspective,this paper proposes a novel state-based control feature extraction approach,which regards the finite control operations as different states.Furthermore,the procedure of state transition can adequately express the change of successive control operations,and the statistical information between different states can be used to calculate the feature values.Additionally,OCSVM(One Class Support Vector Machine)and BPNN(BP Neural Network),which are optimized by PSO(Particle Swarm Optimization)and GA(Genetic Algorithm)respectively,are introduced as alternative detection engines to match with our feature extraction approach.All experimental results clearly show that the proposed feature extraction approach can effectively coordinate with the optimized classification algorithms,and the optimized GA-BPNN classifier is suggested as a more applicable detection engine by comparing its average detection accuracies with the ones of PSO-OCSVM classifier.展开更多
We solve the local uniaxial tension of an infinite rod in the framework of non-ordinary state-based peridynamics.The singular solutions of stress and displacement are acquired.When the influencing range of the window ...We solve the local uniaxial tension of an infinite rod in the framework of non-ordinary state-based peridynamics.The singular solutions of stress and displacement are acquired.When the influencing range of the window function approaches zero,these two solutions will return to the solutions of the classical elasticity.The analysis shows that the singularities of the solutions stem from such a feature of the window function that must be represented by a rapidly decreasing function in physics.Contrary to the classical elasticity,the stress solution of peridynamics is smoother than the displacement solution.In addition,a criterion used to select the window function is proposed in this paper.展开更多
This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of model...This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of modeling the PD unit cell(UC)of continuous fiber-reinforced composite is presented.Periodic boundary conditions are derived and implemented through the Lagrange multiplier method.A matrix-dominated approach for modeling the interphase properties between dissimilar materials is proposed.The periodicity and continuity assumptions are employed to determine the stress and strain fields,as well as the effective elastic properties.The PD-UCs of square and hexagonal packs as well as the 0/90 laminate microstructure are modeled and compared with the analytical,numerical and experimental results from the literature.Good agreement of predicted effective properties can be observed.Unlike other PD homogenization approaches,the effective material properties can be directly and individually obtained from simple loading conditions.展开更多
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 order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
This study summarizes the examination data of registration labels for ordinary cosmetics in Beijing from May 2021 to April 2024.It analyzes and categorizes the issues identified during label evaluations,explores the u...This study summarizes the examination data of registration labels for ordinary cosmetics in Beijing from May 2021 to April 2024.It analyzes and categorizes the issues identified during label evaluations,explores the underlying causes,and proposes regulatory countermeasures and recommendations for registrants,regulatory authorities,and social organizations.The objective is to offer practical insights and regulatory guidance to support the enhancement of cosmetic registration and regulatory standards.展开更多
In rock engineering,natural cracks in rock masses subjected to external loads tend to initiate and propagate,leading to potential safety hazards.To investigate the effect of cracking behavior on the mechanical propert...In rock engineering,natural cracks in rock masses subjected to external loads tend to initiate and propagate,leading to potential safety hazards.To investigate the effect of cracking behavior on the mechanical properties of rocks,the cracking processes of pre-cracked rocks have been extensively studied using numerical modeling methods.The peridynamics(PD)exhibits advantages over other numerical methods due to the absence of the requirements for remeshing and external crack growth criterion.However,for modeling pre-cracked rock cracking processes under impact,current PD implementations lack generally applicable rock constitutive models and impact contact models,which leads to difficulties in determining rock material parameters and efficiently calculating impact loads.This paper proposes a non-ordinary state-based peridynamics(NOSBPD)modeling method integrating the Drucker-Prager(DP)plasticity model and an efficient contact model to address the above problems.In the proposed method,the Drucker-Prager plasticity model is integrated into the NOSBPD,thereby equipping NOSBPD with the capability to accurately characterize the nonlinear stress-strain relationship inherent in rocks.An efficient contact model between particles and meshes is designed to calculate the impact loads,which is essentially a coupling method of PD with the finite element method(FEM).The effectiveness of the proposed NOSBPD modeling method is verified by comparison with other numerical methods and experiments.Experimental results indicate that the proposed method can effectively and accurately predict the 3D cracking processes of pre-cracked cracks under impact loading,and the maximum principal stress is the key driver behind wing crack formation in pre-cracked rocks.展开更多
基金supported by the National Key R&D Program of China(2020YFA0710500).
文摘The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.
基金supported by the Fundamental Research Funds for the Central Universities(Grant B200202231)the National Natural Science Foundation of China(Grants 11932006,11672101,U1934206,and 12002118)+1 种基金the National Key Research&Development Plan of China(Grants 2018 YFC0406703 and 2017YFC1502603)the China Postdoctoral Science Foundation(Grant 2019M651667).
文摘The non-ordinary state-based peridynamic(NOSB PD)model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics.In the present work,we first develop an NOSB PD model corresponding to the Johnson–Holmquist II(JH-2)constitutive damage model,which can describe the severe damage of concrete under intense impact compression.Besides,the numerical oscillation problem of the NOSB PD caused by zero-energy mode is analyzed and hence a bond-associated non-ordinary state-based peridynamic(BA-NOSB PD)model is adopted to remove the oscillation.Then,the elastic deformation of a three-dimensional bar is analyzed to verify the capability of BA-NOSB PD in eliminating the numerical oscillation.Furthermore,concrete spalling caused by the interaction of incident compression wave and reflected tension wave is simulated.The dynamic tensile fracture process of concrete multiple spalling is accurately reproduced for several examples according to the spalling number and spalling thickness analysis,illustrating the approach can well simulate and analyze the concrete spalling discontinuities.
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.
文摘In this study,a new state-based peridynamic formulation is developed for functionally graded Euler-Bernoulli beams.The equation of motion is developed by using Lagrange’s equation and Taylor series.Both axial and transverse displacements are taken into account as degrees of freedom.Four different boundary conditions are considered including pinned support-roller support,pinned support-pinned support,clamped-clamped and clamped-free.Peridynamic results are compared against finite element analysis results for transverse and axial deformations and a very good agreement is observed for all different types of boundary conditions.
基金This work is supported by the Program of Hainan Association for Science and Technology Plans to Youth R&D Innovation(Grant No.QCXM201910)the Natural Science Foundation of Liaoning Province(Grant No.2019-MS-149),the Social Science Planning Foundation of Liaoning Province(Grant No.L18AGL007)+1 种基金the National Natural Science Foundation of China(Grant Nos.61802092,51704138 and 61501447)the Scientific Research Setup Fund of Hainan University(Grant No.KYQD(ZR)1837).
文摘In process industries,the characteristics of industrial activities focus on the integrality and continuity of production process,which can contribute to excavating the appropriate features for industrial anomaly detection.From this perspective,this paper proposes a novel state-based control feature extraction approach,which regards the finite control operations as different states.Furthermore,the procedure of state transition can adequately express the change of successive control operations,and the statistical information between different states can be used to calculate the feature values.Additionally,OCSVM(One Class Support Vector Machine)and BPNN(BP Neural Network),which are optimized by PSO(Particle Swarm Optimization)and GA(Genetic Algorithm)respectively,are introduced as alternative detection engines to match with our feature extraction approach.All experimental results clearly show that the proposed feature extraction approach can effectively coordinate with the optimized classification algorithms,and the optimized GA-BPNN classifier is suggested as a more applicable detection engine by comparing its average detection accuracies with the ones of PSO-OCSVM classifier.
基金the National Natural Science Foundation of China (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We solve the local uniaxial tension of an infinite rod in the framework of non-ordinary state-based peridynamics.The singular solutions of stress and displacement are acquired.When the influencing range of the window function approaches zero,these two solutions will return to the solutions of the classical elasticity.The analysis shows that the singularities of the solutions stem from such a feature of the window function that must be represented by a rapidly decreasing function in physics.Contrary to the classical elasticity,the stress solution of peridynamics is smoother than the displacement solution.In addition,a criterion used to select the window function is proposed in this paper.
基金This work is supported by the National Natural Science Foundation of China under Grant Nos.1190219711972234 and is sponsored by Shanghai Sailing Program under Contract No.19YF1421700.
文摘This study demonstrates a homogenization approach via a modified state-based peridynamic(PD)method to predict the effective elastic properties of composite materials with periodic microstructure.The procedure of modeling the PD unit cell(UC)of continuous fiber-reinforced composite is presented.Periodic boundary conditions are derived and implemented through the Lagrange multiplier method.A matrix-dominated approach for modeling the interphase properties between dissimilar materials is proposed.The periodicity and continuity assumptions are employed to determine the stress and strain fields,as well as the effective elastic properties.The PD-UCs of square and hexagonal packs as well as the 0/90 laminate microstructure are modeled and compared with the analytical,numerical and experimental results from the literature.Good agreement of predicted effective properties can be observed.Unlike other PD homogenization approaches,the effective material properties can be directly and individually obtained from simple loading conditions.
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.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
文摘This study summarizes the examination data of registration labels for ordinary cosmetics in Beijing from May 2021 to April 2024.It analyzes and categorizes the issues identified during label evaluations,explores the underlying causes,and proposes regulatory countermeasures and recommendations for registrants,regulatory authorities,and social organizations.The objective is to offer practical insights and regulatory guidance to support the enhancement of cosmetic registration and regulatory standards.
基金support from the National Natural Science Foundation of China(Grant Nos.42277161 and 42230709).
文摘In rock engineering,natural cracks in rock masses subjected to external loads tend to initiate and propagate,leading to potential safety hazards.To investigate the effect of cracking behavior on the mechanical properties of rocks,the cracking processes of pre-cracked rocks have been extensively studied using numerical modeling methods.The peridynamics(PD)exhibits advantages over other numerical methods due to the absence of the requirements for remeshing and external crack growth criterion.However,for modeling pre-cracked rock cracking processes under impact,current PD implementations lack generally applicable rock constitutive models and impact contact models,which leads to difficulties in determining rock material parameters and efficiently calculating impact loads.This paper proposes a non-ordinary state-based peridynamics(NOSBPD)modeling method integrating the Drucker-Prager(DP)plasticity model and an efficient contact model to address the above problems.In the proposed method,the Drucker-Prager plasticity model is integrated into the NOSBPD,thereby equipping NOSBPD with the capability to accurately characterize the nonlinear stress-strain relationship inherent in rocks.An efficient contact model between particles and meshes is designed to calculate the impact loads,which is essentially a coupling method of PD with the finite element method(FEM).The effectiveness of the proposed NOSBPD modeling method is verified by comparison with other numerical methods and experiments.Experimental results indicate that the proposed method can effectively and accurately predict the 3D cracking processes of pre-cracked cracks under impact loading,and the maximum principal stress is the key driver behind wing crack formation in pre-cracked rocks.
