The Boundary Element Method for Ordinary State-Based Peridynamics

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.

Nonlocal thermo-elastic constitutive relation of fibre-reinforced composites

The effective properties of composite materials have been predicted by various micromechanical schemes.For composite materials of constituents which are described by the classical governing equations of the local form,the conventional micromechanical schemes usually give effective properties of the local form.However,it is recognized that under general loading conditions,spatiotemporal nonlocal constitutive equations may better depict the macroscopic behavior of these materials.In this paper,we derive the thermo-elastic dynamic effective governing equations of a fibre-reinforced composite in a coupled spatiotemporal integral form.These coupled equations reduce to the spatial nonlocal peridynamic formulation when the microstructural inertial effects are neglected.For static deformation and steady-state heat conduction,we show that the integral formulation is superior at capturing the variations of the average displacement and temperature in regions of high gradients than the conventional micromechanical schemes.The approach can be applied to analogous multi-field coupled problems of composites.

A Peridynamic Model for the Dynamics of Defects with Asymmetric Potential Wells

The peridynamic model of a solid is suitable for studying the dynamics of defects in materials.We use the bond-based peridynamic theory to propose a one-dimensional nonlocal continuum model to study a defect in equilibrium and in steady propagation.As the defect propagates,the material particles undergo a transition between two states.By using the Wiener–Hopf method,an explicit analytical solution of the problem is obtained.The relation between the applied force and the propagation speed of the defect is determined;our results show that the defect does not propagate if the applied force is less than a critical value,whereas propagation occurs when the force exceeds that value.The energy properties of the system are investigated.