Abstract
In this paper, the meshless integral method based on the regularized boundary integral equation [1] has been extended to analyze the large deformation of elastoplastic materials. The updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity based on Green-Naghdi’s theory over a local sub-domain, and the moving least-squares approximation is used for meshless function approximation. Green-Naghdi’s theory starts with the additive decomposition of the Green-Lagrange strain into elastic and plastic parts and considers aJ2elastoplastic constitutive law that relates the Green-Lagrange strain to the second Piola-Kirchhoff stress. A simple, generalized collocation method is proposed to enforce essential boundary conditions straightforwardly and accurately, while natural boundary conditions are incorporated in the system governing equations and require no special handling. The solution algorithm for large deformation analysis is discussed in detail. Numerical examples show that meshless integral method with large deformation is accurate and robust.
Highlights
Over the past two decades the meshless methods have attracted much attention owing to their advantages in adaptivity, higher degree of continuity in the solution field, and the capability to handle moving boundaries and changing geometry
The updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity based on Green-Naghdi’s theory over a local sub-domain, and the moving least-squares approximation is used for meshless function approximation
Belytschko et al [8] proposed a 3D Element-Free Galerkin (EFG) method intended for dynamic problems with geometric and material nonlinearities solved with explicit time integration
Summary
Over the past two decades the meshless methods have attracted much attention owing to their advantages in adaptivity, higher degree of continuity in the solution field, and the capability to handle moving boundaries and changing geometry. Belytschko et al [8] proposed a 3D Element-Free Galerkin (EFG) method intended for dynamic problems with geometric and material nonlinearities solved with explicit time integration. A nonlinear formulation of meshless local Petrov-Galerkin finite-volume mixed method was developed by Han et al to analyze static and dynamic large deformation problems [14]. Li et al [15] developed a coupled finite element and meshless local Petrov-Galerkin method to analyze large deformation problems. The authors have developed a meshless integral method for linear elasticity [1] and later extended it to elastoplasticity for small deformation [29]. The governing integral equation is obtained from the weak form based on Green-Naghdi’s large deformation elastoplasticity theory over a local subdomain, and moving least-squares approximation is used for meshless function approximation.
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