TITLE:
Elastoplastic Large Deformation Using Meshless Integral Method
AUTHORS:
Jianfeng Ma, X. J. Xin
KEYWORDS:
Meshless Method; Large Deformation; Local Boundary Integral Equation; Moving Least-Squares Approximation; Subtraction Method; Singularity Removal; Elastoplasticity; Green-Naghdi’s Theory
JOURNAL NAME:
World Journal of Mechanics,
Vol.2 No.6,
December
31,
2012
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.