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In this paper, the meshless integral method based on the regularizedboundary integral equation 1 has been extended to analyze the largedeformation of elastoplastic materials. The updated Lagrangian governingintegral equation is obtained from the weak form of elastoplasticity based onGreen-Naghdi’s theory over a local sub-domain, and the moving least-squares approximationis used for meshless function approximation. Green-Naghdi’s theory starts withthe additive decomposition of the Green-Lagrange strain into elastic andplastic parts and considers aJ2elastoplastic constitutive law that relates the Green-Lagrangestrain to the second Piola-Kirchhoff stress. A simple, generalized collocationmethod is proposed to enforce essential boundary conditions straightforwardlyand accurately, while natural boundary conditions are incorporated in thesystem governing equations and require no special handling. The solutionalgorithm for large deformation analysis is discussed in detail. Numericalexamples show that meshless integral method with large deformation is accurateand robust.


Meshless Method; Large Deformation; Local Boundary Integral Equation; Moving Least-Squares Approximation; Subtraction Method; Singularity Removal; Elastoplasticity; Green-Naghdi’s Theory

Cite this paper

J. Ma and X. Xin -Elastoplastic Large Deformation Using Meshless Integral Method,- World Journal of Mechanics, Vol. 2 No. 6, 2012, pp. 339-360. doi: 10.4236-wjm.2012.26040.

Author: Jianfeng Ma, X. J. Xin

Source: http://www.scirp.org/


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