A robust finite element approach for large deformation elastoplastic plane-strain problems

Abstract

This paper presents a decoupled Arbitrary Lagrangian–Eulerian (ALE) approach for the large deformation analysis of plane-strain elastoplastic problems. In this decoupled approach, the Eulerian step consists of first remeshing the deformed continuum and then remapping the state variables at the new quadrature points. Remeshing is performed without altering the element topology of the original mesh with the aid of the Spring Analogy Method enhanced with torsional springs. Before remeshing, nodes at free boundaries are relocated using an analytical approach, in order to preserve a good node distribution throughout the analysis. State variable remapping is achieved through the Radial Basis Point Interpolation Functions scheme. Large deformation elastoplastic analyses of two plane strain example problems are conducted using the presented ALE approach to test its robustness and effectiveness. The continuum is modeled as a Tresca or Mohr–Coulomb elastic–perfectly plastic material, while the meshes consist of second-order finite elements. The numerical results demonstrate that the present methodology is capable of predicting with adequate accuracy the load–displacement response even in analyses involving very large translations of the loaded boundary.