A Study of Decoupled FEM for Incompressible Hyperelastic Material

(GSMAC-FEM Analysis of Mooney-Rivlin Material)

Abstract

Hyperelastic material is regarded as incompressible material. Solving of simultaneous equations which consist of incompressible restraint condition and the equation of motion is necessary to incompressible material analysis. Mixed FEM is generally used in hyperelastic material analysis. In this method the simultaneous equations are directly solved. Meanwhile in incompressible fluid analysis decoupled FEM which has developed from MAC method in FDM and has superior features is used besides mixed FEM. In this method the simultaneous equations are indirectly solved by introducing decoupled equations which consist of predictor step, corrector step and Poisson equation. In this study decoupled FEM for incompressible hyperelastic material is constructed. The hyperelastic material of Mooney-Rivlin model and GSMAC-FEM, decoupled FEM suitable for calculation on a large scale, are especially used. Lagrangian method and Newmark-β method is introduced to Eulerian basic equation to apply decoupled FEM to solid analysis. The discretized equations are verified in plane strain problem.