Lagrangian Meshfree Formulation for Analysis of Geotechnical Materials

A Lagrangian reproducing kernel formulation is introduced as an approximation of field variables under the Galerkin meshfree framework of geomechanics. The reproducing kernel approximation is formulated with reference to the material coordinates, yielding an approach that is applicable to both total and updated Lagrangian formulations. In the method presented, geotechnical materials described by pressure-sensitive multisurface plasticity with a cap hardening rule are considered in the meshfree formulation. The solution obtained from the meshfree method with linear basis was compared to that of bilinear finite elements for elastoplastic analysis of geotechnical materials.