Formulation for the Cam-clay model based on the finite deformation theory with the multiplicative decomposition of the deformation gradient and avoidance of the volumetric locking by using the F-bar method

Abstract

This paper presents a formulation for the Cam-clay model based on the finite deformation theory with the multiplicative decomposition of the deformation gradient. We developed an implicit stress-update scheme using the return-mapping algorithm and derived the consistent tangent modulus analytically. We also demonstrated that the scheme had high accuracy and quadratic convergence. By conducting the finite element analysis, we obtained the following conclusions. 1) Even though the Cam-clay model has compressibility both elastically and plastically, volumetric locking occurs. That is because the model shows the nearly incompressible property in the vicinity of the critical state. 2) F-bar method is useful for avoidance of the volumetric locking.