Stress Integration of Matsuoka-Nakai Constitutive Model Using Incremental Plasticity Method

Abstract

This paper presents the integration of constitutive relations for Matsuoka-Nakai non-associative constitutive model using incremental plasticity method. The basic idea of this method is the calculation of plastic matrix thus, the calculation of the stress increment needs only total strain increment. Presented constitutive model consists of a yield surface similar to Mohr-Coulomb yield surface, but completely smooth, avoiding corners which can be problematic in numerical calculations. The yield surface divides stress 3D space into the pure elastic region and pure plastic region. In addition to the basic equations for stress integration, the paper presents the development of elastic-plastic constitutive matrix and algorithm for the implementation in the program for finite elements. Presented procedure is implemented in the PAK software. Verification is performed using examples from the literature and compared with the results obtained using Mohr-Coulomb constitutive model.