Constitutive modeling and simulation of pressure dependent plasticity

Abstract

The field of plasticity has been a very active field of research for the past few decades in engineering and mathematics communities. It is a branch of solid mechanics which deals with the plastic deformation and the limit load-carrying capacities of materials and structures. The deformation of a material is said to be plastic if it is irreversible i.e the material undergoes permanent deformation on the removal of loads. The theory of plasticity deals with the methods of yield initiation of materials under various stress states and evaluation of stresses and strains of a deformed material after a part or the whole material has yielded. Brittle materials such as glass, ceramic, graphite only undergo elastic deformation before failure. On the other hand metals, rocks, soils and concrete undergo substantial plastic deformation before failure. Granular materials such as soils exhibit pressure-dependent behaviour and so metal plasticity is different from soil plasticity. The aim of this Master’s Thesis is to consider advanced pressure-dependent plasticity models such as the Ducker Prager model and to implement their constitutive formulations and return mapping procedures into a common finite element environment. Also, a detailed comparison between pressure-sensitive and pressure insensitive material models is presented. Pressurised cylinder, Strip footing and slope stability problems are used to compare the different plasticity models using numerical simulations in Julia