This course is designed for graduate students who are interested in learning how solid materials such as steel, soil, and rock respond to loading and deformation. Constitutive models are mathematical constructs founded on fundamental mechanics that relate loads and deformations through various components of stresses and strains. Students will learn how to use tensors to describe stresses and strains in 3D space, what various loading conditions solids may experience, how solid materials respond to loading by elastic and plastic deformations, and how presence of other material phases such as fluids may contribute to material behaviour.

The course includes three main sections: First a summary of some continuum mechanics concepts including tensor notation and operations, deformation gradient, strain and stress tensors, principal vectors, and invariants will be explained. Then basic concepts from plasticity including definitions of elastic and plastic strains, yielding, hardening, coaxially, normality and flow rule will be introduced. The final and most extensive part of the course includes going through a range of constitutive relations starting with classic elasto-plastic models and moving on to classic and advanced critical state and bounding surface plasticity models. Materials will be general in nature, but examples and some of the specific models will focus on soil behaviour. The course will be useful to all students who are studying Geomechanics, and those Structural Engineering students who are interested in modelling material behaviour, or soil-structure interaction.