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ME6110J – Constitutive Modeling and Constitutive Updates of Solids

Instructors:

Credits: 3

Pre-requisites: VM513 (Continuum Mechanics) or VM512 (Elasticity) or VM505 (Finite Element Methods) or VM518 (Composite Mechanics)

Description:

This course introduces the general principles of constitutive modeling of solids, and algorithms for the constitutive updates of some of such models. The first part of the course focuses on homogeneous material modeling. First, the general thermodynamic and objectivity concerns of modeling are presented, and then hyperelastic constitutive models are elaborated in the context of large deformations, of which anisotropic linear elasticity will be treated as a special case. Then models with internal variables such as plasticity, viscoplasticity, and damage will be discussed, together with the relevant updating algorithms such as return mapping The second part of the course is on the modeling of heterogeneous materials, with a focus on methods to obtain their effective properties, from analytic methods to asymptotic homogenization.

Course Topics:

General consideration of constitutive modeling

Objectivity

Hyperelastic materials

Elasticity tensors

Incompressible and compressible isotropic materials

Some forms of strain energy functions

Transversely isotropic materials

Composites with two families of fibers

Anisotropic linear elasticity

Consideration of crystallography

Constitutive models with internal variables

Damage

Phase field approach to fracture

Rate-independent plasticity

Return mapping algorithm

Viscoplasticity and return mapping algorithm

Composites

Representative volume. Hill-Mandel condition

Asymptotic homogenization