Introductory description

N/A.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Topic 1: Fundamentals of Nonlinear Solid Mechanics
a. Theory of finite deformations - brief recap
b. Nonlinear constitutive equations (e.g. hyperelasticity, plasticity, viscoplasticity)
i) Phenomenological
ii) Physically-based
iii) Data-driven
Topic 2: Methods for predicting macroscopic properties of nonlinear heterogeneous solids
a. Mean-field approaches
i) Self-consistent methods
ii) Mori-Tanaka methods
b. Homogenisation
i) Homogenisation for linear periodic heterogeneous materials
ii) Homogenisation for nonlinear periodic heterogeneous materials
Topic 3: Extensions to multi-physics problems in nonlinear heterogeneous solids
a. Mean-field approaches
b. Homogenisation

Learning outcomes

By the end of the module, students should be able to:

• Understand sources of material nonlinearity.
• Be familiar with common constitutive models.
• Be able to implement nonlinear constitutive models into nonlinear solution process.
• Understand the concept of homogenisation.
• Apply a nonlinear mean-field approach to a simple problem.
• Be able to design and implement a simple two-scale nonlinear simulation process.

Indicative reading list

[1] J. Fish, Practical Multiscaling, Wiley, 2013.
[2] S. Torquato, Random heterogeneous materials: Microstructure and Macroscopic Properties. Springer, 2002.

Subject specific skills

Understand sources of material nonlinearity
Be familiar with common constitutive models
Be able to implement nonlinear constitutive models into nonlinear solution process
Understand the concept of homogenisation
Apply a nonlinear mean-field approach to a simple problem
Be able to design and implement a simple two-scale nonlinear simulation process

Transferable skills

Programming, data analysis, problem-solving