Table of Contents – Non-linear Mechanics of Materials
Note: Lectures notes are available in Microsoft OneNote upon enrollment into the course
Unit 1: Constitutive theory for large deformations
- Introduction and motivation
- Constitutive principles
i. Field equations
ii. Thermodynamics
iii. Coleman and Noll procedure - Material frame-indifference
i. Frames and observers
ii. Objectivity requirements
iii. Kinematics
iv. Stress rates - Constitutive theory with internal variables
i. Dissipation and kinetic relationships
ii. Large deformation kinematics - Numerical aspects of the constitutive theory
i. Weak formulations
ii. Tangent modulus
Work 1: Incremental material frame-indifference of the shear test (PDF 2023-1)
Unit 2: Non-linear viscoelasticity
- Introduction to rheology
- One dimensional analogy models
i. Maxwell
ii. Kelvin-Voigt
iii. Standard solid - Extension to continuum mechanics and thermodynamic consistency
i. Non-linear kinematics of the analogy models
ii. Stresses of the analogy models
iii. Coleman and Noll procedure - Numerical integration
i. Stress-update algorithm
ii. Tangent modulus derivation
Work 2: Non-linear viscoelastic analysis using the Burgers model (PDF 2023-1)
Unit 3: Infinitesimal theory of plasticity
- Phenomenology
- General constitutive equations
i. Assumptions
ii. Yield criteria
iii. Flow rule
iv. Hardening - Computational plasticity
i. Return-mapping algorithm
ii. Continuum and algorithmic tangent modulus
Work 3: Tensile test in a steel bar (PDF 2023-1)