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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)