RES.2-002 | Spring 2010 | Graduate

Finite Element Procedures for Solids and Structures

Nonlinear Analysis

Lecture 3: Lagrangian Continuum Mechanics Variables for Analysis

Topics: Lagrangian continuum mechanics variables for general nonlinear analysis

  • The principle of virtual work in terms of the 2nd Piola-Kirchhoff stress and Green-Lagrange strain tensors
  • Deformation gradient tensor
  • Physical interpretation of the deformation gradient
  • Change of mass density
  • Polar decomposition of deformation gradient
  • Green-Lagrange strain tensor
  • 2nd Piola-Kirchhoff stress tensor
  • Important properties of the Green-Lagrange strain and 2nd Piola-Kirchhoff stress tensors
  • Physical explanations of continuum mechanics variables
  • Examples demonstrating the properties of the continuum mechanics variables

Instructor: Klaus-Jürgen Bathe

Course Info

As Taught In
Spring 2010