Selected Topics in Continuum Mechanics

Institution:
University of Grenoble Joseph Fourier
Specialisation:
ES
Term:
Fall 2011
Teacher(s):
/
Credits:
6
Date (from - to):
01/09/2011 – 30/11/2011
  • Kinematics : Physical space ‐ frames ‐ continuous media ‐ deformation function ‐ Lagrange and Euler variables
  • Strains : Deformation gradient ‐ metric tensor ‐ Green deformation tensor ‐ small strains ‐ strain rate
  • Material derivative  and conservation laws
  • Mass conservation ‐ volume change ‐ balance of momentum
  • Stresses : Fundamental principle of dynamics ‐ Cauchy stress tensor‐equation of motion and boundary conditions ‐ Piola‐Kirchhoff stress tensors ‐ virtual power formulation ‐ linearization of equation of motion
  • Examples of formulations of problems of continuum mechanics
  • Frame invariance
  • Constitutive equations: Large elasticity ‐ elastoplasticity incremental constitutive equations, generalized continuous media, Non local, second grade, Cosserat and micromorphic continuum mechanics ‐ an introduction

Suggested readings:

  • Gurtin M. ‐ An Introduction to Continuum Mechanics. Academic Press, San Diego, 1981
  • Truesdell C. ‐ A First Course in Rational Continuum Mechanics. Academic Press, New‐York, 1977
  • Truesdell C. and Noll W. ‐ The Non‐Linear Field Theories of Mechanics. Handbuch der Physik III/3. Berlin Springer‐Verlag 1965
  • Malvern L. ‐ Introduction to the Mechanics of a Continuous Medium. Englewood Cliffs, NJ, Prentice‐Hall, 1969
  • Washizu K. ‐ Variational Methods in Elasticity and Plasticity, Pergamon Press, 1975