Master's and PhD Degrees
Introductory Soil Mechanics
MECH_ENG 466: Inelastic Constitutive Relations for Solids

Quarter Offered

Winter : TTh 12:30-1:50 ; J. Rudnicki


CIV ENG 317, CIV ENG 415, MECH ENG 362 or equivalent.


bubblegumIntroduction to the formulation and implementation of inelastic constitutive relations for solids. Viscoelasticity, rate-independent plasticity, viscoplasticity. State variable descriptions and thermodynamic restrictions.

Who Takes It

Although increases in computing power have made it possible to solve complex problems in the deformation of solid materials, a prerequisite is a mathematical idealization of the material behavior or a constitutive relation. Technologically advanced materials, extreme operating conditions, such as high termperatures or long lifetimes, biological and geological materials, and fluid-infiltrated materials present formidable challenges.

Consequently, this course will be of interest to graduate students in a variety of areas, structural and solid mechanics, material science, biomechanics, geotechnical engineering, and geological sciences who are interested in the deformation of inelastic solids. The course assumes an understanding of three dimensional stress and strain and basic continuum mechanics.

What It's About

The objective of this course is to give students a solid foundation in the formulation and application of mathematical descriptions of the behavior or solids.


  • One dimensional idealizations:
    • Nonlinear elasticity
    • Viscoelasticity
    • Rate independent plasticity
    • Viscoplasticity
  • Multiaxial generalizations
  • Applications to pressure-sensitive, compressible materials, such as:
    • Voided metals
    • Geomaterials
  • State variable descriptions and connections to microstructure
  • Thermodynamic restrictions on the form of constitutive relations; applications to thermoelasticity and poroelasticity
  • Numerical algorithms for rate-independent and rate-dependent plasticity



Reference material

Malvern (Introduction to the Mechanics of a Continuous Medium)
Mase and Mase (Continuum Mechanics for Engineers)


Homework and final exam


Professor: John Rudnicki