General Constitutive Equations for Simple and Non-Simple Materials

  • P. R. Gummert
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 399)


Stress and deformation are related by constitutive equations. Using the symmetric stress tensor field S(X, t) at the place of X and at the present time t and a (symmetric) deformation field, e.g. B(X, τ) at the same place of X and the past time τ, it is necessary and possible to postulate six equations S(B). Together with three equations of NEWTON’s law (resp. with three equilibrium conditions) and six equations of displacement-deformation conditions between B(X, τ) and the displacement field u(X, τ) an array of fifteen equations is generated to solve the fifteen unknowns as scalar components of the two tensor fields S(X, t), B(X, τ) and the vector field u(X, τ). Embedded in a consistent mathematical and physical frame theory, this paper is an attempt to derive constitutive laws in a general way and to classify the materials in a systematical way. The knowledge about a material is complete, if in addition to the constitutive equations a procedure of determination of the appropriate material functions and/or parameters is provided (material identification).


Constitutive Equation Reference Configuration Deformation Tensor Incompressible Material Material Function 
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Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • P. R. Gummert
    • 1
  1. 1.Technical University BerlinBerlinGermany

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