Thermodynamics of Damaged Material

  • Sumio MurakamiEmail author
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 185)


In the preceding chapter, we discussed the mechanical modeling of the damaged state of materials by means of internal variables, and called them damage variables. The present chapter is concerned with the thermodynamic constitutive theory with internal variables, which furnishes a consistent basis to formulate the mechanical behavior of damaged materials. In Section 3.1, the fundamental principles and the basic laws of the non-equilibrium continuum thermodynamics are presented as the foundations for the succeeding discussions. In Section 3.2, the notion and the procedure of the thermodynamic constitutive theory with internal variables will be described in detail. It is shown that the inelastic constitutive equations and the evolution equations for internal variables are formulated as a set of generalized normality rule defined by a dissipation potential function and a common multiplier.


Evolution Equation Constitutive Equation Internal Variable Inelastic Deformation Helmholtz Free Energy 
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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Nagoya UniversityNagoyaJapan

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