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Classification of Constitutive Equations for Dissipative Materials—General Review

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Mechanics of Anisotropic Materials

Part of the book series: Engineering Materials ((ENG.MAT.))

Abstract

In the present chapter the general features of thermodynamically based constitutive modeling are described. In such approach a basic hypothesis is that the state of a material is entirely determined by certain values of some independent variables, called variables of state. This type of constitutive modeling is particularly well adapted to the formulation of constitutive equations for deformable solids with several dissipative phenomena. A common three-stage procedure in the definition of a constitutive model is discussed: (1) choice of the state variables, (2) definition of the state potential from which the state relations (between strain-like variables and their dual conjugated forces) are derived, and (3) choice of the dissipation potential from which the rate equations of state variables are derived. The classification of constitutive equations is then presented for elastic-damage, elastic-plastic, thermo-elastic-(visco)plastic, and elastic-plastic-damage materials. Damage-induced anisotropy and unilateral damage effect are accounted. When plasticity is considered, an alternative multiscale approach, based on polycrystalline calculations for the description of yielding anisotropy and its evolution with accumulated deformation, is also discussed. As an example of thermoplastic coupling, the fatigue behavior of martensitic hot work tool steel in nonisothermal conditions is analyzed. In this example two cases are compared: (1) partial coupling, when changing temperature is accounted only in changing material parameters, and (2) full coupling, when additional terms proportional to temperature rate are added in the kinetic equations of thermodynamic conjugate forces. Numerical simulations are performed, which indicate the significant influence of temperature rate on the response of constitutive model when cyclic thermomechanical loading is considered.

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Authors and Affiliations

  1. Solid Mechanics Division, Institute of Applied Mechanics, Cracow University of Technology, al. Jana Pawła II 37, 31-864, Kraków, Poland

    H. Egner

  2. Division of Technical Mechanics, Institute of Applied Mechanics, Cracow University of Technology, al. Jana Pawła II 37, 31-864, Kraków, Poland

    W. Egner

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  1. H. Egner
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Editors and Affiliations

  1. Solid Mechanics Division, Institute of Applied Mechanics, Cracow University of Technology, Al. Jana Pawła II 37, 31-864, Krakow, Poland

    Jacek J. Skrzypek

  2. Solid Mechanics Division, Institute of Applied Mechanics, Cracow University of Technology, Al. Jana Pawła II 37, 31-864, Krakow, Poland

    Artur W. Ganczarski

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Egner, H., Egner, W. (2015). Classification of Constitutive Equations for Dissipative Materials—General Review. In: Skrzypek, J., Ganczarski, A. (eds) Mechanics of Anisotropic Materials. Engineering Materials. Springer, Cham. https://doi.org/10.1007/978-3-319-17160-9_7

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