Engineering Transactions, 53, 3, pp. 235–316, 2005

The Thermodynamical Theory of Elasto-Yiscoplasticity (Review Paper)

P. Perzyna
Polish Academy of Sciences
Poland

The main objective of this paper is to survey some recent developments in the constitutive modelling of inelastic polycrystalline solids, which may be used for the description of important problems in modern manufacturing processes, and particularly for mesomechanical issues. This description is needed for the investigation by using the numerical methods how to avoid unexpected plastic strain localization and fracture phenomena in manufacturing technology. Since modern manufacturing processes lead to very complex states of stress and deformation for a solid body under consideration, then in the description we have to take into account the influence of stress triaxiality and plastic spin effects. In this paper emphasis is laid on experimental and physical foundations as well as on mathematical constitutive modelling for the description of localization of plastic deformation and various modes of fracture phenomena in polycrystalline solids. The description of kinematics of finite deformations and the stress tensors is given. The development of a thermo-elasto-viscoplastic model within the thermo-dynamic framework of the rate-type covariance constitutive structure with finite set of the internal state variables is presented. Particular attention is focused on the determination of the evolution laws for the internal state variables. Fracture criterion based on the evolution of microdamage is formulated. By assuming that the mechanical relaxation time is equal to zero, the thermo-elasto-plastic (rate-independent) response of the damaged material can be accomplished. The thermodynamical theory of elasto-viscoplasticity of polycrystalline solids presented has important features as follows: (i) invariance with respect to diffeomorphism; (ii) finite plastic deformation and plastic spin effects; (iii) plastic non-normality; (iv) softening effects generated by microdamage mechanism; (v) plastic deformation-induced anisotropic effects; (vi) thermomechanical couplings (thermal plastic softening and thermal expansion); (vii) influence of stress triaxiality on the evolution of microdamage; (viii) ratę sensitivity; (ix) length scale sensitivity; (x) regularization of the evolution problem; (xi) dissipation and dispersion effects; (xii) synergetic effects generated by cooperative phenomena. Ali these fundamental features have been carefully discussed. It should be noted that the very important part of constitutive modelling is the identification procedure for the material functions and constants involved in the constitutive equations proposed.
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