Constitutive Modelling of Dissipative Solids for Localization and Fracture

  • P. Perzyna
Part of the International Centre for Mechanical Sciences book series (CISM, volume 386)


The main objective of the lectures is to survey some recent developments in the constitutive modelling of inelastic single and polycrystalline solids which can be used for the description of plastic deformation localization and fracture phenomena. Physical foundations and experimental motivations are given. Particular attention is focused on dynamic fracture (adiabatic shear band localized, spall, ductile and brittle fracture phenomena). The physical and experimental foundations for the microdamage processes are presented. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history dependent, nonlinear process.

The description of the kinematics of finite elasto-viscoplastic deformations is based on notions of the Riemannian space on manifolds and tangent space. A multiplicative decomposition of the deformation gradient is adopted and the Lie derivative is used to define all objective rates for introduced vectors and tensors.

A general constitutive model is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A notion of covariance is understood in the sense of invariance under arbitrary spatial diffeomorphism. The thermodynamic theory of elasto-viscoplasticity of inelastic single crystals and damaged polycrystalline solids is developed. The relaxation time is used as a regularization parameter. By assuming that the relaxation time is equal to zero the thermo-elastic-plastic (rate independent) response for both single crystals and polycrystalline solids is accomplished.

An adiabatic inelastic flow process is analysed and the well-posedness of the Cauchy problem is investigated. The analytical methods for the investigation of plastic deformation localization phenomena are developed. The formation of the adiabatic shear band region is investigated. Criteria for adiabatic shear band localization of plastic deformation are obtained by assuming that some of eigenvalue of the instantaneous adiabatic acoustic tensor for rate independent response is equal to zero.

Numerical solution of the initial-boundary value problem (evolution problem) is discussed. Particular attention is focused on the well-posedness of the evolution problem. Convergence, consistency and stability of the discretised evolution problem are examined. The Lax equivalence theorem is formulated and the conditions of its validity are investigated. Utilizing the finite element method for regularized elasto-viscoplastic model the numerical investigation of localization and fracture phenomena is presented. The results obtained are compared with available experimental observations.


Constitutive Modelling Adiabatic Shear Band Void Volume Fraction Internal State Variable Cooperative Phenomenon 
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© Springer-Verlag Wien 1998

Authors and Affiliations

  • P. Perzyna
    • 1
  1. 1.Polish Academy of SciencesWarsawPoland

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