Damage and fracture: Classical continuum theories

This paper reports the research results on the continuum theory of damage which goes back to the works of Kachanov, Gurson, and Rabotnov. In these models, internal variables that generally have different mathematical structure are explicitly introduced to constitutive relations. The internal variabl...

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Bibliographic Details
Published in:Physical mesomechanics 2017-04, Vol.20 (2), p.157-173
Main Authors: Volegov, P. S., Gribov, D. S., Trusov, P. V.
Format: Article
Language:English
Subjects:
Classical Mechanics
Computer simulation
Constitutive models
Damage localization
Deformation effects
Dynamic characteristics
Finite element method
Formulations
Materials Science
Mathematical models
Physics
Physics and Astronomy
Solid State Physics
Stability analysis
Strain localization
Structural analysis
Tensors
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Summary:This paper reports the research results on the continuum theory of damage which goes back to the works of Kachanov, Gurson, and Rabotnov. In these models, internal variables that generally have different mathematical structure are explicitly introduced to constitutive relations. The internal variables describe a non-oriented (using scalar damage parameters) or oriented (using different-order tensors) damage distribution in the material. Then, a fracture criterion is introduced based on mechanical or thermodynamic considerations. Models of this type are still most frequently used in the structural analysis of strength of some materials (e.g., composites). Since damage nucleation and growth are closely related to strain localization, consideration is given to formulations and methods for analyzing the stability of inelastic deformation processes. Much attention is given to the effect of the finite element mesh on simulation results, to solution algorithms for such problems, and to the possibilities of using non-local constitutive models. The studies that use gradient models are also included, because damage formation is associated with sharp spatial variations of kinematic and/or dynamic characteristics which must be described by non-classical constitutive relations (gradient, non-local, micromorphic continuum).
ISSN:1029-9599
1990-5424
DOI:10.1134/S1029959917020060