On the rheological instability of an elastic damaging medium
type: Item
instance of: scholarly article
title: On the rheological instability of an elastic damaging medium
zbMATH Open document ID: 0778.73011
DOI: 10.1016/0021-8928(91)90066-4
author: V. I. Kondaurov
published in: Journal of Applied Mathematics and Mechanics
publication date: 1992-09-26T00:00:00Z
review text: This is an interesting paper on the mathematical description of rheological instabilities in elastic damaged solids. The damage under consideration is of the microcrack type. The behaviour of materials is described by the author's model of continuum fracture in elastic bodies [J. Appl. Math. Mech. 52, No. 2, 237-243 (1988; Zbl 0724.73178)]derived by using the local balance between effective surface energy of microcracks and the cumulative elastic energy of the material surrounding these microcracks. The constraints on the allowable strain values are derived from Hadamard condition, via a process of isothermal approximation, and the violation of this condition is identified with the rheological instability of material. Propagation of weak discontinuities is analysed, generation conditions and spatial characteristics of discontinuity surfaces are examined, and some examples are given.
Mathematics Subject Classification ID: 74B99
Mathematics Subject Classification ID: 74R99
zbMATH DE Number: 56643
zbMATH Keywords: local balance
zbMATH Keywords: effective surface energy
zbMATH Keywords: cumulative elastic energy
zbMATH Keywords: Hadamard condition
zbMATH Keywords: microcrack
zbMATH Keywords: isothermal approximation
zbMATH Keywords: weak discontinuities
reviewed by: Gheorghe Gr. Ciobanu
MaRDI profile type: Publication
full work available at URL: 0021-8928(91)90066-4
OpenAlex ID: W2004050028
cites work: Q3238949
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cites work: Integral equations in the coupling problem for semiopen dielectric waveguides
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description: scientific article; zbMATH DE number 56643