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An energy-based damage model of geomaterials. II: Deduction of damage evolution laws. (English) Zbl 0973.74009
By considering damage evolution law in the linear irreversible thermodynamics, the authors correlate the phenomenological equation to the rate of second-order damage tensor by means of a coefficient – the damage characteristic tensor of rank four. Further, by describing the macrocrack by a damage vector (d.v.), expressing the tensor as an average measure of d.v., describing a group of parallel microcracks by a new d.v. and condensing such vectors into three characteristic sets, d.v. is realized as a “smoothing procedure”. This allows to constitute a “normality structure”, i.e. to construct an associated thermodynamic theory which includes the free energy, its Legendre transform (the complementary Gibbs energy), and contains the kinetic equations. Meanwhile, in order to account for the time-independent behaviour when not all internal variables are active under loading, the authors introduce the damage (yield) surfaces, the kinetic equations being recast into an form analogous to the von Mises plastic potential gradient equations. Using the Griffith’s cracking initiation which correlates the energy release to the crack resistance and kinking, the authors express the crack threshold in terms of history-recording parameters. Numerical tests for parallel cracks in perfectly brittle solids confirm the correlation between crack angle and kinking angle. Uniaxial tests for parallel cracks conclude this important work.

74A45 Theories of fracture and damage
74L05 Geophysical solid mechanics
74L10 Soil and rock mechanics
74A15 Thermodynamics in solid mechanics
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