Structured deformations as energy minimizers in models of fracture and hysteresis
Rutsum Choksi, Gianpetro del Piero, Irene Fonseca, and D. Owen
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Submission date: 06. Jul. 1998
published in: Mathematics and mechanics of solids, 4 (1999) 3, p. 321-356
DOI number (of the published article): 10.1177/108128659900400304
We review recent theories of non-classical, structured deformations and integral representations for their Helmholtz free energy. Energy minimizers for a body undergoing shearing at two different length scales and for a bar experiencing both smooth extension and macroscopic fractures then are determined, and applications to the shearing of single crystals and to the cohesive fracture of solids are discussed. Yield, hysteresis, and the associated dissipation in two-level shears are shown to arise from instabilities at the microlevel, and the dichotomy between brittle and ductile fracture is related precisely to a critical length of a bar.