A theory of mechanical behavior of elastic media with growing damage and other changes in structure.

*(English)*Zbl 0704.73073Summary: Strain energy-like potentials are used to model the mechanical behavior of linear and nonlinear elastic media with changing structure, such as micro- and macrocrack growth in monolithic and composite materials. Theory and experiment show that the applied work for processes in which changes in structure occur is in certain cases independent of some of the deformation history. Consequences of this limited path-independence are investigated, and various relationships for stable mechanical response are derived. For example, it is shown that work is at a minimum during stable changes in structure, which should be useful for developing approximate solutions by variational methods. Some final remarks indicate how the theory may be extended to include thermal, viscoelastic and fatigue effects.

##### MSC:

74R99 | Fracture and damage |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74P10 | Optimization of other properties in solid mechanics |

74C15 | Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) |

74C20 | Large-strain, rate-dependent theories of plasticity |

74E30 | Composite and mixture properties |

74A15 | Thermodynamics in solid mechanics |

74D10 | Nonlinear constitutive equations for materials with memory |

##### Keywords:

linear and nonlinear elastic media; micro- and macrocrack growth; monolithic; composite materials; limited path-independence
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\textit{R. A. Schapery}, J. Mech. Phys. Solids 38, No. 2, 215--253 (1990; Zbl 0704.73073)

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