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Damage problems for viscous locking materials. (English) Zbl 1158.74310
Summary: We propose a mathematical model describing damage evolution in viscous locking materials like concrete or some composite materials. The model, which is derived from a free energy and a pseudo-potential dissipation by the non-smooth thermo-mechanical approach [cf. M. Frémond, Non-smooth thermomechanics. Berlin: Springer (2002; Zbl 0990.80001)], is a system of nonlinear parabolic partial differential equations which govern the (small) displacement and the damage quantity with thresholds 0 and 1; in our model the material is undamaged (resp. completely damaged) when the damage quantity is 0 (resp. 1). We shall give a weak formulation of this model and prove the existence of a weak global solution in time.

74A45 Theories of fracture and damage
35Q72 Other PDE from mechanics (MSC2000)
74A15 Thermodynamics in solid mechanics
74A40 Random materials and composite materials