Models of dynamic damage and phase-field fracture, and their various time discretisations

Tomáš Roubíček

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arXiv · 1906.04110

Models of dynamic damage and phase-field fracture, and their various time discretisations

Tomáš Roubíček

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Abstract

Several variants of models of damage in viscoelastic continua under small strains in the Kelvin-Voigt rheology are presented and analyzed by using the Galerkin method. The particular case, known as a phase-field fracture approximation of cracks, is discussed in detail. All these models are dynamic (i.e. involve inertia to model vibrations or waves possibly emitted during fast damage/fracture or induced by fast varying forcing) and consider viscosity which is also damageable. Then various options for time discretisation are devised. Eventually, extensions to more complex rheologies or a modification for large strains are briefly exposed, too.

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Tomáš Roubíček. 2019-06-10. Models of dynamic damage and phase-field fracture, and their various time discretisations. https://arxiv.org/abs/1906.04110

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