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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© 2019 Springer Nature Switzerland AG
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Roubícek, T. (2019). Models of Dynamic Damage and Phase-field Fracture, and their Various Time Discretisations. In: Hintermüller, M., Rodrigues, J. (eds) Topics in Applied Analysis and Optimisation. CIM Series in Mathematical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-030-33116-0_14
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DOI: https://doi.org/10.1007/978-3-030-33116-0_14
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-33115-3
Online ISBN: 978-3-030-33116-0
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