Models of Dynamic Damage and Phase-field Fracture, and their Various Time Discretisations

  • Tomáš RoubícekEmail author
Conference paper
Part of the CIM Series in Mathematical Sciences book series (CIMSMS)


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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mathematical Institute, Charles UniversitySokolovská 83, CZ-186 75 Praha 8Czech Republic

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