  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.

Analysis of PDEs;Numerical Analysis