We consider classical variational inequalities modeling elastic plastic problems with kinematic and isotropic hardening. It is shown that the stress velocities have fractional derivatives of order in in time direction on the whole existence interval. In space direction an analogous result holds in the interior of the domain. In the case of kinematic hardening, these results are also true for the strain velocity.
This paper deals with a strongly elliptic perturbation for the Stokes equation in exterior three-dimensional domains Ω with smooth boundary. The continuity equation is substituted by the equation -ε²Δp + div u = 0, and a Neumann boundary condition for the pressure is added. Using parameter dependent Sobolev norms, for bounded domains and for sufficiently smooth data we prove convergence for the velocity part and convergence for the pressure to the solution of the Stokes problem, with δ arbitrarily...
Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a...
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