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We consider a quasistatic system involving a Volterra kernel modelling
an hereditarily-elastic aging body. We are concerned with the behavior of
displacement and stress fields in the neighborhood of cracks. In this paper, we
investigate the case of a straight crack in a two-dimensional domain with a possibly
anisotropic material law.
We study the asymptotics of the time dependent solution near the crack tips.
We prove that, depending on the regularity of the material
law and the Volterra kernel,...
We consider the initial value problem for the nonlinear partial differential equations describing the motion of an inhomogeneous and anisotropic hyperelastic medium. We assume that the stored energy function of the hyperelastic material is a function of the point x and the nonlinear Green-St. Venant strain tensor . Moreover, we assume that the stored energy function is with respect to x and . In our description we assume that Piola-Kirchhoff’s stress tensor depends on the tensor . This means...
In these notes we give some examples of the interaction of mathematics with experiments and numerical simulations on the search for singularities.
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