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Rate-independent problems are considered, where the stored energy
density is a function of the gradient. The stored energy density may
not be quasiconvex and is assumed to grow linearly. Moreover,
arbitrary behaviour at infinity is allowed. In particular, the
stored energy density is not required to coincide at infinity with a
positively 1-homogeneous function. The existence of a
rate-independent process is shown in the so-called energetic
formulation.
Continuing earlier work by Székelyhidi, we describe the
topological and geometric structure of so-called
-configurations which are the most prominent examples of
nontrivial rank-one convex hulls. It turns out that the structure of
-configurations in is very rich; in particular,
their collection is open as a subset of . Moreover a previously purely algebraic criterion is
given a geometric interpretation. As a consequence, we sketch an
improved algorithm...
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