For the purpose of these lectures, a microstructure is any structure on a scale between the
macroscopic scale (on which we usually make observations) and the atomic scale. Such …

Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

In the context of shape optimization, we seek minimizers of the sum of the elastic compliance
and of the weight of a solid structure under specified loading. This problem is known not to …

A mathematical model for a finite–strain elastoplastic evolution problem is proposed in
which one time–step of an implicit time–discretization leads to generally non–convex …

We establish a general structure theorem for the singular part of 𝓐-free Radon measures,
where 𝓐 is a linear PDE operator. By applying the theorem to suitably chosen differential …

We consider a new class of problems in elasticity, referred to as Data-Driven problems,
defined on the space of strain-stress field pairs, or phase space. The problem consists of …

Abstract Let Ω⊂ R 3 be an open and bounded set with Lipschitz boundary and outward unit
normal ν. For 1< p<∞ we establish an improved version of the generalized L p-Korn …

We show that positively 1-homogeneous rank one convex functions are convex at 0 and at
matrices of rank one. The result is a special case of an abstract convexity result that we …

Lower semicontinuity results for multiple integrals with quasiconvex integrand are obtained
in the setting of Sobolev spaces with respect to a measure and in the setting of generalised …

We characterise all linear maps A: R n× n→ R n× n such that, for 1≤ p< n, PL p∗(R n)≤ c (A
[P] L p∗(R n)+ Curl PL p (R n)) holds for all compactly supported P∈ C c∞(R n; R n× n) …