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- M. Silhavy
- 2000

1. Introduction. Let Sym denote the linear space of all symmetric second-order tensors on an n-dimensional real vector space Vect with scalar product. (If Vect is identified with R n , then Sym may be identified with the set of all symmetric n-by-n matrices.) A function f : Sym → R is said to be isotropic if f (A) = f (QAQ T) for all A ∈ Sym and all Q… (More)

- M. Silhavy
- 2009

For interfacial interactions of “separable type” the existence is proved of stable multiphase equilibrium states minimizing the total energy which includes a sharp interface contribution along interfaces separating the phases. The second gradients of deformation do not occur; the theory is based on interfacial null lagrangians as determined in [11–12]. The… (More)

- M. Silhavy
- 2008

A version of Cauchy’s stress theorem is given in which the stress describing the system of forces in a continuous body is represented by a tensor valued measure with weak divergence a vector valued measure. The system of forces is formalized in the notion of an unbounded Cauchy flux generalizing the bounded Cauchy flux by Gurtin & Martins [12]. The main… (More)

- M. Silhavy
- 2002

Let f be a rotationally invariant (with respect to the proper orthogonal group) function defined on the set M2×2 of all 2 by 2 matrices. Based on conditions for the rank 1 convexity of f in terms of signed invariants of A (to be defined below), an iterative procedure is given for calculating the rank 1 convex hull of a rotationally invariant function. A… (More)

- M. Lucchesi, M. Silhavy, Nicola Zani
- 2010

In this paper we consider masonry bodies undergoing loads that can be represented by vector valued measures, and prove a result which is an appropriate formulation to this context of the static theorem of the limit analysis. As applications, we study the equilibrium of panels that are subjected both to distributed loads and concentrated forces, and… (More)

- M. Silhavy
- 2010

The sharp interface limit of a diffuse interface theory of phase transitions is considered in static situations. The diffuse interface model is of the Allen–Cahn type with deformation, with a parameter ε measuring the width of the interface. Equilibrium states of a given elongation and a given interface width are considered and the asymptotics for ε r 0 of… (More)

- M. Silhavy
- 2014

The differentiability of the metric projection P onto a closed convex set K in Rn is examined. The boundary ãK can have singular points of orders k ̈ −1Ù 0Ù 1ÜÙ n − 1. Here k ̈ −1 corresponds to the interior points of K , k ̈ 0 to regular points of the boundary (i.e., faces), k ̈ 1ÙÜ Ù n − 2 to edges and k ̈ n − 1 to vertices. It is assumed that for… (More)

- M. Silhavy
- NHM
- 2007

- M. Silhavy
- 2015

The paper deals with nets formed by two families of fibers (cords) which can grow shorter but not longer, in a deformation. The nets are treated as two dimensional continua in the three dimensional space. The inextensibility condition places unilateral constraint on the partial derivatives yÙ 1 and yÙ 2 of the deformation y Ú Ω r R 3 of the form |yÙ 1 x | 2… (More)

- M. Silhavy
- 2009

This note proposes to modify the definition of quasiconvexity of a function f Úìmn r Ï ñ Ú ̈ ñ T −ðÙð( on the spaceìmn of m n matrices in such a way that (i) the polyconvexity implies quasiconvexity without any additional measurability or continuity assumption on f and (ii) the pointwise supremum of any family of quasiconvex functions is a quasiconvex… (More)