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- M. Šilhavý
- 2009

The article presents a variational theory of sharp phase interfaces bearing a deformation dependent energy. The theory involves both the standard and Eshelby stresses. The constitutive theory is outlined including the symmetry considerations and some particular cases. The existence of phase equilibria is proved based on appropriate convexity properties of… (More)

- M. Šilhavý
- 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. Šilhavý
- 2008

The paper proves the existence of equilibrium two phase states with elastic solid bulk phases and deformation dependent interfacial energy. The states are pairs E consisting of the deformation on the body and the region E occupied by one of the phases in the reference configuration. The bulk energies of the two phases are polyconvex functions representing… (More)

- M. Silhavy
- NHM
- 2007

- MIROSLAV ŠILHAVÝ
- 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. Šilhavý
- 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].… (More)

- Miroslav Šilhavý
- 2014

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

- Miroslav Šilhavý
- 2015

Let S k n denote the kth elementary symmetric function of n variables (k n n). The class of all infinitely differentiable functions f is studied which satisfy the following condition: for all n we have f x + +f x n f y + +f y n whenever x x n and y y n satisfy S k x x n S k y y n for k n − Two sufficient conditions, themselves mutually equivalent, are… (More)

- Miroslav Šilhavý
- 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 y and y of the deformation y Ω of the form |y x| |y x| x x x Ω ⊂… (More)

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