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arXiv · 1508.06825

Variational problems of nonlinear elasticity theory in certain classes of mappings with finite distortion

A. O. Molchanova·S. K. Vodop'yanov
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Abstract

We study the problem of minimizing the functional $$ I(φ)=\int\limits_Ω W(x,Dφ)\,dx $$ on a new class of mappings. We relax summability conditions for admissible deformations to $φ\in W^1_n(Ω)$ and growth conditions on the integrand $W(x,F)$. To compensate for that, we impose the finite distortion condition and the condition $\frac{|Dφ(x)|^n}{J(x,φ)} \leq M(x) \in L_{s}(Ω)$, $s>n-1$, on the characteristic of distortion. On assuming that the integrand $W(x,F)$ is polyconvex and coercive, we obtain an~existence theorem for the problem of minimizing the functional $I(φ)$ on a new family of admissible deformations. KEYWORDS: functional minimization problem, nonlinear elasticity, mapping with finite distortion, polyconvexity.

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A. O. Molchanova, S. K. Vodop'yanov. 2015-08-27. Variational problems of nonlinear elasticity theory in certain classes of mappings with finite distortion. https://arxiv.org/abs/1508.06825

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