Istituto di Scienza e Tecnologie dell'Informazione     
Padovani C., Miroslav S. Relaxed energy for transversely isotropic two-phase materials. In: Journal of elasticity, vol. 67 pp. 187 - 204. Kluwer Academic Publisher, 2002.
The paper gives a simple derivation of the relaxed energy Wqc for the quadratic double-well material with equal elastic moduli and analyzes Wqc in the transversely isotropic case. We observe that the energy W is a sum of a degenerate quadratic quasiconvex function and a function that depends on the strain only through a scalar variable. For such a W, the relaxation reduces to a one-dimensional convexification. Wqc depends on a constant g defined by a three-dimensional maximum problem. It is shown that in the transversely isotropic case the problem reduces to a maximization of a fraction of two quadratic polynomials over [0,1]. The maximization reveals several regimes and explicit formulas are given in the case of a transversely isotropic, positive definite displacement of the wells.
Subject Double-well materials
Transverse isotropy
J.2 Physical Sciences and Engineering

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