We consider energies modelling the interaction of two media parameterized by the same reference set, such as those used to study interactions of a thin film with a stiff substrate, hybrid laminates or skeletal muscles. Analytically, these energies consist of a (possibly non-convex) functional of hyperelastic type and a second functional of the same type such as those used in variational theories of brittle fracture, paired by an interaction term governing the strength of the interaction depending on a small parameter. The overall behaviour is described by letting this parameter tend to zero and exhibiting a limit effective energy using the terminology of Gamma-convergence. Such energy depends on a single state variable and is of hyperelastic type. The form of its energy function highlights an optimization between microfracture and microscopic oscillations of the strain, mixing homogenization and high-contrast effects. © 2018 The Author(s) Published by the Royal Society. All rights reserved.
A homogenization result for interacting elastic and brittle media / Braides, Andrea; Causin, Andrea; Solci, Margherita. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A. - ISSN 1364-5021. - 474:2218(2018), pp. 1-21. [10.1098/rspa.2018.0118]
A homogenization result for interacting elastic and brittle media
Causin, Andrea;Solci, Margherita
2018-01-01
Abstract
We consider energies modelling the interaction of two media parameterized by the same reference set, such as those used to study interactions of a thin film with a stiff substrate, hybrid laminates or skeletal muscles. Analytically, these energies consist of a (possibly non-convex) functional of hyperelastic type and a second functional of the same type such as those used in variational theories of brittle fracture, paired by an interaction term governing the strength of the interaction depending on a small parameter. The overall behaviour is described by letting this parameter tend to zero and exhibiting a limit effective energy using the terminology of Gamma-convergence. Such energy depends on a single state variable and is of hyperelastic type. The form of its energy function highlights an optimization between microfracture and microscopic oscillations of the strain, mixing homogenization and high-contrast effects. © 2018 The Author(s) Published by the Royal Society. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.