18 citations · 26 across the 10 of their papers we have counts for
14 papers
SBH-ellipticity of the relaxed interfacial energy density in the context of second-order structured deformations
A. C. Barroso, J. Matias, E. Zappale
Starting from an energy comprised of both a bulk term and a surface term, set in the space of special functions of bounded hessian, , a relaxation problem in the context of se…
A Global Method for Relaxation for Multi-levelled Structured Deformations
Ana Cristina Barroso, José Matias, Elvira Zappale
We prove an integral representation result for a class of variational functionals appearing in the framework of hierarchical systems of structured deformations via a global method…
Asymptotic analysis of a clamped thin multidomain allowing for fractures and discontinuities
G. Carvalho, J. Matias, E. Zappale
We consider a thin multidomain of consisting of a vertical rod upon a horizontal disk. The equilibrium configurations of the thin hyperelastic multidomain, allowing…
The variational modeling of hierarchical structured deformations
Ana Cristina Barroso, José Matias, Marco Morandotti +2
Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theore…
Periodic homogenization in the context of structured deformations
Micol Amar, José Matias, Marco Morandotti +1
An energy for first-order structured deformations in the context of periodic homogenization is obtained. This energy, defined in principle by relaxation of an initial energy of int…
Relaxation for an optimal design problem in
Ana Cristina Barroso, José Matias, Elvira Zappale
We obtain a measure representation for a functional arising in the context of optimal design problems under linear growth conditions. The functional in question corresponds to the…
Upscaling and spatial localization of non-local energies with applications to crystal plasticity
José Matias, Marco Morandotti, David R. Owen +1
We describe multiscale geometrical changes via structured deformations and the non-local energetic response at a point via a function of the weighted averages of th…
Dimension reduction in the context of structured deformations
Graça Carita, José Matias, Marco Morandotti +1
In this paper we apply both the procedure of dimension reduction and the incorporation of structured deformations to a three-dimensional continuum in the form of a thinning domain.…
Differential Equations and A-quasiconvexity
A. C. Barroso, J. Matias, P. M. Santos
In this paper we extend to the abstract A-framework some existence theorems for differential inclusion problems with Dirichlet boundary conditions.
Optimal Design of Fractured Media with Prescribed Macroscopic Strain
José Matias, Marco Morandotti, Elvira Zappale
In this work we consider an optimal design problem for two-component fractured media for which a macroscopic strain is prescribed. Within the framework of structured deformations,…
Second-order structured deformations: relaxation, integral representation and applications
Ana Cristina Barroso, José Matias, Marco Morandotti +1
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submac…
Explicit Formulas for Relaxed Disarrangement Densities Arising from Structured Deformations
Ana Cristina Barroso, José Matias, Marco Morandotti +1
Structured deformations provide a multiscale geometry that captures the contributions at the macrolevel of both smooth geometrical changes and non-smooth geometrical changes (disar…
Homogenization problems in the Calculus of Variations: an overview
José Matias, Marco Morandotti
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundament…
Homogenization of functional with linear growth in the context of -quasiconvexity
José Matias, Marco Morandotti, Pedro M. Santos
This work deals with the homogenization of functionals with linear growth in the context of -quasiconvexity. A representation theorem is proved, where the new integran…