Articles in peer reviewed journals:


Gurtin, M.E.e J. Matias: Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces, Quaterly of Applied Mathematics, LIII, N4, 761-782, 1995.

Giga, Y., M.E.Gurtin e J.Matias:On the Dynamics of Crystalline motions,Japan journal of Industrial and Applied Mathematics, Vol 15, N1, 7-50,1998.

Barroso, A.C.e J. Matias: On a volume constrained variational problem in SBV2:part I, ESAIM/COCV/2002.

Barroso, A.C. e J.Matias:Necessary and sufficient conditions for existence of solutions of a variational problem involving the curl. 
Discrete and Continuous Dynamicals Systems, series A, Vol. 12, Nº 1, 87-114, 2005.

S. Bandyopadhyay, A.C.Barroso, B.Dacorogna and J.Matias,Differential
inclusions for differential forms, Calc. Var. and PDE's (2207) 28:449-469

Matias, J. Differential inclusions in SBV_0 and applications to the calculus of variations,Journal of Convex Analysis 14, nª 3, 2007.

Matias, J. Necessary and Sufficient conditions for existence of solutions of a Divergence-type problem, São Paulo J.Math.Sci. Vol.2 Nº 2, 2008.

A. C. Barroso e J. Matias, On an ill posed problem in $SBV_0^2(\Omega)$, 
Journal of Convex Analysis 17, Nº 2, 357-380, 2010.

J. Matias, Sufficient conditions for existence of solutions of a lower dimensional variational problem, São Paulo J.Math.Sci., Vol.5 Nº 1, 37-50, 2011.

M. Baía, J. Matias, P.M.Santos, A survey on structured deformations, São Paulo J.Math.Sci. Vol.5 Nº 2, 185 - 201, 2011.

M. Baía. A. C. Barroso, J. Matias, Singular perturbations for phase transitions, São Paulo J.Math.Sci. Vol. 6, Nº 2, 1-18, 2012.
 
Baía M., J. Matias e P.M. Santos, A relaxation result in the framework of structured deformations in a bounded variation setting, Proc. Royal Soc. Edinburgh, 142A, 239-271, 2012.

M. Baía, A. C. Barroso, M. Chermisi e J. Matias, Coupled second order singular perturbations for phase transitions, Nonlinearity 26, 1271-1311, 2013.

M. Baía. M. Chermisi, J. Matias e P. M. Santos, Lower semicontinuity and relaxation of signed functionals with linear growth in the context of A-quasiconvexity, Calc. Var. and PDE's, 47, 465-498, 2013.

M. Baía, J. Matias e P. M. Santos, Characterization of generalized Young measures in the context of A-quasiconvexity and application to lower semicontinuity, Indiana U. Mathematics Journal, 2013. 

Matias, J. e Pedro M. Santos, A dimension reduction result in the framework of structured deformations, Appl. Math Optim  69:, 459–485, 2014

J. Matias, M. Morandotti, P. M. Santos, Homogenization of functionals with linear growth in the context of A-quasiconvexity, Appl. Math Optim.  72,  issue 3, 523-547, 2015 Preprint

J. Matias, M. Morandotti, Homogenization problems in the calculus of variations: an overview. Preprint
Accepted for publication in São Paulo J.Math.Sci.

Ana C. Barroso, J. Matias, M. Morandotti, David R. Owen: Explicit Formulas for Relaxed Disarrangement Densities Arising from
Structured Deformations. Math. Mech. Complex Syst., 5(2):163-189, 2017 Preprint

J. Matias, M. Morandotti, E. Zappalle: Optimal Design of Fractured Media with Prescribed Macroscopic Strain. Journal of Mathematical Analysis and Applications, 449:1094-1132, 2017.​ Preprint


M. Baía, Ana C. Barroso, J. Matias: A model for phase transitions with competing terms. Accepted for publication in Quaterly Journal of Mathematics Preprint


Ana C. Barroso, J. Matias, P. M. Santos: Differential inclusions and A-quasiconvexity. Accepted for publication in Mediterranean Jornal of Mathematics. Preprint
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Ana C. Barroso, J. Matias, M. Morandotti, D. Owen: Second Order Structured Deformations: Relaxation, Integral Representation and Applications. Arch. Rational Mech. Anal. 225:1025-1072, 2017. Preprint.


J. Matias, Structured Deformations in Composite Media, Proceedings of the
XXIII Conference of AIMETA, (2017) page 1018.

Graça Carita, José Matias, Marco Morandotti, and David R. Owen: Dimension reduction in the context of structured deformations. arXiv:1709.02869. J. Elasticity. 2018


José Matias, M. Morandotti, D.  R. Owen, E. Zappale. Upscaling and spatial localization of non-local energies with applications to crystal plasticity.  Mathematics and Mechanics of Solids.e 20212
2202 
deformations with
Ana Cristina Barroso, José Matias and Elvira Zappale: ​Relaxation for an optimal design problem in BD(Omega)   2022 Proc. Royal Soc. Edinburgh A (2022)


Amar, M. J. Matias, M. Morandotti and E. Zappale, Periodic homogenization in the context of structured deformations, ZAMP 73 N. 173 (2022)

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Barroso, A. C. , J. Matias, M. Morandotti, D.R. Owen and E. Zappale, The Variational Modelling of Hierarchical Structured Deformations, J. Elasticity (2022)
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BOOKS

J.Matias, M. Morandotti & D. R. Owen, Structured Deformations, A Multiscale Geometrical Basis for Variational Problems in Continuum Mechanics, Springer Briefs on PDEs and Data Science. To be published in March 2023
al Soc