Journal•ISSN: 1081-2865
Mathematics and Mechanics of Solids
SAGE Publishing
About: Mathematics and Mechanics of Solids is an academic journal published by SAGE Publishing. The journal publishes majorly in the area(s): Boundary value problem & Isotropy. It has an ISSN identifier of 1081-2865. Over the lifetime, 1803 publications have been published receiving 22692 citations. The journal is also known as: MMS.
Topics: Boundary value problem, Isotropy, Nonlinear system, Constitutive equation, Elasticity (economics)
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TL;DR: In this article, a third gradient theory has been proposed to describe the homogenized energy associated with a microscopic structure using pantographic-type structures, where the deformation energies involve combinations of nodal displacements in the form of second-order or third-order finite differences.
Abstract: Until now, no third gradient theory has been proposed to describe the homogenized energy associated with a microscopic structure. In this paper, we prove that this is possible using pantographic-type structures. Their deformation energies involve combinations of nodal displacements havin the form of second-order or third-order finite differences. We establish the Gamma convergence of these energies to second and third gradient functionals. Some mechanical examples are provided so as to illustrate the special features of these homogenized models.
441 citations
TL;DR: Gabrio Piola's scientific papers have been underestimated in mathematical physics literature as mentioned in this paper, but a careful reading of them proves that they are original, deep and far-reaching, and even even...
Abstract: Gabrio Piola’s scientific papers have been underestimated in mathematical physics literature. Indeed, a careful reading of them proves that they are original, deep and far-reaching. Actually, even ...
362 citations
TL;DR: In this article, two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained.
Abstract: Two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained, uniqueness an...
300 citations
TL;DR: A review of the state of the art in the study of mechanical metamaterials is given in this article, where the very attractive property of having a microstructure capable of determining exotic and specific properties is discussed.
Abstract: In this paper, we give a review of the state of the art in the study of mechanical metamaterials. The very attractive property of having a microstructure capable of determining exotic and specifica...
266 citations
TL;DR: In this article, generalizations to anisotropic conditions of the invariants of the deviatoric stress are proposed within the framework of the theory of representation, using these generalized invariants, any isotropic yield criterion can be extended such as to describe any type of material symmetry.
Abstract: Within the framework of the theory of representation, generalizations to anisotropic conditions of the invariants of the deviatoric stress are proposed. Using these generalized invariants, any isotropic yield criterion can be extended such as to describe any type of material symmetry. In this paper, we apply this method to extend to orthotropy Drucker's isotropic criterion. Comparison with data on aluminum alloys show that this new criterion describes with improved accuracy the anisotropy of the plastic response.
264 citations