Hellinger-Reissner variational principle for stress gradient elastic bodies with embedded coherent interfaces

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Abstract

An Hellinger-Reissner (H-R) variational principle is proposed for stress gradient elasticity material models. Stress gradient elasticity is an emerging branch of non-simple constitutive elastic models where the infinitesimal strain tensor is linearly related to the Cauchy stress tensor and to its Laplacian. The H-R principle here proposed is particularized for a solid composed by several sub-domains connected by coherent interfaces, that is interfaces across the which both displacement and traction vectors are continuous. In view of possible stress-based finite element applications, a reduced form of the H-R principle is also proposed in which the field linear momentum balance equations are satisfied a-priori, the continuity condition of the displacements across the interfaces is relaxed and the analogous continuity condition of the traction is enforced as a side condition.
Original languageEnglish
Publication statusPublished - 2017

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Tensors
Elasticity
Momentum

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Mechanics of Materials

Cite this

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title = "Hellinger-Reissner variational principle for stress gradient elastic bodies with embedded coherent interfaces",
abstract = "An Hellinger-Reissner (H-R) variational principle is proposed for stress gradient elasticity material models. Stress gradient elasticity is an emerging branch of non-simple constitutive elastic models where the infinitesimal strain tensor is linearly related to the Cauchy stress tensor and to its Laplacian. The H-R principle here proposed is particularized for a solid composed by several sub-domains connected by coherent interfaces, that is interfaces across the which both displacement and traction vectors are continuous. In view of possible stress-based finite element applications, a reduced form of the H-R principle is also proposed in which the field linear momentum balance equations are satisfied a-priori, the continuity condition of the displacements across the interfaces is relaxed and the analogous continuity condition of the traction is enforced as a side condition.",
keywords = "HR Variational Principle, Stress gradient elasticity, coherent interfaces",
author = "Guido Borino and Francesco Parrinello and Castrenze Polizzotto",
year = "2017",
language = "English",

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TY - CONF

T1 - Hellinger-Reissner variational principle for stress gradient elastic bodies with embedded coherent interfaces

AU - Borino, Guido

AU - Parrinello, Francesco

AU - Polizzotto, Castrenze

PY - 2017

Y1 - 2017

N2 - An Hellinger-Reissner (H-R) variational principle is proposed for stress gradient elasticity material models. Stress gradient elasticity is an emerging branch of non-simple constitutive elastic models where the infinitesimal strain tensor is linearly related to the Cauchy stress tensor and to its Laplacian. The H-R principle here proposed is particularized for a solid composed by several sub-domains connected by coherent interfaces, that is interfaces across the which both displacement and traction vectors are continuous. In view of possible stress-based finite element applications, a reduced form of the H-R principle is also proposed in which the field linear momentum balance equations are satisfied a-priori, the continuity condition of the displacements across the interfaces is relaxed and the analogous continuity condition of the traction is enforced as a side condition.

AB - An Hellinger-Reissner (H-R) variational principle is proposed for stress gradient elasticity material models. Stress gradient elasticity is an emerging branch of non-simple constitutive elastic models where the infinitesimal strain tensor is linearly related to the Cauchy stress tensor and to its Laplacian. The H-R principle here proposed is particularized for a solid composed by several sub-domains connected by coherent interfaces, that is interfaces across the which both displacement and traction vectors are continuous. In view of possible stress-based finite element applications, a reduced form of the H-R principle is also proposed in which the field linear momentum balance equations are satisfied a-priori, the continuity condition of the displacements across the interfaces is relaxed and the analogous continuity condition of the traction is enforced as a side condition.

KW - HR Variational Principle, Stress gradient elasticity, coherent interfaces

UR - http://hdl.handle.net/10447/263388

UR - http://www.aimeta2017.unisa.it/node/52

M3 - Paper

ER -