Displaying similar documents to “Measure-valued solutions of a heterogeneous Cahn-Hilliard system in elastic solids”

Unique global solvability of 1D Fried-Gurtin model

Zenon Kosowski (2007)

Applicationes Mathematicae

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We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified...

General method of regularization. III: The unilateral contact problem

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

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The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak* lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet....

Dynamics of shock waves in elastic-plastic solids

N. Favrie, S. Gavrilyuk (2011)

ESAIM: Proceedings

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The Maxwell type elastic-plastic solids are characterized by decaying the absolute values of the principal components of the deviatoric part of the stress tensor during the plastic relaxation step. We propose a mathematical formulation of such a model which is compatible with the von Mises criterion of plasticity. Numerical examples show the ability of the model to deal with complex physical phenomena.

Extended irreversible thermodynamics in hypoelasticity

Sebastiano Giambò, Annunziata Palumbo (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The constitutive equations of rate type for a class of thermo-hypo-elastic materials are derived within the framework of the extended irreversible thermodynamics.

A frictionless contact problem for elastic-viscoplastic materials with internal state variable

Lynda Selmani (2013)

Applicationes Mathematicae

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We study a mathematical model for frictionless contact between an elastic-viscoplastic body and a foundation. We model the material with a general elastic-viscoplastic constitutive law with internal state variable and the contact with a normal compliance condition. We derive a variational formulation of the model. We establish existence and uniqueness of a weak solution, using general results on first order nonlinear evolution equations with monotone operators and fixed point arguments....

Regularization of noncoercive constraints in Hencky plasticity

Jarosław L. Bojarski (2005)

Applicationes Mathematicae

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The aim of this paper is to find the largest lower semicontinuous minorant of the elastic-plastic energy of a body with fissures. The functional of energy considered is not coercive.

Extended irreversible thermodynamics in hypoelasticity

Sebastiano Giambò, Annunziata Palumbo (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

The constitutive equations of rate type for a class of thermo-hypo-elastic materials are derived within the framework of the extended irreversible thermodynamics.

Phase field model for mode III crack growth in two dimensional elasticity

Takeshi Takaishi, Masato Kimura (2009)

Kybernetika

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A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter ϵ > 0 and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method. ...