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On some viscoelastic models

Pasquale Renno (1983)

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

Sia ℬ n un sistema linearmente viscoelastico, omogeneo ed isotropo, caratterizzato dalla funzione di memoria g n ⁢ ( t ) = ∑ k = 1 n B k ⁢ exp ⁡ ( - β k ⁢ t ) , tipica di numerosi polimeri solidi. Si dimostra che la soluzione fondamentale E n dell’operatore integrodifferenziale che descrive i moti di ℬ n è, in ogni punto del suo supporto, maggiorata da quella relativa ad un opportuno solido standard ℬ 1 Di conseguenza, è possibile applicare all’analisi qualitativa dei moti di ℬ n alcuni risultati stabiliti in [10], quali proprietà asintotiche, principi...

On symmetrically growing bodies.

Reuven Segev (1997)

Extracta Mathematicae

This work presents a setting for the formulation of the mechanics of growing bodies. By the mechanics of growing bodies we mean a theory in which the material structure of the body does not remain fixed. Material points may be added or removed from the body.

On the accuracy of Reissner–Mindlin plate model for stress boundary conditions

Sheng Zhang (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the...

On the analysis of elastic layers by a Fourier series, Green's function approach

Giorgio Novati (1987)

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

The plane strain elastic analysis of a homogeneous and isotropic layer of constant thickness, is formulated using Fourier series expansions in the direction parallel to the layer and suitable Green's functions in the transversal direction. For each frequency the unknown distributions of the Fourier coefficients relevant to the symmetric or skew-symmetric problems are governed by one-dimensional equations which can be solved exactly. The proposed method is used to critically discuss the "transfer"...

On the Asymptotic Analys of a Non-Symmetric Bar

Abderrazzak Majd (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the 3-D elasticity problem in the case of a non-symmetric heterogeneous rod. The asymptotic expansion of the solution is constructed. The coercitivity of the homogenized equation is proved. Estimates are derived for the difference between the truncated series and the exact solution.

On the Cauchy problem in linear viscoelasticity

Pasquale Renno (1983)

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

Con riferimento all’operatore integrodifferenziale della viscoelasticità lineare nella formulazione creep, si determina la soluzione fondamentale E in corrispondenza di un’arbitraria funzione di memoria. Di conseguenza viene risolto esplicitamente il problema di Cauchy relativo al moto unidimensionale di un sistema viscoelastico ℬ , omogeneo ed isotropo, determinato da dati iniziali e storia di stress comunque prefissati. Successivamente, nell’ambito di opportune ipotesi di memoria labile, si dimostrano...

On the change of energy caused by crack propagation in 3-dimensional anisotropic solids

Martin Steigemann, Maria Specovius-Neugebauer (2014)

Mathematica Bohemica

Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a...

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