Displaying similar documents to “A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates”

Material constraints in continuum mechanics

Stuart S. Antman (1981)

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

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Si dimostra che ci sono valide ragioni per considerare la teoria standard dei vincoli interni, nella meccanica dei continui, insufficientemente generale. In particolare, con l’unica eccezione dell’iperelasticità, l’extra-stress dovrebbe dipendere anche dai moltiplicatori di Lagrange, cioè, dallo stress che non effettua lavoro (virtuale).

Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics

Xavier Blanc, Claude Le Bris, Frédéric Legoll (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones...

Molecular modelling of stresses and deformations in nanostructured materials

Gwidon Szefer (2004)

International Journal of Applied Mathematics and Computer Science

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A molecular dynamics approach to the deformation and stress analysis in structured materials is presented. A new deformation measure for a lumped mass system of points is proposed. In full consistency with the continuum mechanical description, three kinds of stress tensors for the discrete system of atoms are defined. A computer simulation for a set of 10^5 atoms forming a sheet undergoing tension (Case 1) and contraction (Case 2) is given. Characteristic microstress distributions evoked...

A study of a unilateral and adhesive contact problem with normal compliance

Arezki Touzaline (2014)

Applicationes Mathematicae

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The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational...

Unilateral contact applications using FEM software

M. Stavroulaki, G. Stavroulakis (2002)

International Journal of Applied Mathematics and Computer Science

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Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with...

The role of Mechanics in Tumor growth : Modelling and Simulation

D. Ambrosi (2011)

ESAIM: Proceedings

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A number of biological phenomena are interlaced with classical mechanics. In this review are illustrated two examples from tumor growth, namely the formation of primordial networks of vessels (vasculogenesis) and the avascular phase of solid tumors. In both cases the formalism of continuum mechanics, accompanied by accurate numerical simulations, are able to shed light on biological controversies. The converse is also true: non-standard mechanical problems suggest new challenging mathematical...