Displaying similar documents to “Numerical approach to a rate-independent model of decohesion in laminated composites”

Reliable numerical modelling of malaria propagation

István Faragó, Miklós Emil Mincsovics, Rahele Mosleh (2018)

Applications of Mathematics

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We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should preserve the basic qualitative properties of the original phenomenon. Our main goal is to give the conditions for the discrete (numerical) models of the malaria phenomena under which they possess some given qualitative property, namely, to be between zero and one. The conditions which guarantee this requirement are related to the time-discretization...

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...

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. ...