Book ChapterDOI
Applications in continuum mechanics and physics of solids
Alexander Mielke,Tomáš Roubíček,Tomáš Roubíček +2 more
- pp 235-458
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TLDR
The theory of rate-independent processes has a large variety of applications in continuum mechanics of solids as mentioned in this paper, and rate independent effects typically can occur inside the bulk and at the surface or along interfaces.Abstract:
The theory of rate-independent processes has a large variety of applications in continuum mechanics of solids. Rate-independent effects typically can occur inside the bulk and at the surface or along interfaces. These effects may be unidirectional, as, for example, in damage, or bidirectional. In case of a deformable continuum, one can consider the general concept of large strains or confine oneself to small strains. There might be rate-independent processes on lower-dimensional objects, typically surfaces of codimension 1 or lines (as dislocations) of dimension 1. See Table 4.1 on p. 236 for examples that will be considered in this chapter. Of course, various processes can combine with each other.read more
Citations
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Rate-independent damage processes in nonlinear elasticity
TL;DR: In this article, an elastic body undergoing large deformations by a "hard-device" loading possibly combined with an impact (modeled by a unilateral frictionless contact) of another, ideally rigid body is formulated as an activated, rate-independent process.
A self consistent generalized model for the calculation of minor loop excursions in the theory of hysteresis
TL;DR: In this paper, a generalization of the theory of hysteresis to cover asymmetric or minor loop excursions is presented. But the model presented is completely self-consistent with the original formulation and requires no additional parameters to describe the minor loops.
Crack growth in polyconvex materials
TL;DR: In this paper, a model for crack propagation in an elastic body, where the crack path is described a priori, is presented, and the model is formulated in terms of the Clarke differential of the energy, generalizing the classical crack evolution models for elasticity with strictly convex energies.
Posted Content
Quasistatic evolution problems for linearly elastic - perfectly plastic materials
TL;DR: In this article, the authors studied the problem of quasistatic evolution in small strain associative elastoplasticity in the framework of the variational theory for rate-independent processes.
Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints
Dorothee Knees,Andreas Schroeder +1 more
TL;DR: In this article, a global higher differentiability result in Besov spaces is proved for the displacement fields of linear elastic models with self contact, where nonpenetration conditions/Signorini conditions are imposed on the crack faces.
References
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Journal ArticleDOI
The Phenomena of Rupture and Flow in Solids
TL;DR: In this article, the authors investigated the effect of surface scratches on the mechanical strength of solids, and some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion.
Book
Functions of Bounded Variation and Free Discontinuity Problems
TL;DR: The Mumford-Shah functional minimiser of free continuity problems as mentioned in this paper is a special function of the Mumfordshah functional and has been shown to be a function of free discontinuity set.
Book
Navier-Stokes Equations
TL;DR: Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.
Book ChapterDOI
Mixed mode cracking in layered materials
John W. Hutchinson,Zhigang Suo +1 more
TL;DR: In this article, the authors describe the mixed mode cracking in layered materials and elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness, showing that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip.
Journal ArticleDOI
Elastic materials with couple-stresses
TL;DR: HAL as discussed by the authors is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.