A Density Result in Two-Dimensional Linearized Elasticity, and Applications

By Antonin Chambolle. 2003

168 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d001abef26d5f0528a430babbe9602e20bf20065

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In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

An adaptive finite element approximation of a generalized Ambrosio-Tortorelli functional (2013, background): “[17] A. Chambolle, A density result in two-dimensional linearized elasticity, and applications, Arch.”
Compactness and lower semicontinuity in $GSBD$ (2018, background): “Another possible assumption is, in 2d, that the crack set K be connected [22, 10].”
Existence results for energetic models for rate-independent systems (2005, methodology): “To avoid confusion with the notations in [ Cha03 ] we denote our energy functional by”
Existence and convergence for quasi‐static evolution in brittle fracture (2003, unknown): “This was immediately followed by the work of A. Chambolle [ 8 ] who tackled the planar elasticity setting under the same restrictive assumptions.”
Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, background): “In fact, for models in damage and fracture, see [9], [12], [15], [16], [22], it is desirable to avoid all di¤erentiable structures, i.”
Structural optimization using sensitivity analysis and a level-set method (2004, background): “We also consider the case of a nonlinear elasticity model.”
Quasistatic Crack Growth in Nonlinear Elasticity (2005, background): “These results were extended to the case of planar linear elasticity by Chambolle in [7].”
MULTI-PHASE STRUCTURAL OPTIMIZATION VIA A LEVEL SET METHOD ∗, ∗∗ (2014, background): “, on the measure of the interface Γ [8], or a constraint on the regularity of admissible shapes [16] or on their maximum number of ‘holes’ [14, 48]).”
Quasi-static crack growth for a cohesive zone model with prescribed crack path (2005, methodology): “For this reason we cannot apply directly the tools developed so far in the applications to fracture mechanics of the theory of free discontinuity problems (see [10], [5], [6], [1], [9], [3], [4]).”
A level-set method for vibration and multiple loads structural optimization (2005, background): “Actually the existence of local minima has been rigorously proved in 2-d by Chambolle [15] since he proved that, for any fixed maximal number of holes N , there exists an optimal shape within the class of shapes with fewer holes than N (and we know in some instances that increasing N strictly decrea”
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments (2009, background): “Proofs of existence of solutions and convergence of the time-discrete quasi-static evolution are available for antiplane linear elasticity (Dal Maso and Toader, 2002; Francfort and Larsen, 2003) and for general linear (Chambolle, 2003) and non-linear (Dal Maso et al.”
The Variational Approach to Fracture (2008, background): “result for the strong variational evolution is obtained in [41] in the quadratic case and in [28] in the case of linearized elasticity.”
A Γ-Convergence Approach to Stability of Unilateral Minimality Properties in Fracture Mechanics and Applications (2006, background): “1 also holds in the following discretized in time version, which is closer in spirit to the approach of Francfort and Marigo [22] to quasistatic crack propagation, and of the subsequent papers on the subject ([1], [16], [18], [19], [21], [23] and [24]).”
A level-set method for shape optimization (2002, background): “Let us simply mention that the existence theory for (4) is quite involved: it is well-known that, in general, (4) admits a minimizer only if some geometrical or topological restrictions on the shapes r enforced [6], [7].”