Detecting Rigid Inclusions, or Cavities, in an Elastic Body

Morassi, Antonino; Rosset, Edi

doi:10.1023/b:elas.0000029955.79981.1d

Cited by 35 publications

(26 citation statements)

References 20 publications

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“…If we have no crack g on X, relations (4)-(6) should be omitted. This specific problem formulation for the particular case F ¼ 0 in o can be found in Morassi and Rosset (2003). The problem formulation with the crack and nonpenetration conditions seem to be new.…”

Section: Problem Formulationmentioning

confidence: 99%

Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

Khludnev

Novotny

Sokołowski

et al. 2009

Journal of the Mechanics and Physics of Solids

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a b s t r a c tWe consider an elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that nonpenetration conditions are imposed at the crack faces which do not allow the opposite crack faces to penetrate each other. We analyze the variational formulation of the problem and provide shape and topology sensitivity analysis of the solution in two and three spatial dimensions. The differentiability of the energy with respect to the crack length, for the crack located at the boundary of rigid inclusion, is established.

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Section: Problem Formulationmentioning

confidence: 99%

Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

Khludnev

Novotny

Sokołowski

et al. 2009

Journal of the Mechanics and Physics of Solids

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“…Let us observe, however, that also the extreme cases, when D is totally rigid or represents a cavity, are of great interest, and size estimates for such cases have indeed been obtained in [MR02]. We refer also to [AMR03] for an overview of all such results, in both the electrical and elastic settings.…”

Section: Introductionmentioning

confidence: 99%

Detecting an Inclusion in an Elastic Body by Boundary Measurements

Alessandrini¹,

Morassi²,

Rosset³

2004

SIAM Rev.

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“…By (12), we conclude that v = ρ 0 ∈ R(ω). Convergence (14) allows us to pass to the limit in (9), (10). Indeed, let us takē v ∈ R(ω) in (10) as a test function.…”

Section: Limit Problem As δ →mentioning

confidence: 99%

On crack problem with overlapping domain

Khludnev

2008

Z Angew Math Mech

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Key words Crack with non-penetration, derivative of energy functional, Griffith criterion, overlapping domain. MSC (2000) 49J40, 49K10, 49Q10, 74R10Overlapping domain problem describing an equilibrium state for two elastic bodies with a crack is analyzed. Nonlinear boundary conditions are considered providing a mutual non-penetration between the crack faces. We prove a solution existence for the problem with suitable boundary conditions imposed at a glue set. The main interest of the paper is the derivative of the energy functional with respect to the crack length. Assuming the rigidity of the second body is increasing to infinity a convergence in the formula for the derivative of energy functionals is established.

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Detecting Rigid Inclusions, or Cavities, in an Elastic Body

Cited by 35 publications

References 20 publications

Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

Detecting an Inclusion in an Elastic Body by Boundary Measurements

On crack problem with overlapping domain

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