A note on crack propagation paths inside elastic bodies

DOI10.1016/j.aml.2017.11.023zbMath1458.74127OpenAlexW2774104404MaRDI QIDQ1996382

Alexandr Mikhailovich Khludnev, Viktor Shcherbakov

Publication date: 4 March 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2017.11.023

zbMATH Keywords

regularityBesov spacevariational inequalityenergy release rateGriffith energy criterion

Mathematics Subject Classification ID

Variational inequalities (49J40) PDEs in connection with fluid mechanics (35Q35) Classical linear elasticity (74B05) Anisotropy in solid mechanics (74E10) Brittle fracture (74R10) Regularity of solutions of equilibrium problems in solid mechanics (74G40)

Related Items (12)

Equilibrium problem for a Timoshenko plate with a geometrically nonlinear condition of nonpenetration for a vertical crack ⋮ Optimal control of a thin rigid stiffener for a model describing equilibrium of a Timoshenko plate with a crack ⋮ Shape derivative for penalty-constrained nonsmooth-nonconvex optimization: cohesive crack problem ⋮ The Boussinesq flat-punch indentation problem within the context of linearized viscoelasticity ⋮ Equilibrium problem for an inhomogeneous two-dimensional elastic body with two interacting thin rigid inclusions ⋮ Equilibrium problem for an thermoelastic Kirchhoff-Love plate with a nonpenetration condition for known configurations of crack edges ⋮ First-order shape derivative of the energy for elastic plates with rigid inclusions and interfacial cracks ⋮ Equilibrium problems for Kirchhoff–Love plates with nonpenetration conditions for known configurations of crack edges ⋮ Optimal location of a thin rigid inclusion for a problem describing equilibrium of a composite Timoshenko plate with a crack ⋮ Fictitious Domain Method for Equilibrium Problems of the Kirchhoff-Love Plates with Nonpenetration Conditions for Known Configurations of Plate Edges ⋮ Crack growth by vanishing viscosity in planar elasticity ⋮ On the connection between two equilibrium problems for cracked bodies in the cases of thin and volume rigid inclusions

Cites Work

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• Energy release rate and stress intensity factor in antiplane elasticity
• Shape sensitivity of curvilinear cracks on interface to nonlinear perturbations
• Griffith formulae for elasticity systems with unilateral conditions in domains with cracks
• On crack propagation shapes in elastic bodies
• Computational aspects of quasi-static crack propagation
• Primal–dual methods of shape sensitivity analysis for curvilinear cracks with nonpenetration
• ON THE INVISCID LIMIT OF A MODEL FOR CRACK PROPAGATION
• Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints
• Differentiation of Energy Functionals in Two-Dimensional Elasticity Theory for Solids with Curvilinear Cracks
• VI. The phenomena of rupture and flow in solids

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