Convergence of alternate minimization schemes for phase-field fracture and damage
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Publication:4977918
DOI10.1142/S0218202517500312zbMath1376.49038MaRDI QIDQ4977918
Publication date: 17 August 2017
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
numerical exampledamagevanishing viscositymechanical propertiesphase-field fractureGriffith's criterionBV-evolutionalternate minimizationAmbrosio-Tortorelli energyconvergence of discretizations
Related Items (27)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Generalised functions of bounded deformation
- A density result for GSBD and its application to the approximation of brittle fracture energies
- Stress-driven local-solution approach to quasistatic brittle delamination
- Integrability of displacement and stresses in linear and nonlinear elasticity with mixed boundary conditions
- A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains
- An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems
- A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
- An introduction to \(\Gamma\)-convergence
- Numerical experiments in revisited brittle fracture
- Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures
- An approximation result for special functions with bounded deformation
- Rate-independent systems. Theory and application
- Numerical implementation of the variational formulation for quasi-static brittle fracture
- Balanced-Viscosity solutions for multi-rate systems
- Differential, Energetic, and Metric Formulations for Rate-Independent Processes
- Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics
- Linearly constrained evolutions of critical points and an application to cohesive fractures
- Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
- Thermodynamics of Rate-independent Processes in Viscous Solids at Small Strains
- BV solutions and viscosity approximations of rate-independent systems
- Damage of nonlinearly elastic materials at small strain - Existence and regularity results -
- EXISTENCE OF SOLUTIONS TO A REGULARIZED MODEL OF DYNAMIC FRACTURE
- Rate-independent processes in viscous solids at small strains
- A VANISHING VISCOSITY APPROACH TO A RATE-INDEPENDENT DAMAGE MODEL
- RATE-INDEPENDENT DAMAGE PROCESSES IN NONLINEAR ELASTICITY
- AN ADAPTIVE FINITE ELEMENT APPROXIMATION OF A GENERALIZED AMBROSIO–TORTORELLI FUNCTIONAL
- Stress-driven solution to rate-independent elasto-plasticity with damage at small strains and its computer implementation
- An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture
- Quasistatic adhesive contact of visco‐elastic bodies and its numerical treatment for very small viscosity
- On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms
- Direct methods in the calculus of variations
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