Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities
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Publication:2020933
DOI10.1016/j.cma.2020.113353zbMath1506.74351arXiv2005.01332OpenAlexW3080276208MaRDI QIDQ2020933
Publication date: 26 April 2021
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.01332
brittle fracturemultiple solutionsrandom perturbationYoung measurephase-field modelstochastic solution
Brittle fracture (74R10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stochastic and other probabilistic methods applied to problems in solid mechanics (74S60)
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Cites Work
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- Variational theory and computations in stochastic plasticity
- Regularized variational theories of fracture: a unified approach
- A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework
- Oscillations and concentrations in weak solutions of the incompressible fluid equations
- A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits
- Young-measure quasi-static damage evolution
- Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
- Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi
- The variational approach to fracture
- Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments
- The variational approach to fracture mechanics. A practical application to the French Panthéon in Paris
- A variational model for fracture mechanics: Numerical experiments
- Approximation of free-discontinuity problems
- Parametrized measures and variational principles
- Numerical experiments in revisited brittle fracture
- Large deformation shape uncertainty quantification in acoustic scattering
- Localization analysis of an energy-based fourth-order gradient plasticity model
- Statistical solutions of hyperbolic conservation laws: foundations
- An overview of the modelling of fracture by gradient damage models
- Validation simulations for the variational approach to fracture
- Optimal control problems with oscillations, concentrations and discontinuities
- An approximation result for special functions with bounded deformation
- Finite elements for stochastic media problems
- Revisiting brittle fracture as an energy minimization problem
- On penalization in variational phase-field models of brittle fracture
- A review on phase-field models of brittle fracture and a new fast hybrid formulation
- High-accuracy phase-field models for brittle fracture based on a new family of degradation functions
- Analysis of parametric models. Linear methods and approximations
- A line search assisted monolithic approach for phase-field computing of brittle fracture
- Rate-independent systems. Theory and application
- Construction of approximate entropy measure-valued solutions for hyperbolic systems of conservation laws
- Numerical implementation of the variational formulation for quasi-static brittle fracture
- Nonlinear functions of weak processes. I
- Introduction to Uncertainty Quantification
- Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- Tensor Algebras Over Hilbert Spaces. I
- Distributions in Hilbert Space and Canonical Systems of Operators
- Computation of measure-valued solutions for the incompressible Euler equations
- Optimization Problems With Concentration And Oscillation Effects: Relaxation Theory And Numerical Approximation
- Weak Lower Semicontinuity of Integral Functionals and Applications
- Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
- Numerical Approximation of Statistical Solutions of Scalar Conservation Laws
- Stochastic Optimization Methods
- Mathematical Methods in Continuum Mechanics of Solids
- Anisotropic Adaptive Meshes for Brittle Fractures: Parameter Sensitivity
- An Error-Oriented Newton/Inexact Augmented Lagrangian Approach for Fully Monolithic Phase-Field Fracture Propagation
- AN ADAPTIVE FINITE ELEMENT APPROXIMATION OF A GENERALIZED AMBROSIO–TORTORELLI FUNCTIONAL
- The variational formulation of brittle fracture: numerical implementation and extensions
- Inelastic Media under Uncertainty: Stochastic Models and Computational Approaches
- An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture
- Anisotropic Mesh Adaptation for Crack Detection In Brittle Materials
- QUASI-STATIC CRACK PROPAGATION BY GRIFFITH'S CRITERION
- On the computation of measure-valued solutions
- Young measure approximation in micromagnetics