65 research outputs found
Mesh adaptivity for quasi-static phase-field fractures based on a residual-type a posteriori error estimator
In this work, we consider adaptive mesh refinement for a monolithic
phase-field description for fractures in brittle materials. Our approach is
based on an a posteriori error estimator for the phase-field variational
inequality realizing the fracture irreversibility constraint. The key goal is
the development of a reliable and efficient residual-type error estimator for
the phase-field fracture model in each time-step. Based on this error
estimator, error indicators for local mesh adaptivity are extracted. The
proposed estimator is based on a technique known for singularly perturbed
equations in combination with estimators for variational inequalities. These
theoretical developments are used to formulate an adaptive mesh refinement
algorithm. For the numerical solution, the fracture irreversibility is imposed
using a Lagrange multiplier. The resulting saddle-point system has three
unknowns: displacements, phase-field, and a Lagrange multiplier for the crack
irreversibility. Several numerical experiments demonstrate our theoretical
findings with the newly developed estimators and the corresponding refinement
strategy.Comment: This is the preprint version of an accepted article to be published
in the GAMM-Mitteilungen 2019.
https://onlinelibrary.wiley.com/journal/1522260
An hp-adaptive discontinuous Galerkin method for phase field fracture
The phase field method is becoming the de facto choice for the numerical analysis of complex problems that involve multiple initiating, propagating, interacting, branching and merging fractures. However, within the context of finite element modelling, the method requires a fine mesh in regions where fractures will propagate, in order to capture sharp variations in the phase field representing the fractured/damaged regions. This means that the method can become computationally expensive when the fracture propagation paths are not known a priori. This paper presents a 2D -adaptive discontinuous Galerkin finite element method for phase field fracture that includes a posteriori error estimators for both the elasticity and phase field equations, which drive mesh adaptivity for static and propagating fractures. This combination means that it is possible to be reliably and efficiently solve phase field fracture problems with arbitrary initial meshes, irrespective of the initial geometry or loading conditions. This ability is demonstrated on several example problems, which are solved using a light-BFGS (BroydenâFletcherâGoldfarbâShanno) quasi-Newton algorithm. The examples highlight the importance of driving mesh adaptivity using both the elasticity and phase field errors for physically meaningful, yet computationally tractable, results. They also reveal the importance of including -refinement, which is typically not included in existing phase field literature. The above features provide a powerful and general tool for modelling fracture propagation with controlled errors and degree-of-freedom optimised meshes
Adaptive and Pressure-Robust Discretization of Incompressible Pressure-Driven Phase-Field Fracture
In this work, we consider pressurized phase-field fracture problems in nearly
and fully incompressible materials. To this end, a mixed form for the solid
equations is proposed. To enhance the accuracy of the spatial discretization, a
residual-type error estimator is developed. Our algorithmic advancements are
substantiated with several numerical tests that are inspired from benchmark
configurations. Therein, a primal-based formulation is compared to our newly
developed mixed phase-field fracture method for Poisson ratios approaching . Finally, for , we compare the numerical results of the
mixed formulation with a pressure robust modification
A posteriori estimator for the adaptive solution of a quasi-static fracture phase-field model with irreversibility constraints
Within this article, we develop a residual type a posteriori error estimator
for a time discrete quasi-static phase-field fracture model. Particular
emphasize is given to the robustness of the error estimator for the variational
inequality governing the phase-field evolution with respect to the phase-field
regularization parameter . The article concludes with numerical
examples highlighting the performance of the proposed a posteriori error
estimators on three standard test cases; the single edge notched tension and
shear test as well as the L-shaped panel test
Numerical Methods for Variational Phase-Field Fracture Problems
In these lectures notes, the variational phase-field approach for modeling fracture propagation is edited for the usage in classes and summer schools. Basic modeling is briefly reviewed first. The main emphasis is on the design of numerical methods. All algorithmic and theoretical advancements are illustrated with many examples and numerical tests.DFG/SPP1748/392587580/E
Phase-field fracture modeling, numerical solution, and simulations for compressible and incompressible solids
In this thesis, we develop phase-field fracture models for simulating fractures in compressible and incompressible solids. Classical (primal) phase-field fracture models fail due to locking effects. Hence, we formulate the elasticity part of the phase-field fracture problem in mixed form, avoiding locking. For the elasticity part in mixed form, we prove inf-sup stability, which allows a stable discretization with Taylor-Hood elements. We solve the resulting (3x3) phase-field fracture problem - a coupled variational inequality system - with a primal-dual active set method. In addition, we develop a physics-based Schur-type preconditioner for the linear solver to reduce the computational workload. We confirm the robustness of the new solver for five benchmark tests. Finally, we compare numerical simulations to experimental data analyzing fractures in punctured strips of ethylene propylene diene monomer rubber (EPDM) stretched until total failure to check the applicability on a real-world problem in nearly incompressible solids. Similar behavior of measurement data and the numerically computed quantities of interest validate the newly developed quasi-static phase-field fracture model
in mixed form.DFG/SPP 1748/392587580/E
A comparative review of peridynamics and phase-field models for engineering fracture mechanics
Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized. © 2022, The Author(s)
A comparative review of peridynamics and phase-field models for engineering fracture mechanics
Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized
A New Nodal Stress Recovery Technique in Finite Element Method Using Colliding Bodies Optimization Algorithm
In Finite Element Method (FEM), the stress components are calculated within the elements firstly, and then these components are recovered to the nodes. For the recovery process, there are several well-known methods in which the increase of their accuracy imposes additional costs into the problem. In this paper, a new nodal stress recovery technique is proposed in which Colliding Bodies Optimization (CBO) Algorithm fits an appropriative function for nodal stress fields. The CBO employs this function to compute the stress components in the nodal coordinates. Therefore, a particular model to stress fields and its components will be available. It can be considered as a connection between analytical approaches and numerical methods, providing benefits of both categories. Finally, the accuracy, efficiency, and applicability of the new technique are investigated employing three diverse examples
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