Interior-point methods for the phase-field approach to brittle and ductile fracture

Wambacq, Jef; Ulloa, Jacinto; Lombaert, Geert; François, Stijn

doi:10.1016/j.cma.2020.113612

Cited by 44 publications

(29 citation statements)

References 71 publications

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“…The main challenge in solving this evolution problem lies on imposing the irreversibility condition d ≥ d n , which allows to replace the set-valued expressions (44) or (46) by equalities. Several alternatives are available in the literature to tackle this problem, including simple penalization methods [92], augmented Lagrangian penalization [93], the primal-dual active set method [94], interior point methods [95], and the complementary system with Lagrange multipliers [96]. In this work, we employ the maximum crackdriving state function method based on the history field, as outlined in [53,97] and related works.…”

Section: Fracturementioning

confidence: 99%

Bayesian inversion for unified ductile phase-field fracture

et al. 2021

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The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the $$\hat{R}{-}convergence$$ R ^ - c o n v e r g e n c e tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

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Section: Fracturementioning

confidence: 99%

Bayesian inversion for unified ductile phase-field fracture

et al. 2021

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“…As students master the key steps of a structural analysis, they easily customize and extend the Stabil toolbox for their specific problems. This has resulted in a variety of applications, ranging from uncertainty quantification in structural dynamics [41], optimization of frame structures [40,46], geotechnical applications such as dynamic soil‐structure interaction [16,31] and modeling of grouted anchors in soils [43], to phase‐field modeling of brittle and ductile fracture [44,47].…”

Section: The Use Of Stabil Throughout the Curriculummentioning

confidence: 99%

Stabil: An educational Matlab toolbox for static and dynamic structural analysis

François

Schevenels

Dooms

et al. 2021

Comp Applic In Engineering

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The capability to analyze structures under static and dynamic loads is an essential skill for structural engineers. Structural analysis therefore is a key component in civil and architectural engineering education, where analytical methods are traditionally complemented by the use of (commercial) software packages. The latter are often closed source, which may obscure the links to the underlying matrix structural analysis or finite element formulation. To stimulate active, cooperative, and solution‐oriented learning, we developed Stabil, an electronic learning environment implemented as a Matlab toolbox. Stabil has an open structure to elucidate the links between theory and implementation and is presently used throughout the curricula of Civil and Architectural Engineering at KU Leuven. This paper explains the main principles of Stabil and discusses teaching experiences over the past 15 years. Stabil can be downloaded from http://bwk.kuleuven.be/bwm/stabil.

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“…The example of the single-edge notched specimen was originally proposed by Bourdin et al, 53 and was later adopted as a benchmark problem by many authors. 2,3,5,6,[8][9][10][11][12][13]32,35,39 In this example, a square specimen with sides of 1 mm and a pre-existing notch is considered (Figure 1). The bottom edge remains completely fixed, while a vertical load is imposed on the top edge.…”

Section: Single-edge Notched Specimen Subject To Tensionmentioning

confidence: 99%

“…In order to capture the post-peak response of solids and structures, most studies on the phase-field approach to quasi-static fracture [1][2][3][4][5][6][7][8][9][10][11][12][13] rely on displacement-controlled simulations. As such, simulations involving solids loaded by external forces are precluded, and snap-backs in the post-peak regime of the equilibrium path cannot be captured.…”

Section: Introductionmentioning

confidence: 99%

“…In order to control the energy dissipated in both mechanisms, the evolution equations of damage and plasticity must be solved simultaneously. Therefore, this article presents an extension of the monolithic scheme for brittle and ductile fracture proposed by Wambacq et al 13 to include a dissipation‐based path‐following constraint that accounts for both plastic and damage dissipation. As such, an equilibrium path with a continuous increase of dissipated energy is followed, ensuring energy balance and avoiding time‐discontinuous jumps and brutal crack propagation, which is expected to result in a more robust monolithic scheme.…”

Section: Introductionmentioning

confidence: 99%

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A dissipation‐based path‐following technique for the phase‐field approach to brittle and ductile fracture

Wambacq

Ulloa

Lombaert

et al. 2021

Numerical Meth Engineering

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This article presents a dissipation-based path-following technique for the phase-field approach to brittle and ductile fracture. This technique allows computing the post-peak response of solids loaded by external forces and snap-backs in the softening stage. By controlling the dissipated energy during loading, the solid is prevented from unloading elastically, and an equilibrium branch with a continuous increase of dissipated energy is followed. Because solids can dissipate in both tension and compression, a discontinuous equilibrium path can be obtained. To avoid this occurrence, two novel techniques are presented, which ensure a continuous equilibrium path for which the solid is either in tension or compression. In addition, the thermodynamic constraints present in the phase-field model are rigorously solved using an interior-point method.In order to allow for simultaneous dissipation due to both plastic and damage mechanisms, the governing equations are solved monolithically. The presented method is tested on four benchmark problems, and it is observed that by tracing snap-backs, time-discontinuous evolutions are avoided, which restores energy balance and enhances the convergence of the monolithic scheme.

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Interior-point methods for the phase-field approach to brittle and ductile fracture

Cited by 44 publications

References 71 publications

Bayesian inversion for unified ductile phase-field fracture

Bayesian inversion for unified ductile phase-field fracture

Stabil: An educational Matlab toolbox for static and dynamic structural analysis

A dissipation‐based path‐following technique for the phase‐field approach to brittle and ductile fracture

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