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In this manuscript, the phase-field fracture irreversibility constraint is transformed into an equality-based constraint using the slack variable approach. The equality-based fracture irreversibility constraint is then introduced in the…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…
In traditional phase-field modeling of multiphase materials, a significant challenge arises from the non-local nature of fracture energy regularization, where interfacial toughness is inherently coupled with the properties of the…
A crucial aspect in phase-field modeling, based on the variational formulation of brittle fracture, is the accurate representation of how the fracture surface energy is dissipated during the fracture process in the energy competition within…
In a probabilistic latent variable model, factorized (or mean-field) variational inference (F-VI) fits a separate parametric distribution for each latent variable. Amortized variational inference (A-VI) instead learns a common inference…
Recent years have seen a significant interest in using phase field approaches to model hydraulic fracture, so as to optimise a process that is key to industries such as petroleum engineering, mining and geothermal energy extraction. Here,…
As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable…
Ti-6Al-4V is a titanium alloy with excellent properties for lightweight applications and its production through Additive Manufacturing processes is attractive for different industrial sectors. In this work, the influence of mechanical…
We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…
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…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
In this contribution, a variational diffuse modeling framework for cracks in heterogeneous media is presented. A static order parameter smoothly bridges the discontinuity at material interfaces, while an evolving phase-field captures the…
In recent decades, the study of fracture propagation in solids has increasingly relied on phase-field models. Several recent contributions have highlighted the potential of this approach in both static and dynamic frameworks. However, a…
In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a global-local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In the surrounding medium, a simplified and…
Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While…
Variational inference is a fast and scalable alternative to Markov chain Monte Carlo and has been widely applied to posterior inference tasks in statistics and machine learning. A traditional approach for implementing mean-field variational…
Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be…
In this work, a Bayesian inversion framework for hydraulic phase-field transversely isotropic and orthotropy anisotropic fracture is proposed. Therein, three primary fields are pressure, displacements, and phase-field while…
We present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws…