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Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family.…
This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack…
In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance…
The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a…
We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between…
This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et…
The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith's criterion. This method requires a…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
This article proposes an open-source implementation of a phase-field model for brittle fracture using a recently developed finite element toolbox, Gridap in Julia. The present work exploits the advantages of both the phase-field model and…
In the hydraulic fracturing of natural rocks, understanding and predicting crack penetrations into the neighboring layers is crucial and relevant in terms of cost-efficiency in engineering and environmental protection. This study…
We present a new numerical approach for wave induced dynamic fracture. The method is based on a discontinuous Galerkin approximation of the first-order hyperbolic system for elastic waves and a phase-field approximation of brittle fracture…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
Current variational inference methods for hierarchical Bayesian nonparametric models can neither characterize the correlation structure among latent variables due to the mean-field setting, nor infer the true posterior dimension because of…
Variational phase-field methods have been shown powerful for the modeling of complex crack propagation without a priori knowledge of the crack path or ad hoc criteria. However, phase-field models suffer from their energy functional being…
The core principle of Variational Inference (VI) is to convert the statistical inference problem of computing complex posterior probability densities into a tractable optimization problem. This property enables VI to be faster than several…
This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…