Related papers: FeynKrack: A continuum model for quasi-brittle dam…
We present a continuum theory which predicts the steady state propagation of cracks. The theory overcomes the usual problem of a finite time cusp singularity of the Grinfeld instability by the inclusion of elastodynamic effects which…
In this study, the crack propagation of the pre-cracked mono-crystal nickel with the voids and inclusions has been investigated by molecular dynamics simulations. Different sizes of voids, inclusions and materials of inclusions are used to…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…
Computational solid mechanics has become an indispensable approach in engineering, and numerical investigation of fracture in composites is essential as composites are widely used in structural applications. Crack evolution in composites is…
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general types of model, corresponding to whether the reference process…
We develop a cut finite element method (CutFEM) for convection-diffusion problems posed on mixed-dimensional domains, i.e., unions of manifolds of different dimensions arranged in a hierarchical structure where lower-dimensional components…
In this study, we introduce a novel stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm…
Magma-driven fractures are the main mechanism for magma emplacement in the crust. A fundamental question is how the released fluid controls the propagation dynamics and fracture geometry (depth and breadth) in three dimensions. Analog…
Understanding crack tip - dislocation interaction is critical for improving the fracture resistance of semi-brittle materials like room-temperature plastically deformable ceramics. Here, we use a modified double cleavage drilled compression…
This study suggests a fast computational method for crack propagation, which is based on the extended finite element method (X-FEM). It is well known that the X-FEM might be the most popular numerical method for crack propagation. However,…
Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fracture…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
The complete lack of theoretical understanding of the quantum critical states found in the heavy fermion metals and the normal states of the high-T$_c$ superconductors is routed in deep fundamental problem of condensed matter physics: the…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
We present a novel image-based adaptive domain decomposition FEM framework to accelerate the solution of continuum damage mechanics problems. The key idea is to use image-processing techniques in order to identify the moving interface…
In this study, we address damage initiation and micro-crack formation in ductile failure of polycrystalline metals. We show how our recently published thermodynamic framework for ductile phase-field fracture of single crystals can be…
In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in material microstructures, and to provide statistic metrics…
In this paper we derive a new two-dimensional brittle fracture model for thin shells via dimension reduction, where the admissible displacements are only normal to the shell surface. The main steps include to endow the shell with a small…
We develop a new simulation method for multidimensional diffusions with sticky boundaries. The challenge comes from simulating the sticky boundary behavior, for which standard methods like the Euler scheme fail. We approximate the sticky…
Crackling dynamics is characterized by a release of incoming energy through intermittent avalanches. The shape, i.e. the internal temporal structure of these avalanches, gives insightful information about the physical processes involved. It…