Variational phase field fracture models are now widely used to simulate crack propagation in structures. A critical aspect of these simulations is the correct determination of the propagation threshold of pre-existing cracks, as it highly relies on how the initial cracks are implemented. While prior studies briefly discuss initial crack implementation techniques, we present here a systematic investigation. Various techniques to introduce initial cracks in phase field fracture simulations are tested, from the crack explicit meshing to the replacement by a fully damaged phase field, including different variants for the boundary conditions. Our focus here is on phase field models aiming to approximate, in the $\Gamma$-convergence limit, Griffith quasi-static propagation in the framework of Linear Elastic Fracture Mechanics. Therefore, a sharp crack model from classic linear elastic fracture mechanics based on Griffith criterion is the reference in this work. To assess the different techniques to introduce initial cracks, we rely on path-following methods to compute the sharp crack and the phase field smeared crack solutions. The underlying idea is that path-following ensures staying at equilibrium at each instant so that any difference between phase field and sharp crack models can be attributed to numerical artifacts. Thus, by comparing the results from both models, we can provide practical recommendations for reliably incorporating initial cracks in phase field fracture simulations. The comparison shows that an improper initial crack implementation often requires the smeared crack to transition to a one-element-wide phase band to adequately represent a displacement jump along a crack. This transition increases the energy required to propagate the crack, leading to a significant overshoot in the force-displacement response. The take-home message is that to predict the propagation threshold accurately and avoid artificial toughening; the crack must be initialized either setting the phase field to its damage state over a one-element-wide band or meshing the crack explicitly as a one-element-wide slit and imposing the fully cracked state on the crack surface.
Andrey Latyshev, Jérémy Bleyer, Corrado Maurini
et al.
Many problems in solid mechanics involve general and non-trivial constitutive models that are difficult to express in variational form. Consequently, it can be challenging to define these problems in automated finite element solvers, such as the FEniCS Project, that use domain-specific languages specifically designed for writing variational forms. In this article, we describe a methodology and software framework for FEniCSx / DOLFINx that enables the expression of constitutive models in nearly any general programming language. We demonstrate our approach on two solid mechanics problems; the first is a simple von Mises elastoplastic model with isotropic hardening implemented with Numba, and the second a Mohr-Coulomb elastoplastic model with apex smoothing implemented with JAX. In the latter case we show that by leveraging JAX's algorithmic automatic differentiation transformations we can avoid error-prone manual differentiation of the terms necessary to resolve the constitutive model. We show extensive numerical results, including Taylor remainder testing, that verify the correctness of our implementation. The software framework and fully documented examples are available as supplementary material under the LGPLv3 or later license.
In this article, we propose CE-Prompt, an enhanced version of Prompt-Tuning designed to address issues such as the instability of random initialization and inefficiencies caused by long text in pre-trained large language models (LLMs). Inspired by the multi-head attention mechanism, CE-Prompt introduces the concept of composite embedding, which utilizes multiple randomly initialized embedding layers to generate more expressive prompt representations. To effectively integrate the information expressed by these composite embeddings, an additive fusion approach is employed, allowing each prompt vector to capture task-specific information more comprehensively, thereby improving the model’s task adaptability and inference efficiency. Experimental results show that CE-Prompt outperforms traditional Prompt-Tuning methods, with average improvements of 0.82% in Bilingual Evaluation Understudy (BLEU)-4 and 0.65% in ROUGE-L. Additionally, time complexity analysis indicates that CE-Prompt significantly reduces computational costs during inference. Compared to other methods, it achieves higher efficiency with the same training parameter budget, providing a more efficient solution for practical deployment.
This paper presents a seismic activity simulator that models the effects of fault lines on surface pressure. This project uses C programming to create a fully interactive learning resource intended to educate users on the mechanics of earthquakes. The motivation behind this project is to make studying seismic activity more accessible, engaging and cost effective.
Comments to K.M. Pervaiz Fathima, René de Borst, Implications of single or multiple pressure degrees of freedom at fracture in fluid saturated porous media, Engineering Fracture Mechanics, 213 (2019), 1-20.
We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US state of Michigan. For system inference, we use recent advances; specifically our framework for Variational System Identification (Wang et al. in Comput Methods Appl Mech Eng 356:44–74, 2019; arXiv:2001.04816 [cs.CE]) as well as Bayesian machine learning methods.
This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex stretched-coordinate viewpoint, and also discusses the limitations of PML.
Zhenlin Wang, Xiaoxuan Zhang, Gregory Teichert
et al.
We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US state of Michigan. For system inference, we use recent advances; specifically our framework for Variational System Identification (Wang et al., Comp. Meth. App. Mech. Eng., 356, 44-74, 2019; arXiv:2001.04816 [cs.CE]) as well as Bayesian machine learning methods.
This document is a short and informal tutorial on some aspects of calculating phase diagrams with the ATAT-tools emc2 and phb and on creating cluster expansions with maps. It is neither complete, nor in any way an official document, but mainly a set of collected notes I took during experimentation with ATAT.
Motivation: Since susceptibility to diseases increases with age, studying aging gains importance. Analyses of gene expression or sequence data, which have been indispensable for investigating aging, have been limited to studying genes and their protein products in isolation, ignoring their connectivities. However, proteins function by interacting with other proteins, and this is exactly what biological networks (BNs) model. Thus, analyzing the proteins' BN topologies could contribute to understanding of aging. Current methods for analyzing systems-level BNs deal with their static representations, even though cells are dynamic. For this reason, and because different data types can give complementary biological insights, we integrate current static BNs with aging-related gene expression data to construct dynamic, age-specific BNs. Then, we apply sensitive measures of topology to the dynamic BNs to study cellular changes with age. Results: While global BN topologies do not significantly change with age, local topologies of a number of genes do. We predict such genes as aging-related. We demonstrate credibility of our aging-related predictions by: 1) observing significant overlap between the predictions and "ground truth" aging-related genes; 2) showing that our predictions group by functions and diseases that are different than functions and diseases of genes that we do not predict as aging-related; 3) observing significant overlap between functions and diseases that are enriched in our predictions and those that are enriched in "ground truth" aging-related data; 4) providing evidence that diseases which are enriched in our predictions are linked to human aging; and 5) validating our predictions in the literature. This work was published in arXiv:1307.3388 [cs.CE], 2013.
We propose a discontinuous finite element method for small strain elasticity allowing for cohesive zone modeling. The method yields a seamless transition between the discontinuous Galerkin method and classical cohesive zone modeling. Some relevant numerical examples are presented.
The Synchrosqueezing transform is a time-frequency analysis method that can decompose complex signals into time-varying oscillatory components. It is a form of time-frequency reassignment that is both sparse and invertible, allowing for the recovery of the signal. This article presents an overview of the theory and stability properties of Synchrosqueezing, as well as applications of the technique to topics in cardiology, climate science and economics.
EnKF-C provides a compact generic framework for off-line data assimilation into large-scale layered geophysical models with the ensemble Kalman filter (EnKF). It is coded in C for GNU/Linux platform and can work either in EnKF, ensemble optimal interpolation (EnOI), or hybrid (EnKF/EnOI) modes.
json2run is a tool to automate the running, storage and analysis of experiments. The main advantage of json2run is that it allows to describe a set of experiments concisely as a JSON-formatted parameter tree. It also supports parallel execution of experiments, automatic parameter tuning through the F-Race framework and storage and analysis of experiments with MongoDB and R.