Related papers: Phase-Field Modeling of Fracture with Physics-Info…
This study presents a phase field model for brittle fracture in fluid-infiltrating vuggy porous media. While the state-of-the-art in hydraulic phase field fracture considers Darcian fracture flow with enhanced permeability along the crack,…
Brittle fracturing of materials is common in natural and industrial processes over a variety of length scales. Knowledge of individual particle dynamics is vital to obtain deeper insight into the atomistic processes governing crack…
In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training…
Recent advances in scanning transmission electron and scanning probe microscopies have opened exciting opportunities in probing the materials structural parameters and various functional properties in real space with angstrom-level…
We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent…
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
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…
Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and…
Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field…
Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters,…
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional…
A field theory is presented for predicting damage and fracture in quasi brittle materials incorporating effects of irreversible (plastic) deformation as well as elastic moduli that soften with damage. The new observation made here is that…
Due to its computational robustness and versatility, the phase field fracture model has become the preferred tool for predicting a wide range of cracking phenomena. However, in its conventional form, its intrinsic tension-compression…
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…
In context of the universal presence of defects in additively manufactured (AM) metals, efficient computational tools are required to rapidly screen AM microstructures for mechanical integrity. To this end, a deep learning approach is used…
We present an application of Physics-Informed Neural Networks to handle MultiPhase-Field simulations of microstructure evolution. It has been showcased that a combination of optimization techniques extended and adapted from the PINNs…