Related papers: Phase Field Benchmark Problems for Dendritic Growt…
This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…
In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show…
In this paper, we propose and analyze an efficient numerical method for the anisotropic phase field dendritic crystal growth model, which is challenging because we are facing the nonlinear coupling and anisotropic coefficient in the model.…
The high computational cost of phase field simulations remains a major limitation for predicting dendritic solidification in metals, particularly in additive manufacturing, where microstructural control is critical. This work presents a…
Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological…
A new phase field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model's thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al (Phys…
We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu…
Engineering alloys generally exhibit multi-phase microstructures. For simulating their microstructure evolution during solid-state phase transformation, CALPHAD-guided multi-phase-field models coupled with micro-mechanics have proven to be…
We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of…
We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a…
In functionally graded materials (FGMs) fabricated using directed energy deposition (DED) additive manufacturing (AM), cracks may form due to interdendritic stress during solidification, the formation of intermetallics, or the buildup of…
Accurate prediction of phase equilibria remains a central challenge in chemical engineering. Physics-consistent machine learning methods that incorporate thermodynamic structure into neural networks have recently shown strong performance…
A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
We present a first implementation of the Dendritic Needle Network (DNN) model for dendritic crystal growth in three dimensions including convective transport in the melt. The numerical solving of the Navier-Stokes equations is performed…
Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic…
This paper presents several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media. A number of solution strategies are compared, including a vertex and a cell-centered finite volume…
Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…