Related papers: Phase Field Benchmark Problems for Dendritic Growt…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
The goal of quantitative elastography is to identify biomechanical parameters from interior displacement data, which are provided by other modalities, such as ultrasound or magnetic resonance imaging. In this paper, we analyze the stability…
Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…
In this paper, we have formulated a phase-field model based on the grand-potential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns…
The mechanical properties of metal matrix fiber-reinforced composites depend on many aspects of their structure in a complicated way. In this paper, we propose a \emph{minimalistic} approach to study interface debonding, matrix cracking,…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
A thin-interface phase-field model of electrochemical interfaces is developed based on Marcus kinetics for concentrated solutions, and used to simulate dendrite growth during electrodeposition of metals. The model is derived in the grand…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
Fatigue fracture is one of the main causes of failure in structures. However, the simulation of fatigue crack growth is computationally demanding due to the large number of load cycles involved. Metals in the low cycle fatigue range often…
We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems - the stability of a Lomer dislocation pair under shear and the stability of a lattice to plastic slip under tensile loading.…
A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method…
Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of…
The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due…
Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering…
In recent years, researchers have increasingly sought batteries as an efficient and cost-effective solution for energy storage and supply, owing to their high energy density, low cost, and environmental resilience. However, the issue of…
It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…
This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field…
Solidification, coupled with melt flow, plays a critical role in determining the microstructure and properties of materials in several manufacturing processes. Phase-field models coupled with the Navier-Stokes equations are widely used to…
Data driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning…