Related papers: Phase field model for multi-material shape optimiz…
A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during…
We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…
We consider a particular phase field system which physical context is that of tumor growth dynamics. The model we deal with consists of a Cahn-Hilliard type equation governing the evolution of the phase variable which takes into account the…
A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical…
We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…
A phase-field approach is proposed for interface failure between two possibly dissimilar materials. The discrete adhesive interface is regularised over a finite width. Due to the use of a regularised crack model for the bulk material, an…
The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models,…
This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and…
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…
Amorphous materials of homogeneous structures usually suffer from nonuniform deformation under shear, which can develop into shear localization and eventually destructive shear band. One approach to tackle this issue is to introduce an…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated…
We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…
We present a new phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the…