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The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…
A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal…
Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with…
Elastic interaction of pressurized spherical cavities embedded in a three-dimensional hyperelastic medium is computationally analyzed. Using finite element analysis across several positive and negative pressure scenarios, we calculate the…
The forces generated by moving interfaces usually include the parts due to tangential stretching. We derive an evolution equation for the tangential stretching, which then forms the basis of an Eulerian formulation based on level set…
This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can…
Continuum modeling of a free-standing graphene monolayer, viewed as a two dimensional 2-lattice, requires specifications of the components of the shift vector that act as an auxiliary variable. The field equations are then the equations…
We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response…
This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably,…
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…
Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…
This study proposes and explores a linear hydrodynamic thermo-elasticity system within mixture models, comprising fluid and solid phases, with a focus on biological tissues, particularly tumor-related phenomena. Although tumor growth is not…
In this paper, we propose the unfitted spectral element method for solving elliptic interface and corresponding eigenvalue problems. The novelty of the proposed method lies in its combination of the spectral accuracy of the spectral element…
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting…
This paper is concerned with the 2-dim two-phase interface Euler equation linearized at a pair of monotone shear flows in both fluids. We extend the Howard's Semicircle Theorem and study the eigenvalue distribution of the linearized Euler…
The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…
We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…
We study the effect of a uniform shear flow on an interface separating the two broken-symmetry ordered phases of a two-dimensional system with nonconserved scalar order parameter. The interface, initially flat and perpendicular to the flow,…
We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two-phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated…