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We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk…
In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracking domains.
We investigate the role of the evaporation regime on the stability of a volatile liquid film flowing over an inclined heated surface while considering the dynamics of both the liquid phase and the diffusion of its vapor. We (i) modify the…
The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue, and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning…
We obtain an exact strain consistency equation for full, elastic, and plastic strain characteristics that have a clear physical meaning and are naturally related to stresses. The dynamic equations are represented in a form that does not use…
We investigate the encapsulation of water by a thin elastic film as a minimal model of elastocapillary self-folding with fluid transport. An equilateral triangular polydimethylsiloxane film is lifted quasi-statically from a water surface,…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…
This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…
A consistent, small scale description of plastic motion in a crystalline solid is presented based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
The morphology of crystalline thin films evolving on flat rigid substrates by condensation of extra film atoms or by evaporation of their own atoms in the surrounding vapor is studied in the framework of the theory of Stress Driven…
Periodic wrinkling of a rigid capping layer on a deformable substrate provides a useful method for templating surface topography for a variety of novel applications. Many experiments have studied wrinkle formation during the compression of…
The elastic moduli of four numerical random isotropic packings of Hertzian spheres are studied. The four samples are assembled with different preparation procedures, two of which aim to reproduce experimental compaction by vibration and…
This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the…
In this paper we study the existence of solutions to an isotropic differential inclusion.
In the field of soft dielectric elastomers, the notion electrostriction indicates the dependency of the permittivity on strain. The present paper is aimed at investigating the effects of electrostriction onto the stability behaviour of…
In this work, we show the short-time existence of solutions of the evolution equations that represent the solid state dewetting of thin films through evaporation-condensation as a two dimensional sharp interface variational model. The…
The stability to dislocations of the elastic phase, or ``Bragg glass'', of a randomly pinned elastic medium in two dimensions is studied using the minimum-cost-flow algorithm for a disordered fully-packed loop model. The elastic phase is…
We consider nonlinear viscoelastic materials of differential type and for some special models we derive exact solutions of initial boundary value problems. These exact solutions are used to investigate the reasons of non-existence of global…
We discuss a recent effort in the modelling of binary component thin films, which yielded the same conclusions and stability limits as earlier work, despite a different method of incorporating constraints into the gradient dynamics…