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The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Previously, a class of 2D cellular models has been shown to undergo a rigidity transition controlled by a mechanical parameter that…
In this paper, we classify the rotational surfaces with constant skew curvature in $3$-space forms. We also give a variational characterization of the profile curves of these surfaces as critical points of a curvature energy involving the…
Soft colloids allow to explore high density states well beyond random close packing. An important open question is whether softness controls the dynamics under these dense conditions. While experimental works reported conflicting results,…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
Plastic deformation in solids induced by external shear stress is of huge practical interest. Presence of local crystalline order in polycrystals, consisting of many grains, distinguishes its deformation pattern from that of amorphous…
Elucidating versatile configurations of spiral folding, and investigating the deployment performance is of relevant interest to extend the applicability of deployable membranes towards large-scale and functional configurations. In this…
Stochastic geometry provides a powerful framework for modelling complex random structures, with applications in physics, materials science, biology, and other fields. The three-dimensional microstructure of polycrystalline materials is…
This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…
The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that due to elasticity. This article studies how surface tension changes the contact mechanics of a small…
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
We investigate theoretically the morphology of a thin nematic film adsorbed at flat substrate patterned by stripes with alternating aligning properties, normal and tangential respectively. We construct a simple "exactly-solvable" effective…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…
In the real world, we often come across soft objects having spatially varying stiffness, such as human palm or a wart on the skin. In this paper, we propose a novel approach to render thin, deformable objects having spatially varying…
Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…
We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry (e.g. a shell) or…
In this paper we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures.…
We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing `pleats'; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on…
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…