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The characteristic ``in-plane" bending associated with soft robots' deformation make them preferred over rigid robots in sophisticated manipulation and movement tasks. Executing such motion strategies to precision in soft deformable robots…
Compliant grippers, owing to adaptivity and safety, have attracted considerable attention for unstructured grasping in real applications, such as industrial or logistic scenarios. However, accurately modeling the bidirectional relationship…
The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties such as…
Investigation of inhomogeneities has wide applications in different areas of mechanics including the study of composite materials. Here, we analytically study an arbitrarily-shaped isotropic inhomogeneity embedded in a finite-sized…
Thin surfaces are ubiquitous in nature, from leaves to cell membranes, and in technology, from paper to corrugated containers. Structural thinness imbues them with flexibility, the ability to easily bend under light loads, even as their…
Elasticity has long been regarded as a property exclusive to material media. Here we uncover its hidden existence in the spin degree of freedom. We introduce spin elasticity-an intrinsic mechanism that governs recoverable deformation of…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
We consider the fluctuation modes around a hypersurface $\Sigma_c$ in a $(d+2)$-dimensional product Einstein manifold, with $\Sigma_c$ taken either near the horizon or at some finite cutoff from the horizon. By mapping the equations that…
A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a…
We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local…
We consider a system of evolutionary equations that is capable of describing certain viscoelastic effects in linearized yet nonlinear models of solid mechanics. The essence of the paper is that the constitutive relation, involving the…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
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…
The paper is devoted to the controllability problem for 3D compressible Euler system. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are…
An initial stress within a solid can arise to support external loads or from processes such as thermal expansion in inert matter or growth and remodelling in living materials. For this reason it is useful to develop a mechanical framework…
A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d + 1 dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic…
Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into non-trivial shapes with…
This paper establishes a unified element-based framework for formation control by introducing the concept of the deformation gradient from continuum mechanics. Unlike traditional methods that rely on geometric constraints defined on graph…
The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of…