Related papers: Evaluating the snappability of bar-joint framework…
A bar-joint framework $(G,p)$ is the combination of a graph $G$ and a map $p$ assigning positions, in some space, to the vertices of $G$. The framework is rigid if every edge-length-preserving continuous motion of the vertices arises from…
For solving the longstanding materials science problem of correlating elastic properties of a solid material to the formation of cracks we present a new general concept. This concept is applied to the technologically most important cracks…
Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
Using a thermodynamical approach, we calculate the deformation of a spherical elastic particle placed on a rigid substrate, under zero external load, and including an ingredient of importance in soft matter: the interfacial tension of the…
We study the interaction between capillary forces and deformation in the context of a deformable capillary adhesive: a clamped, tense membrane is adhered to a rigid substrate by the surface tension of a liquid droplet. We find that the…
Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…
We develop a theory of static friction by modeling the homogeneous surfaces of contact as being composed of a regular array of compressible elastic smooth microscopic inclines. Static friction is thought of as the resistance due to having…
A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are…
The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven…
Snapping instabilities in soft structures offer a powerful pathway to achieve rapid and energy-efficient actuation. In this study, an eccentric dome-shaped snapping actuator is developed to generate controllable asymmetric motion through…
A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…
In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime…
Many organisms have an elastic skeleton that consists of a closed shell of epithelial cells that is filled with fluid, and can actively regulate both elastic forces in the shell and hydrostatic pressure inside it. In this work we introduce…
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
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…
Dissipated energy, representing a monotonically increasing state variable in nonlinear fracture mechanics, can be used as a restraint for tracing the dissipation instead of the elastic unloading path of the structure response. In this work,…
Mechanical characteristics of single biological cells are used to identify and possibly leverage interesting differences among cells or cell populations. Fluidity---hysteresivity normalized to the extremes of an elastic solid or a viscous…
Disordered network materials abound in both nature and synthetic situations while rigorous analysis of their nonlinear mechanical behaviors still is very challenging. The purpose of this paper is to connect the mathematical framework of…