相关论文: Singularities, Structures and Scaling in Deformed …
Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the…
Under suitable regularity assumptions the $p$-elastic energy of a planar set $E\subset\mathbb{R}^2$ is defined to be $\int_{\partial E} 1 + |k_{\partial E}|^p \,\, d\mathcal{H}^1,$ where $k_{\partial E}$ is the curvature of the boundary…
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area…
Architected materials that exploit buckling instabilities to reversibly trap energy have been shown to be effective for impact protection. The energy-absorbing capabilities of these architected materials can be enhanced further by…
Wrinkles are often observed on the surfaces of compressed soft materials in nature. In the past few decades, the fascinating surface patterns have been studied extensively by using the linear bifurcation analysis under plane strain. The…
Using high-resolution digital recordings, we study the crackling sound emitted from crumpled sheets of mylar as they are strained. These sheets possess many of the qualitative features of traditional disordered systems including frustration…
In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…
We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical and experimental methods. Such sheets occur in packaging, surgery and nanotechnology. We…
Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd-viscosity [de Wit \textit{et al.}, Nature \textbf{627}, 515 (2024)], the two-dimensionalization of the flow at small…
We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness…
Minimizing the elastic free energy of a thin sheet of nematic polymer network among smooth isometric immersions is the strategy purported by the mainstream theory. In this paper, we broaden the class of admissible spontaneous deformations:…
Numerical simulations of a thin layer of turbulent flow in stably stratified conditions within the Boussinesq approximation have been performed. The statistics of energy transfer among scales have been investigated for different values of…
We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show parallels between asymptotic expansions for the energy of elastic surfaces in…
In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multi-subunit size which results from the competition between the elastic costs of…
Differential growth processes play a prominent role in shaping leaves and biological tissues. Using both analytical and numerical calculations, we consider the shapes of closed, elastic strips which have been subjected to an inhomogeneous…
Like a cr\^epe resting on a plate, a thin elastic sheet can fold smoothly under its own weight, forming reversible shapes without creases or imposed hinges. Such soft folds arise from a balance between elastic bending and gravity, yet their…
We investigate the weakening of elastic materials through randomly distributed circles and cracks numerically and compare the results to predictions from homogenization theories. We find a good agreement for the case of randomly oriented…
The dissipation of kinetic and magnetic energy in the interstellar medium (ISM) can proceed through viscous, Ohmic or ambipolar diffusion (AD). It occurs at very small scales compared to the scales at which energy is presumed to be…
Energy dissipation in sheared dry and wet granulates is considered in the presence of an externally applied confining pressure. Discrete element simulations reveal that for sufficiently small confining pressures, the energy dissipation is…
We study the bending of a book-like system, comprising a stack of elastic plates coupled through friction. The behavior of this layered system is rich and nontrivial, with a non-additive enhancement of the apparent stiffness and a…