Yael Cohen | Searcharxiv

arXiv2025

Curvature Potential Formulation for Thin Elastic Sheets

Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly nonlinear theories, such as the Foppl-von Karman equations, which require small slopes and fail when deflections become large even if strains remain small. We introduce a methodological progress via a geometric reformulation of thin-sheet elasticity based on a stress potential and a curvature potential. This formulation preserves the structure of the classical equations while extending their validity to nonlinear, multivalued configurations, and geometrically frustrated states. The framework provides a unified description of thin-sheet mechanics in regimes inaccessible to existing theories and opens new possibilities for the study of elastic membranes and two-dimensional materials.

cond-mat.soft↗

arXiv2024

Odd dipole screening in disordered matter

Disordered solids, straddling the solid-fluid boundary, lack a comprehensive continuum mechanical description. They exhibit a complex microstructure wherein multiple meta-stable states exist. Deforming disordered solids induces particles rearrangements enabling the system to transition between meta-stable states. A dramatic consequence of these transitions is that quasistatic deformation cycles modify the reference state, facilitating the storage and release of mechanical energy. Here we develop a continuum mechanical theory of disordered solids, which accounts for the absence of a reference state and the lack of conserved potential energy. Our theory, which introduces a new modulus describing non-conservative mechanical screening, reduces to classical elasticity in the absence of screening. We analytically derive predictions for the deformation field for various perturbations and geometries. While our theory applies to general disordered solids, we focus on a two-dimensional disordered granular system and predict accurately the non-affine displacement fields observed in experiments for both small and large deformations, along with the observable vanishing shear modulus. The new proposed moduli satisfy universal relations that are independent of the specific experimental realization. Our work thus forms the basis of an entirely new family of continuum descriptions of the mechanics of disordered solids.

cond-mat.soft↗