A simple microscopic model for the dynamics of adhesive failure

We consider a microscopic model for the failure of soft adhesives in tension based on ideas of bond rupture under dynamic loading. Focusing on adhesive failure under loading at constant velocity, we demonstrate that bi-modal curves of stress against strain may occur due to effects of finite polymer chain or bond length and characterise the loading conditions under which such bi-modal behaviour is observed. The results of this analysis are in qualitative agreement with experiments performed on unconfined adhesives in which failure does not occur by cavitation.Comment: 11 pages, 5 figure

Scale and Nature of Sulcification Patterns

Sulci are surface folds commonly seen in strained soft elastomers and form via a strongly subsubcriticalcritical, yet scale-free instability. Treating the threshold for nonlinear instability as a nonlinear critical point, we explain the nature of sulcus patterns in terms of the scale and translation symmetries which are broken by the formation of an isolated, small sulcus. Our perturbative theory and simulations show that sulcus formation in a thick, compressed slab can arise either as a supercritical or as a weakly subcritical bifurcation relative to this nonlinear critical point, depending on the boundary conditions. An infinite number of competing, equilibrium patterns simultaneously emerge at this critical point, but the one selected has the lowest energy. We give a simple, physical explanation for the formation of these sulcification patterns using an analogy to a solid-solid phase transition with a finite energy of transformation.Comment: 4 pages, 2 figures; new title and abstract; clarification of the role of pre-stress following Eq. 5. Revised and updated to agree with published versio

Dynamics of poroelastic filaments

We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition to the usual terms for the bending of an elastic rod, we find a term that arises from fluid-solid interaction. Using the poroelastica equation as a starting point, we consider the load controlled and displacement controlled planar buckling of a slender rod, as well as the closely related instabilities of a rod subject to twisting moments and compression when embedded in an elastic medium. This work has applications to the active and passive mechanics of thin filaments and sheets made from gels, plant organs such as stems, roots and leaves, sponges, cartilage layers and bones.Comment: 34 pages, 13 figures, to appear in the Proceeding of the Royal Societ

Statistical Mechanics of Developable Ribbons

We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbon-like structures that follows from the geometric separation of scales introduces a coupling between bending and torsional degrees of freedom. Using analytical techniques and Monte Carlo simulations, we find that the tangent-tangent correlation functions always exhibits an oscillatory decay at any finite temperature implying the existence of an underlying helical structure even in absence of a preferential zero-temperature twist. In addition the persistence length is found to be over three times larger than that of a wormlike chain having the same bending rigidity. Our results are applicable to many ribbon-like objects in polymer physics and nanoscience that are not described by the classical worm-like chain model.Comment: 4 pages, 5 figure