Surface plasticity: theory and computation

Surfaces of solids behave differently from the bulk due to different atomic rearrangements and processes such as oxidation or aging. Such behavior can become markedly dominant at the nanoscale due to the large ratio of surface area to bulk volume. The surface elasticity theory (Gurtin and Murdoch in Arch Ration Mech Anal 57(4):291–323, 1975) has proven to be a powerful strategy to capture the size-dependent response of nano-materials. While the surface elasticity theory is well-established to date, surface plasticity still remains elusive and poorly understood. The objective of this contribution is to establish a thermodynamically consistent surface elastoplasticity theory for finite deformations. A phenomenological isotropic plasticity model for the surface is developed based on the postulated elastoplastic multiplicative decomposition of the surface superficial deformation gradient. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and the consistent elastoplastic tangent of the surface contribution is derived. Finally, a series of numerical examples provide further insight into the problem and elucidate the key features of the proposed theory. © 2017 Springer-Verlag GmbH Germany, part of Springer Natur

Variable tilt on lipid membranes

A continuum theory for lipid membranes is developed that accounts for mechanical interactions between lipid tilt and membrane shape. For planar membranes, a linear version of the theory is used to predict tilt variations similar to those observed in experiments and molecular dynamics simulations

Interaction between surface shape and intra-surface viscous flow on lipid membranes

International audienceThe theory of intra-surface viscous flow on lipid bilayers is developed by combining the equations for flow on a curved surface with those that describe the elastic resistance of the bilayer to flexure. The model is derived directly from balance laws and augments an alternative formulation based on a variational principle. Conditions holding along an edge of the membrane are emphasized and the coupling between flow and membrane shape is simulated numerically

Finite elastic wrinkling deformations of incompressible fiber-reinforced plates

A two-dimensional plate theory, valid for finite elastic deformations with small strains, is derived for incompressible, fiber-reinforced materials. Single-layer plates and two-layer laminates are considered. Numerical simulations illustrate the substantial effect that fiber reinforcement has on wrinkling patterns in the sheet