Abstract

Flexibility is becoming a key feature in structural engineering, used for the design of multi-stable, reconfigurable space structures, sensors or soft robots. Thin, deformable structures invade materials science: recent additive manufacturing techniques combine active materials with microstructural design, paving the way towards engineering materials with properties tunable in time. There is a strong need for theoretical and numerical tools that can efficiently predict the mechanical response of these advanced structures. The example of localization highlights this need: it occurs in a variety of slender structures, from necks in polymer bars under traction to bulges in cylindrical party balloons and folds in tape-springs. In all these systems, distinct states of deformation may coexist, and classical one-dimensional (1D) models fail to describe interfaces, or finite size effects. I will first present a discrete, geometrically exact beam formulation that can efficiently and accurately capture the nonlinear deformation of slender beams featuring complex material behaviour. It fully decouples the kinematics from the material behaviour and can thus handle a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. In a second part of the talk, I will introduce a systematic method to establish 1D models depending on strain and on strain gradient, thus accurately capturing interfaces during localisation. It consists in a formal expansion performed near a finitely pre-strained state and therefore retains all sources of nonlinearity, coming from the geometry and from the constitutive law. I will illustrate the method on the example of elastocapillary necking.