Claire Lestringant (Mechanics & Materials, Dept. of Mechanical and Process Engineering, ETH Zürich, Switzerland) New models for highly deformable structures

Flexibility is 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, and 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 beading in cylinders made of soft gels, bulges in cylindrical party balloons and folds in bent 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 present a discrete, geometrically exact beam formulation that can efficiently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior. It fully decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. In the case of composite materials made up of beam lattices, this description can be combined with a numerical homogenization scheme, thus dropping computational costs. In a second part of the talk, I will introduce a systematic method to establish  regularized 1D models for localization, depending on strain and on strain gradient, and thus restoring a description of interfaces. It consists in a formal expansion performed near a finitely pre-strained state and which therefore retains all sources of nonlinearity, coming from the geometry and from the constitutive law. I will illustrate the method on the example of beading in a soft hyperelastic cylinder.