Large-strain poroelastic plate theory for polymer gels with applications to swelling-induced morphing of composite plates

Abstract

We derive a large-strain plate model that allows to describe transient, coupled processes involving elasticity and solvent migration, by performing a dimensional reduction of a three-dimensional poroelastic theory. We apply the model to polymer gel plates, for which a specific kinematic constraint and constitutive relations hold. Finally, we assess the accuracy of the plate model with respect to the parent three-dimensional model through two numerical benchmarks, solved by means of the finite element method. Our results show that the theory offers an efficient computational framework for the study of swelling-induced morphing of composite gel plates.

Dimension reduction via $$\Gamma $$ Γ -convergence for soft active materials

“…Similar issues have been the object of recent intense investigation, see e.g. [3,6,22,23,27] and also [7,9,10,12,13,19,25]. The point of view we adopt here is that of a systematic derivation of dimensionally-reduced models by means of Γ-convergence.…”

“…In particular, we can compute the limiting 2D model. In order to do it, we first compute, for every G ∈ R 2×2 , the relaxed energy density 19) where Q 3 is defined in (2.10) and…”

The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity

“…Similar approaches have also been considered by Papastavrou et al (2013) to model surface growth of bulk materials and Swain and Gupta (2018) to model interface growth. A general surface formulation coupling mechanical deformation and swelling of membranes and shells seems to have appeared only recently by the work of Lucantonio et al (2017).…”

Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry

“…This mechanism is based on the Gauss' Theorema Egregium (Arroyo and DeSimone, 2014;Klein et al, 2007). Both curvature-generating principles can be implemented in polymer gels Kim et al (2012); Lucantonio et al (2014Lucantonio et al ( , 2017; Na et al (2015); Pezzulla et al (2015Pezzulla et al ( , 2016 and in Liquid Crystal Elastomers, an interesting polymeric (hence soft) active material which is receiving increasing attention (Agostiniani and DeSimone, 2017b;Agostiniani et al, 2016;Aharoni et al, 2014;Modes et al, 2011;Mostajeran, 2015). Some of the interesting spontaneous morphing behaviour of Liquid Crystal Elastomers can be reproduced in pre-stretched bilayers, made of simple (i.e., not-active) elastic materials.…”