Actuation performances of anisotropic gels

We investigated the actuation performances of anisotropic gels driven by mechanical and chemical stimuli, in terms of both deformation processes and stroke--curves, and distinguished between the fast response of gels before diffusion starts and the asymptotic response attained at the steady state. We also showed as the range of forces that an anisotropic hydrogel can exert when constrained is especially wide;indeed, changing fiber orientation allows to induce shear as well as transversely isotropic extensions.Comment: 11 pages, 11 figure

Swelling-induced bending and pumping in homogeneous thin sheets

We realize steady curved shapes from homogeneous hydrogel flat structures which are in contact with two environments at different chemical conditions. We numerically investigate the behaviour of beam-like and plate-like structures during the transient state, which realize osmotic pumps. Through numerical experiments, we determine the relationship between the difference in the chemical potentials at the top and bottom of a beam and the curvature of the bent beam as well as the Gaussian curvature of a spherical cap morphed from a flat plate. We also propose an approximate modeling of both the beam and the plate, to evaluate explicitly that relationship and show the good agreement between those formulas and the outcomes of the numerical simulations

Evaluation of the strain-line patterns in a human left ventricle: A simulation study

The aim of this paper is to emphasise the role of the primary strain-line patterns in a human left ventricle (LV) within the complex system that is the heart. In particular, a protocol is proposed for the measurement of the principal strain lines (PSL) in the walls of the LV; this protocol is tested by means of a computational model which resembles a human LV. When the analysis is focused on the epicardial surface, PSL can be used to derive information on the directions of muscle fibres during the entire cardiac cycle, not only the systolic phase. © 2013 Taylor & Francis

Mechanics of bio–hybrid systems

Bio–hybrid system are morphing structures whose shaping can be electrically driven and strongly depends on the geometrical and mechanical characteristics of the system. The estimation of those characteristics which allow for getting target shapes is a great challenge. We present and discuss an approximate model for narrow bio–hybrid strips which works well in plane bending. A generalization towards three–layers bio–hybrid system is presented

Temperature-driven volume transition in hydrogels: phase--coexistence and interface localization

We study volume transition phenomenon in hydrogels within the framework of Flory-Rehner thermodynamic modelling; we show that starting from different models for the Flory parameter different conclusions can be achieved, in terms of admissible coexisting equilibria of the system. In particular, with explicit reference to a one-dimensional problem we establish the ranges of both temperature and traction which allow for the coexistence of a swollen and a shrunk phase. Through consideration of an augmented Flory-Rehner free-energy, which also accounts for the gradient of volume changes, we determine the position of the interface between the coexisting phases, and capture the connection profile between them

Non-affine fiber reorientation in finite inelasticity

This paper introduces a model for the mechanical response of anisotropic soft materials undergoing large inelastic deformations. The composite is constituted by a soft isotropic matrix reinforced with stiff fibres, that can evolve independently from each other. The constitutive equations are provided in terms of the free energy density and the dissipation density which are both required to be thermodynamically consistent and structurally frame-indifferent, i.e., they must be independent of a rotation overimposed on the natural state. This is in contrast to many of the currently used inelastic models for soft fiber-reinforced materials which do not deal with the lack of uniqueness of the natural state. A constraint between the inelastic spin of the matrix and the rotation spin of the fibre is introduced to fully determined the natural state. The resulting flow rules of the inelastic processes incorporate some typical scenarios including viscoelasticity and growth

A structurally frame-indifferent model for anisotropic visco-hyperelastic materials

One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed thoroughly and addressed by introducing a novel anisotropic remodelling equation compatible with the principle of structural frame indifference, a requirement that every inelastic theory based on the multiplicative decomposition of the deformation gradient must obey to. The evolution laws of the dissipative process are %obtained by introducing a novel (remodelling) balance equation which is completely determined by two scalar functions, the elastic strain energy and the dissipation densities. The proper choice of the dissipation function allows us to reduce the proposed model to the Ericksen anisotropic fluid, when deformation is sufficiently slow, or to the anisotropic hyperelastic solid for fast deformations. Finally, a few prototype examples are discussed to highlight the role of the relaxation times in the constitutive response.Comment: 43 pages,, 9 figure

Torque-induced reorientation in active fibre-reinforced materials

We introduce a continuum model for a fibre reinforced material in which the reference orientation of the fibre may evolve with time, under the influence of external stimuli. The model is formulated in the framework of large strain hyperelasticity and the kinematics of the continuum is described by both a position vector and by a remodelling tensor which, in the present context, is an orthogonal tensor representing the fibre reorientation process. By imposing suitable thermodynamical restrictions on the constitutive equation, we obtain an evolution equation of the remodelling tensor governed by the Eshelby torque, whose stationary solutions are studied in absence of any external source terms. It is shown that the fibres reorient themselves in a configuration that minimises the elastic energy and get aligned along a direction that may or may not be of principal strain. The explicit analysis of the Hessian of the strain energy density allows us to discriminate among the stationary solutions, which ones are stable. Examples are given for passive reorientation processes driven by applied strains or external boundary tractions. % Applications of the proposed theory to biological tissues, nematic or magneto-electro active elastomers are foreseen.Comment: 23 pages, 4 figure

Morphing of Geometric Composites via Residual Swelling

Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth--like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques

Geometry and Mechanics of Thin Growing Bilayers

We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness $\gamma$ that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourth's the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude.Comment: 5 pages, 4 figure