Soft Active Mechanics

This page gives a preview of the research on SOFT ACTIVE MECHANICS I am carrying on. For more information, feel free to check the publications page and/or to contact me!

Swelling-driven instabilities

De-hydration induced mechanical instabilities in active elastic spherical shells

Abstract. Active elastic instabilities are common phenomena in the natural world, where they have the character of sudden mechanical morphings. Frequently, the driving force of the instability mechanisms has a chemo-mechanical nature, which makes the instabilities very different from the standard elastic instabilities. In this paper, we describe and study the active elastic instability occurring in a swollen spherical closed shell, confining a water-filled cavity,during a dehydration process. We set up a few numerical experiments based on a stress-diffusion model to give an insight into the phenomenon. Then, we present a study that looks at the chemo-mechanical problem and, through a few simplifying assumptions, allows us to derive a semi-analytical model of the phenomenon. It takes into account both the stress state and the water concentration in the walls of the shell at the onset of the instability. Moreover, it considers the invariance of the cavity volume at the onset of instability, which is due to the impossibility of instantaneously changing the cavity volume filled with water. Eventually, it is shown that the semi- analytic model matches very well the outcomes of the numerical experiments far from the initial regime; the ranges of validity of the approximated analytical model are also discussed.

M. Curatolo, G. Napoli, P. Nardinocchi, S. Turzi. Proc. R. Soc. A 477:20210243.

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Other publications on the same topics are:

Circumferential buckling of a hydrogel tube emptying upon dehydration. M. Curatolo, F. Lisi, G. Napoli, P. Nardinocchi. The European Physical Journal Plus 138 (382), 2023.

Modeling solvent dynamics in polymers with solvent-filled cavities. M. Curatolo, P. Nardinocchi, L. Teresi. Mechanics of Soft Materials 2(13), 2020.
Driving water cavitation in a hydrogel cavity. M. Curatolo, P. Nardinocchi, L. Teresi. Soft Matter 14, 2018.

Swelling-driven soft elastic catapults

Abstract. The paper outlines and analyzes the conditions for optimizing a catapult mechanism that emerges in a soft rod, initially completely adhered to a rigid lubricated substrate, as a result of oil absorption. Oil diffusion causes differential swelling across the rod thickness, inducing rod bending that is counteracted by adhesion to the substrate. The effect culminates in a gradual detachment of the rod from the substrate, followed by a rapid shooting phase when one end detaches. To elucidate this intricate phenomenon, we employ a modified Euler elastica model that incorporates two additional parameters: the spontaneous stretching, that quantifies the relative elongation of the material with respect to its dry, unstressed configuration, and the spontaneous curvature, that captures the rod tendency to deflect due to diffusion-induced non-uniform stretching through the thickness. The two interrelated parameters, spontaneous stretching and curvature, which evolve over time as they are influenced by the diffusion process, are then calculated numerically with a FEM code that combines the finite elasticity model with the Flory-Rehner diffusion model. Finally, we present a comprehensive optimization study of the catapult based on its geometric and material properties, providing insights for the design and control of this novel mechanism.

M. Curatolo, G. Napoli, P. Nardinocchi, S. Turzi. International Journal of Non-Linear Mechanics, 2024.

Fiber reorientation in soft inelastic materials

Passive and active fiber reorientation in anisotropic materials

Abstract. We present a continuum model to describe the reorientation of an anisotropic material structure, characterized by two fiber families able to modify their orientations following different evolution dynamics. The evolution equations are derived in a thermodynamically consistent way, and passive and active contributions to the reorientation process are identified. It is shown that a weaker extension of a well-known coaxiality result holds. The transversely isotropic and orthotropic cases are then recovered by imposing the proper constraint on the fiber rotation. Applications to biological experiments on cell layers under stretch are discussed, showing a good agreement between the model and the experimental results. Even though we focus on cell layers, our framework remains general and may be employed to describe reorientation in engineering materials.

J. Ciambella, G. Lucci, P. Nardinocchi, L. Preziosi. International Journal of Engineering Science 176, 2022.

Other publications on the same topics are:

Non-affine fiber reorientation in finite inelasticity. J. Ciambella, P. Nardinocchi, Journal of Elasticity 153, 2022.
A structurally frame-indifferent model for anisotropic visco-hyperelastic materials. J. Ciambella, P. Nardinocchi, Journal of the Mechanica and Physics of Solids 147, 2021.
Torque induced reorientation in active fiber-reinforced materials. J. Ciambella, P. Nardinocchi, Soft Matter 15, 2019.
Magneto-induced remodeling of fibre-reinforced elastomers. r with solvent-filled cavities. J. Ciambella, P. Nardinocchi, International Journal of Non-Linear Mechanics 117, 2019.

Morphing of soft structures

Morphing of soft tubes by anisotropic growth

Abstract. We present a study of smart growth in layered cylindrical structures. We start from the characterization of a compatible growth field in an anisotropic growing tube with the aim to show a small perturbation in the compatible growth field that may produce a controlled deprivation of compatibility and localization of elastic energy storage in a composite structure made up of anisotropic growing tubes.

P. Nardinocchi, L. Teresi. Acta Mechanica 2021 https://doi.org/10.1007/s00707-021-03065-7.

Other publications on the same topics are:

Shape-shifting of polymer beams and shells due to oil extraction. D. Battista, V. Luchnikov, P. Nardinocchi, Extreme Mechanics Letters 36, 2020.

A biological prototype of soft active material (myocardium)

Myocardium is a worth example of soft active material. We studied the chemo-electro-mechanics of that tissue, focusing on spiral onset and spiral termination (figure from Cherubini et al., Prog. Biophys. Mol. Biol. 97, 2008). We assumed as basic the notion of contraction, a kinematic notion, opposite to that of active tension, stipulating that, when activated, a muscle suffers contraction, which in turn can yield a tension, in case a constraint hampers the motion. Contractions were described as active strains (see also P. Nardinocchi & L. Teresi, "On the active response of soft living tissue", J. Elasticity 88, 2007).

We also modelled cardiac muscle contractions in the framework of anisotropic finite elasticity with large distortions and coupled a mechanical model with reaction–diffusion equations representing electrophysiological activity. The tissue was assumed anisotropic from both the elastic and diffusive point of view, by using anisotropic constitutive relations to relates stresses and elastic strains as well as anisotropic diffusion tensors for both the membrane potential and calcium ions. Activation waves in a small patch of orthotropic tissue are shown in the figure (from Nardinocchi and Teresi, Math Mech Solids 18(6), 2013).

Research on heart mechanics has been carried on at the organ level through a synergic approach combining continuum mechanics and echocardiographic imaging. See here.