G. Puglisi

Mechanics of a discrete chain with bi-stable elements

It has become common to model materials supporting several crystallographic phases as elastic continua with non (quasi) convex energy. This peculiar property of the energy originates from the multi-stability of the system at the microlevel associated with the possibility of several energetically equivalent arrangements of atoms in crystal lattices. In this paper we study the simplest prototypical discrete system—a one-dimensional chain with a finite number of bi-stable elastic elements. Our main assumption is that the energy of a single spring has two convex wells separated by a spinodal region where the energy is concave. We neglect the interaction beyond nearest neighbors and explore in some detail a complicated energy landscape for this mechanical system. In particular we show that under generic loading the chain possesses a large number of metastable configurations which may contain up to one (snap) spring in the unstable (spinodal) state. As the loading parameters vary, the system undergoes a number of bifurcations and we show that the type of a bifurcation may depend crucially on the details of the concave (spinodal) part of the energy function. In special cases we obtain explicit formulas for the local and global minima and provide a quantitative description of the possible quasi-static evolution paths and of the associated hysteresis.

A micromechanics-based model for the Mullins effect

We propose a model for the stress softening of isotropic, incompressible rubberlike materials. The model is derived from a micromechanical scheme of a polymeric network reinforced with fine filler particles, idealized as rigid, and connected by two different types of chains: elastic and breakable. The fraction of breakable chains, assigned through an appropriate distribution function, is responsible for the network alteration. This prototypical system is then extended to a three-dimensional model with isotropic stress softening. In order to illustrate this model, we discuss two explicit examples: the homogeneous deformation of uniaxial extension and the inhomogeneous deformation of azimuthal shear.

Rate independent hysteresis in a bi-stable chain

Abstract The nontrivial behavior of an elastic chain with identical bi-stable elements may be considered prototypical for a large number of nonlinear processes in solids ranging from phase transitions to fracture. The energy landscape of such a chain is extremely wiggly which gives rise to multiple equilibrium configurations and results in a hysteretic evolution and a possibility of trapping. In the present paper, which extends our previous study of the static equilibria in this system (Puglisi and Truskinovsky, J. Mech. Phys. Solids (2000) 1), we analyze the behavior of a bi-stable chain in a soft device under quasi-static loading. We assume that the system is over-damped and explore the variety of available nonequilibrium transformation paths. In particular, we show that the “minimal barrier” strategy leads to the localization of the transformation in a single spring. Loaded periodically, our bi-stable chain exhibits finite hysteresis which depends on the height of the admissible barrier; the cold work/heat ratio in this model is a fixed constant, proportional to the Maxwell stress. Comparison of the computed inner and outer hysteresis loops with recent experiments on shape memory wires demonstrates good qualitative agreement. Finally we discuss a relation between the present model and the Preisach model which is a formal interpolation scheme for hysteresis, also founded on the idea of bi-stability.

Pull-in and wrinkling instabilities of electroactive dielectric actuators

We propose a model to analyse the insurgence of pull-in and wrinkling failures in electroactive thin films. We take into consideration both cases of voltage and charge control, the role of pre-stretch and the size of activated regions, which are all crucial factors in technological applications of electroactive polymers (EAPs). Based on simple geometrical and material assumptions we deduce an explicit analytical description of these phenomena, allowing a clear physical interpretation of different failure mechanisms such as the occurrence of pull-in and wrinkling. Despite our simple assumptions, the comparison with experiments shows a good qualitative and, interestingly, quantitative agreement. In particular our model shows, in accordance with experiments, the existence of different optimal pre-stretch values, depending on the choice of the actuating parameter of the EAP.

Electromechanical instability and oscillating deformations in electroactive polymer films

Based on an energetic approach, we analytically determine inhomogeneous equilibrium configurations of thin electroactive polymeric films of under assigned voltage. We show that our results are useful in the analysis of well known failure phenomena taking place in this type of devices. Moreover, we demonstrate that neglecting inhomogeneity effects may lead to a drastic overestimate of the activation performances.

Damage, Self-Healing, and Hysteresis in Spider Silks

In this article, we propose a microstructure-based continuum model to describe the material behavior of spider silks. We suppose that the material is composed of a soft fraction with entropic elasticity and a hard, damageable fraction. The hard fraction models the presence of stiffer, crystal-rich, oriented regions and accounts for the effect of softening induced by the breaking of hydrogen bonds. To describe the observed presence of crystals with different size, composition, and orientation, this hard fraction is modeled as a distribution of materials with variable properties. The soft fraction describes the remaining regions of amorphous material and is here modeled as a wormlike chain. During stretching, we consider the effect of bond-breaking as a transition from the hard- to the soft-material phase. As we demonstrate, a crucial effect of bond-breaking that accompanies the softening of the material is an increase in contour length associated with chains unraveling. The model describes also the self-healing properties of the material by assuming partial bond reconnection upon unloading. Despite its simplicity, the proposed mechanical system reproduces the main experimental effects observed in cyclic loading of spider silks. Moreover, our approach is amenable to two- or three-dimensional extensions and may prove to be a useful tool in the field of microstructure optimization for bioinspired materials.

Compression-induced failure of electroactive polymeric thin films

The onset of compression induces wrinkling in actuation devices based on electroactive polymer thin films, which leads to a sudden decrease in performances and, eventually, to failure. Inspired by the classical tension field theory for thin membranes, we provide a general framework for the analysis of the insurgence of in-plane compressions. Our main result is the analytical deduction of a voltage-dependent domain of tensile configurations in the principal stretches plane.

Catastrophic thinning of dielectric elastomers

We provide an energetic insight into the catastrophic nature of thinning instability in soft electroactive elastomers. This phenomenon is a major obstacle to the development of giant actuators, yet it is neither completely understood nor modeled accurately. In excellent agreement with experiments, we give a simple formula to predict the critical voltages for instability patterns; we model their shape and show that reversible (elastic) equilibrium is impossible beyond their onset. Our derivation is fully analytical, does not require finite element simulations, and can be extended to include prestretch and various material models.

Multiscale mechanics of macromolecular materials with unfolding domains

Abstract We propose a general multiscale approach for the mechanical behavior of three-dimensional networks of macromolecules undergoing strain-induced unfolding. Starting from a (statistically based) energetic analysis of the macromolecule unfolding strategy, we obtain a three-dimensional continuum model with variable natural configuration and an energy function analytically deduced from the microscale material parameters. The comparison with the experiments shows the ability of the model to describe the complex behavior, with residual stretches and unfolding effects, observed in different biological materials.

An energetic model for macromolecules unfolding in stretching experiments.

We propose a simple approach, based on the minimization of the total (entropic plus unfolding) energy of a two-state system, to describe the unfolding of multi-domain macromolecules (proteins, silks, polysaccharides, nanopolymers). The model is fully analytical and enlightens the role of the different energetic components regulating the unfolding evolution. As an explicit example, we compare the analytical results with a titin atomic force microscopy stretch-induced unfolding experiment showing the ability of the model to quantitatively reproduce the experimental behaviour. In the thermodynamic limit, the sawtooth force–elongation unfolding curve degenerates to a constant force unfolding plateau.