Domenico De Tommasi

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.

Small strain and moderate rotation

Kinematical assumptions leading to the approximate theory of small strain accompanied by moderate rotations are discussed with reference to a three-dimensional continuous body. In particular, the relationship with Korns inequality is examined. It is found that for bounded bodies the coincidence of small strain and moderate rotation on subsets of non-zero volume measure is not possible. Two explicit examples are presented to illustrate this point.

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.

Incompressible Elastic Bodies with Non-Convex Energy under Dead-Load Surface Tractions

In this paper we study the equilibrium deformations of an incompressible elastic body with a non-convex strain energy function which is subjected to a homogeneous distribution of dead-load tractions. To determine the stable solutions we consider the mixtures of the phases which minimize the total energy density. In the special case of a trilinear material we discuss the stability of the equilibrium phases in detail. Finally, we show that multiphase solutions are possible when the surface loads correspond to a critical simple shear and we sketch their possible forms.

Pairwise Deformations of an Incompressible Elastic Body under Dead-Load Tractions

In this paper we obtain necessary conditions for the existence of pairwise deformations of an incompressible, isotropic elastic body subjected to a homogeneous distribution of dead-load tractions. Explicit restrictions on the boundary loads and on the surface of discontinuity between the phases are determined. For hyperelastic bodies with stored energy depending only on the first invariant of strain, we show that pairwise deformations under examination are necessarily (within a rigid rotation) plane deformations.

Phase Transformations in Isotropic Elastic Materials Induced by Shear Stress States

In this paper we study the stable two-phase deformations for an incompressible isotropic elastic body subjected to a homogeneous distribution of dead load tractions on the boundary with two opposite principal forces, whereas the third one is arbitrary. By considering a stored energy function with a nonconvex (rank-one) dependence on the first invariant of strain and an added linear dependence on the second invariant, we determine values of the boundary tractions which support stable two-phase deformations and discuss some kinematical properties of such solutions.

Elastic bodies reinforced with inextensible surfaces

The constraint of in-plane rigidity is examined within the general framework of the theory of internally constrained materials. It is shown that, for in-plane rigid materials, local strain and active stress are both defined by vectorial quantities. Representation formulae for the elastic response mapping are established in the cases of transverse isotropy and maximal symmetry, compatible with the constraint manifold. The equilibrium problem for an elastic body reinforced with parallel inextensible planes is also considered. In particular, universal solutions for bodies with maximal material symmetry are determined within the class of deformations which leave rigid every reinforcing plane.