Printing non-Euclidean solids

Geometrically frustrated solids with non-Euclidean reference metric are ubiquitous in biology and are becoming increasingly relevant in technological applications. Often they acquire a targeted con- figuration of incompatibility through surface accretion of mass as in tree growth or dam construction. We use the mechanics of incompatible surface growth to show that geometrical frustration develop- ing during deposition can be fine-tuned to ensure a particular behavior of the system in physiological (or working) conditions. As an illustration, we obtain an explicit 3D printing protocol for arteries, which guarantees stress uniformity under inhomogeneous loading, and for explosive plants, allowing a complete release of residual elastic energy with a single cut. Interestingly, in both cases reaching the physiological target requires the incompatibility to have a topological (global) component.Comment: 5 pages, 4 figure

Compression-induced failure of electro-active polymeric thin films

The insurgence of compression induces wrinkling in actuation devices based on EAPs thin films leading to a sudden decrease of performances up to failure. Based on the classical tension field theory for thin elastic membranes, we provide a general framework for the analysis of the insurgence of in-plane compression in membranes of electroactive polymers (EAPs). Our main result is the deduction of a (voltage-dependent) domain in the stretch space which represents tensile configurations. Under the assumption of Mooney-Rivlin materials, we obtain that for growing values of the applied voltage the domain contracts, vanishing at a critical voltage above which the polymer is wrinkled for any stretch configuration. Our approach can be easily implemented in numerical simulations for more complex material behaviors and provides a tool for the analysis of compression instability as a function of the elastic moduli.Comment: (15 pages, 7 figures

Catastrophic thinning of dielectric elastomers

We provide a clear energetic insight into the catastrophic nature of the so-called creasing and pull-in instabilities in soft electro-active elastomers. These phenomena are ubiquitous for thin electro-elastic plates and are a major obstacle to the development of giant actuators; yet they are not completely understood nor modelled accurately. Here, in complete agreement with experiments, we give a simple formula to predict the voltage thresholds for these instability patterns and model their shape, and show that equilibrium is impossible beyond their onset. Our analysis is fully analytical, does not require finite element simulations, and can be extended to include pre-stretch and to encompass any material behaviour

Fine tuning the electro-mechanical response of dielectric elastomers

We propose a protocol to model accurately the electromechanical behavior of dielectric elastomer membranes using experimental data of stress-stretch and voltage-stretch tests. We show how the relationship between electric displacement and electric field can be established in a rational manner from this data. Our approach demonstrates that the ideal dielectric model, prescribing linearity in the purely electric constitutive equation, is quite accurate at low-to-moderate values of the electric field and that, in this range, the dielectric permittivity constant of the material can be deduced from stress-stretch and voltage-stretch data. Beyond the linearity range, more refined couplings are required, possibly including a non-additive decomposition of the electro-elastic energy. We also highlight that the presence of vertical asymptotes in voltage-stretch data, often observed in the experiments just prior to failure, should not be associated with strain stiffening effects, but instead with the rapid development of electrical breakdown

Orthogeriatrics in Italy: the Gruppo Italiano di Ortogeriatria (GIOG) audit on hip fractures in the elderly

The Gruppo Italiano di Ortogeriatria (GIOG) is an Italian study group promoted by three Italian Scientific Geriatric Societies with the aim of disseminating orthogeriatric methodology in Italy. In 2015 it has supported a multicenter web-based audit to collect data on functioning of Italian orthogeriatrics. The study, still ongoing, has enrolled until now 2577 cases of elderly patients undergoing surgery for hip fracture from 14 Italian orthogeriatric units. The population in question consists of markedly elderly and frail subjects, due to high prevalence of pre-existing functional deficit conditions, but it is also clinically complex; the most frequent fracture is intertrochanteric and the most performed surgery approach is intramedullary nail. This is the largest multicenter observational study conducted so far in Italy on elderly patients with hip fracture

A discrete model for layered growth

In this work we present a discrete model that captures the fundamental properties of additively manufactured solids in a minimal setting. The model is based on simplified kinematics and allows for the onset of incompatible deformations between discrete layers of an additively manufactured stack. Thanks to the discrete nature of the model, we obtain an averaged formulation of mechanical equilibrium for the growing stack, leading to closed-form solutions that are both analytically simple and physically transparent. In particular, we are able to explain the origin of residual stresses by the accumulation of incompatible deformations between adjacent layers. At the same time, we are able to formulate the technologically relevant inverse problem that provides the deposition protocol required to produce a desired state of internal stress in the manufactured stack. Another important aspect analyzed in the work is the role played by an ideal ``glue'' between the layers, whose presence is fundamental to prevent their sliding and whose mechanical behavior can quantitatively influence the final stress distribution in the stack. Although the model is an elementary approximation of additive manufacturing, its simplicity makes it possible to highlight how the controls exerted during deposition will have qualitative or quantitative effects on the final stress state of the stack. This understanding is crucial in shedding light on the complex mechanical behavior of additive manufactured solids.Comment: 25 pages, 10 figure

Taut domain analysis of transversely isotropic dielectric elastomer membranes

Actuation devices made of dielectric elastomers are prone to compression induced wrinkling instabilities, which can adversely affect their performance and may lead to device failure. On the other hand, wrinkles can be used constructively in certain applications demanding a controlled alternation of the surface morphology. The idea of taut states and the natural width under simple tension plays an important role in the analysis of compression generated instability (wrinkling). In case of electrically driven DE membranes, the domain of taut states in the plane of principal stretches is influenced substantially by the applied voltage and the film's constitutive properties. In the recent past, there has been an increasing interest in exploiting anisotropy in the material behavior of dielectric elastomers for improving their actuation performance. Spurred with these ongoing efforts, this paper presents a continuum mechanics based electromechanical model for predicting the thresholds on the domain of taut states of transversely isotropic planar dielectric elastomers. The developed analytical framework uses an amended energy function that accounts for the electromechanical coupling for a class of incompressible transversely isotropic dielectric membranes. The required expressions for the total Cauchy stress tensor and the associated principal stress components are evaluated utilizing the amended energy function. Finally, the concept of natural width under simple tension is implemented to obtained the nonlinear coupled electromechanical equation that evaluates the associated taut states domain of the transversely isotropic planar dielectric elastomers. Our results indicate that the extent of taut domain can be controlled by modifying the level and the principal direction of the transverse isotropy. The taut states domain for a particular level of applied electric field increases with increase in the anisotropy parameter, while the taut domains depleted with the increase in fiber orientations from 00to 900for an applied level of electrical loading. The fiber-reinforced wrinkle-tunable surfaces can be effectively designed and developed using the underlying analytical framework and the trends obtained in this study

Mechanical behavior of multi-cellular spheroids under osmotic compression

The internal and external mechanical environment plays an important role in tumorogenesis. As a proxy of an avascular early state tumor, we use multicellular spheroids, a composite material made of cells, extracellular matrix and permeating fluid. We characterize its effective rheology at the timescale of minutes to hours by compressing the aggregates with osmotic shocks and modeling the experimental results with an active poroelastic material that reproduces the stress and strain distributions in the aggregate. The model also predicts how the emergent bulk modulus of the aggregate as well as the hydraulic diffusion of the percolating interstitial fluid are modified by the preexisting active stress within the aggregate. We further show that the value of these two phenomenological parameters can be rationalized by considering that, in our experimental context, the cells are effectively impermeable and incompressible inclusions nested in a compressible and permeable matrix