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The final size and shape of organs results from volume expansion by growth and shape changes by contractility. Complex morphologies arise from differences in growth rate between tissues. We address here how differential growth drives epithelial thickening and doming during the morphogenesis of the growing Drosophila wing imaginal disc. We report that 3D morphology results from elastic deformation due to differential growth between the epithelial cell layer and its enveloping extracellular matrix (ECM). Furthermore, the ECM envelope exhibits differential growth anisotropy (i.e. anisotropic expansion in 3D), growing in-plane on one side, but out of plane on the other side. The elasticity, anisotropy and morphogenesis is fully captured by a mechanical bilayer model. Moreover, differential expression of the Matrix metalloproteinase MMP2 controls growth anisotropy of the two ECM layers. This study shows that the ECM is a controllable mechanical constraint whose intrinsic growth anisotropy directs tissue morphogenesis in a developing organ.

Summary In the framework of linear piezoelectric ceramics, we study the deformations of a circular infinite hollow cylinder, subjected to a potential difference between the inner and outer surfaces. When the poling direction is perfectly aligned with the cylinder axis, the solution to this problem is a trivial axisymmetric anti-plane state. However, when the poling direction has an offset angle with respect to the cylinder axis, the corresponding behavior becomes more complex, with the anti-plane state coupled to an in-plane, potentially non axisymmetric, deformation. In this work, we show that this structural coupling, due to the poling direction, can be fruitfully exploited to achieve non-standard actuation and sensing properties, like the possibility to generate a torque under axially symmetric electromechanical controls.

Voltage controlled dielectric membranes exhibit two fundamental types of instability, strongly affecting their performances: the occurrence of wrinkling, which is due to membranal compressive stresses, and the onset of pull-in, a catastrophic thinning localisation that preludes electrical breakdown. In this manuscript we provide a unifying energetic description of both instabilities for large, out-of-plane and inhomogeneous deformations. By using the ideas of relaxation and regularisation of the energy, originally proposed by Pipkin (1986) and Hilgers and Pipkin (1992) for purely elastic membranes, we show that the onset and development of wrinkling can be effectively described by the relaxed electroelastic energy. For axially symmetric membranes and neo-Hookean materials, we show that pull-in corresponds to failure of the strong ellipticity condition of the regularised electroelastic energy, thus extending to out-of-plane deformations the validity of a previous estimate for planar systems (Zurlo et al., 2017). In agreement with ubiquitous experimental evidence, we also show that wrinkled states are always stable below the pull-in voltage. Our theoretical findings are assessed by the comparison with experiments on out-of-plane, voltage-actuated annular membranes, showing good agreement both in terms of description of wrinkled states, and for the prediction of the pull-in instability.

Intuition suggests that twisting a cylinder will shorten it, but here it is shown that for a cylinder of an incompressible material, like rubber, twisting will always produce elongation. This work was supported by the Irish Research Council (Government of Ireland Postgraduate Scholarship GOIPG/ 2018/82) and by the French Embassy in Ireland. G.Z. gratefully acknowledges the support of the Italian Association of Mathematical Physics (G.N.F.M. – Gruppo Nazionale di Fisica Matematica). The authors thank Yangkun Du for most helpful discussions. peer-reviewed

The accumulation of residual stress during welding and additive manufacturing is an important effect that can significantly anticipate the workpiece failure. In this work we exploit the physical and analytical transparency of a 1.5D model to show that the deposition of thermally expanded material onto an elastic substrate leads to the accumulation of strain incompatibility. This field, which is the source of residual stress in the system, introduces memory of the construction history even in the absence of plastic deformations. The model is then applied to describe the onset and the progression of residual stresses during deposition, their evolution upon cooling, and the fundamental role played by the velocity of the moving heat source.

Surface growth is a crucial component of many natural and artificial processes, from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility, leading to residual stresses and triggering various instabilities. In a recent paper [G. Zurlo and L. Truskinovsky, Phys. Rev. Lett. 119, 048001 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.048001] we presented a linearized elasticity theory of incompatible surface growth, which provides a quantitative link between deposition protocols and postgrowth states of stress. Here we extend this analysis to account for both physical and geometrical nonlinearities of an elastic solid. This development reveals the shortcomings of the linearized theory, in particular its inability to describe kinematically confined surface growth and to account for growth-induced elastic instabilities.

International audience; The internal and external mechanical environment plays an important role in tumorogenesis. As a proxy of an avas-cular 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.

Electroactive polymer energy harvesters are promising devices for the conversion of mechanical work to electrical energy. The performances of these devices are strongly dependent on the mechanical response of the polymeric material and on the type of electromechanical cycle, and these are limited by the occurrence of dielectric breakdown, compression induced wrinkling and electromechanical instability (pull-in). To identify the optimal electromechanical cycle that complies with all of these limitations, we set-up and solve a constraint optimization problem and we critically discuss the influence of material behavior of the polymer in the optimal performances of the energy harvesting device. Finally, we show that if the rate-independent dissipative behavior of the polymer (Mullins effect) is neglected, the optimization procedure may lead to quite unsatisfactory predictions: by making reference to explicit experimental data from literature we show that an optimal harvesting cycle deduced by neglecting the Mullins effect is far from being optimal when this is taken in consideration. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 1303–1314

Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper we extend the recently proposed stress-space-centered theory of surface growth (PRL 119, 048001, 2017) by shifting the focus towards growth induced strains. To illustrate the new development we present several analytically tractable examples. The paper is dedicated to the memory of Gerard Maugin, a scientific visionary.

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 figures

In this paper we present a model for the description of rate-independent hysteresis in Electroactive Polymers (EAPs). Our analysis is based on a model proposed by the authors for the description of damage and healing effects in polymeric materials and on a variational formulation for the resulting electromechanical equilibrium problem. The analysis of the class of equibiaxial strain, relevant for many actuation and energy harvesting devices, evidences that the model is effective and computationally efficient. The model shows a significant agreement with important experimental phenomena observed in EAP devices.

In this work we study the onset of inhomogeneous deformations in thin electroactive polymers (EAPs) under voltage control. In order to account for the regularizing effects due both to the constitutive nature of the film and to its mechanical interaction with the compliant electrodes, we introduce a nonlocal energy term depending on the second gradient of deformation. We prove that very small nonlocal effects are sufficient to find realisticinhomogeneous deformations at the onset of the bifurcation, which are characterized by periodic thickness undulations with finite wavelength. Finally we prove that strong regularizing effects can suppress the onset of inhomogeneous de

In this work, some implications of a recent model for the mechanical behavior of biological membranes (Deseri et al. in Continuum Mech Thermodyn 20(5):255-273, 2008) are exploited by means of a prototypical one-dimensional problem. We show that the knowledge of the membrane stretching elasticity permits to establish a precise connection among surface tension, bending rigidities and line tension during phase transition phenomena. For a specific choice of the stretching energy density, we evaluate these quantities in a membrane with coexistent fluid phases, showing a satisfactory comparison with the available experimental measurements. Finally, we determine the thickness profile inside the boundary layer where the order-disorder transition is observed.

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.

Based on physically meaningful choice of the strain measures, we study the equilibrium and stability of an inflated spherical membrane. First, we obtain general results deduced by global geometric properties and then we analyze the possibility of inhomogeneous configurations. The stability analysis shows that under special constitutive assumptions the global energy minimum can be attained by inhomogeneous spherical configurations that we analytically describe. We argue that these deformations can reproduce well-known experimental results.

Based on the choice of two physically meaningful strain measures, we study necessary and sufficient conditions for strong ellipticity of the equilibrium equations for two-dimensional isotropic hyperelastic bodies. Specifically, we show, depending on the values of the derivatives of the energy function, that strong ellipticity is equivalent to a single condition with a clear physical interpretation.

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 the electric field can be established in a rational manner from these 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. Published by AIP Publishing. The work of T.L. was supported by the NSFC (No. 11772249). G.Z. gratefully acknowledges the hospitality of the PMMH-ESPCI ParisTech and the support of the Italian GNFM (Gruppo Nazionale di Fisica Matematica). The authors thank the organisers of the 2016 EMI International Conference of ASCE in Metz, France, where preliminary ideas for this paper were discussed. They also thank Ruisen Yang for providing some of the experimental data in Fig.1. peer-reviewed

A new free energy for thin biomembranes depending on chemical composition, degree of order and membranal-bending deformations is derived in this paper. This is a result of constitutive and geometric assumptions at the three-dimensional level. The enforcement of a new symmetry group introduced in (Deseri et al., in preparation) and a 3D--2D dimension reduction procedure are among the ingredients of our methodology. Finally, the identification of the lower order term of the energy (i.e. the membranal contribution) on the basis of a bottom-up approach is performed; this relies upon standard statistical mechanics calculations. The main result is an expression of the biomembrane free energy density, whose local and non-local counterparts are weighted by different powers of the bilayer thickness. The resulting energy exhibits three striking aspects: (i) the local (purely membranal) energy counterpart turns out to be completely determined through the bottom-up approach mentioned above, which is based on experimentally available information on the nature of the constituents; (ii) the non-local energy terms, that spontaneously arise from the 3D--2D dimension reduction procedure, account for both bending and non-local membranal effects; (iii) the non-local energy contributions turn out to be uniquely determined by the knowledge of the membranal energy term, which in essence represents the only needed constitutive information of the model. It is worth noting that the coupling among the fields appearing as independent variables of the model is not heuristically forced, but it is rather consistently delivered through the adopted procedure.

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.

By means of a bifurcation analysis we show the onset of inhomogeneous equilibrium configurations in thin electroelastic polymeric films under assigned voltage. The resulting activation threshold decreases the diffusely adopted value obtained under the assumption of homogeneous deformations. We argue that the bifurcated inhomogeneous solution describes experimentally observed localization effects.

Actuation devices based on dielectric elastomers, typically exhibit various kinds of instability which may determine a decrease of performances and, eventually, the device failure. In this work we focus on wrinkling instabilities for polymer films subjected to an electric field. The main result is the definition of a domain of taut states in the plane of principal stretches strongly dependent on the applied voltage and on the constitutive properties of the polymer film. We discuss these features, crucial in the perspective of electroactive materials design, through simple boundary value problems for Neo-Hookean and Ogden materials.

Thickness non-uniformities in electrostatic capacitors and in electroactive polymers – arising from manufacturing processes or electromechanical induced inhomogeneous deformations – may lead to drastic charge and electric field localizations and, ultimately, to an anticipated device failure. Based on a geometric interpretation of the Gauss equation enlightening the effect of the electrode curvature, we obtain an analytic expression of the electric field and of the surface charge density localization for non perfectly planar capacitors with symmetric thickness non-uniformities. The efficiency of the model is exploited by analyzing specific boundary value problems of technological interest.

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., (15 pages, 7 figures)

Inflation experiments on thin rubber-like balloons show a complex, history-dependent hysteretic behavior, important for many technological applications. Typically, this is ascribed to the occurrence of damage processes at the micro-scale level. The experimental pressure–strain and stress–strain responses [Johnson, M.A., Beatty, F.M., 1995. The Mullins effect in equibiaxial extension and its influence on the inflation of a balloon. Int. J. Eng. Sci. 33(2), 223–245], suggest that for successive cyclic experiments also the occurrence of healing for previously damaged material may play a crucial role (see [ Diani, J., Fayolle, B., Gilormini, P., 2009. A review on the Mullins effect, Eur. Polym. J. 45, 601–612 ] and references therein). In this work we apply a recently proposed, micro-structure-based model for damage and healing effects in rubber-like materials to the inflation problem of a thin spherical balloon. The model, while keeping a computational efficiency, is shown to be in a significant qualitative agreement with the available experimental results.

Electromechanical harvesters based on dielectric electroactive polymers are promising devices for the production of electrical energy by the conversion of abundant sources of mechanical work available in Nature. However, severe limitations to the performance of these devices arise from various sources of dissipation and failure of the polymeric material. By making use of an energetic approach, we establish a direct and quantitative connection between the Mullins effect taking place in the polymeric material and the harvesting efficiency, showing the prominent role of rate-independent effects in the hysteretic behavior of electromechanical harvesters.

Based on an energy minimization approach, we analyse the elastic deformations of a thin electroactive polymer (EAP) film sandwiched by two elastic electrodes with non-negligible stiffness. We analytically show the existence of a critical value of the electrode voltage for which non-homogeneous solutions bifurcate from the homogeneous equilibrium state, leading to the pull-in phenomenon. This threshold strongly decreases the limit value proposed in the literature considering only homogeneous deformations. We explicitly discuss the influence of geometric and material parameters together with boundary conditions in the attainment of the different failure modes observed in EAP devices. In particular, we obtain the optimum values of these parameters leading to the maximum activation performances of the device.

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.