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Michel Destrade

Publications and source records attributed to Michel Destrade.

At least 91 records · Page 5Linked to original sources
arXiv2018

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.

cond-mat.soft↗
arXiv2018

Finite bending and pattern evolution of the associated instability for a dielectric elastomer slab

We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental version. We first study the static finite bending deformation of the slab. We then derive the three-dimensional equations for the onset of small-amplitude wrinkles superimposed upon the finite bending. We use the surface impedance matrix method to build a robust numerical procedure for solving the resulting dispersion equations and determining the wrinkled shape of the slab at the onset of buckling. Our analysis is valid for dielectrics modeled by a general free energy function. We then present illustrative numerical calculations for ideal neo-Hookean dielectrics. In that case, we provide an explicit treatment of the boundary value problem of the finite bending and derive closed-form expressions for the stresses and electric field in the body. For the incremental deformations, we validate our analysis by recovering existing results in more specialized contexts. We show that the applied voltage has a destabilizing effect on the bending instability of the slab, while the effect of the axial load is more complex: when the voltage is applied, changing the axial loading will influence the true electric field in the body, and induce competitive effects between the circumferential instability due to the voltage and the axial instability due to the axial compression. We even find circumstances where both instabilities cohabit to create two-dimensional patterns on the inner face of the bent sector.

cond-mat.soft↗
arXiv2018

Wrinkles and creases in the bending, unbending and eversion of soft sectors

We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought beyond complete straightening to turn into eversion. We find that the suggested mathematical solution to these problems always exists and is unique when the solid is modelled as a homogeneous, isotropic, incompressible hyperelastic material with a strain-energy satisfying the strong ellipticity condition. We also provide explicit asympto-tic solutions for thin sectors. When the deformations are severe enough, the compressed side of the elastic material may buckle and wrinkles could then develop. We analyse in detail the onset of this instability for the Mooney-Rivlin strain energy, which covers the cases of the neo-Hookean model in exact non-linear elasticity and of third-order elastic materials in weakly non-linear elasticity. In particular the associated theoretical and numerical treatment allows us to predict the number and wavelength of the wrinkles. Guided by experimental observations we finally look at the development of creases, which we simulate through advanced finite element computations. In some cases the linearised analysis allows us to predict correctly the number and the wavelength of the creases, which turn out to occur only a few percent of strain earlier than the wrinkles.

cond-mat.soft↗
arXiv2018

Wrinkles in soft dielectric plates

We show that a smooth giant voltage actuation of soft dielectric plates is not easily obtained in practice. In principle one can exploit, through pre-deformation, the snap-through behavior of their loading curve to deliver a large stretch prior to electric breakdown. However, we demonstrate here that even in this favorable scenario, the soft dielectric is likely to first encounter the plate wrinkling phenomenon, as modeled by the onset of small-amplitude sinusoidal perturbations on its faces. We provide an explicit treatment of this incremental boundary value problem. We also derive closed-form expressions for the two limit cases of very thin membranes (with vanishing thickness) and of thick plates (with thickness comparable to or greater than the wavelength of the perturbation). We treat explicitly examples of ideal dielectric free energy functions (where the mechanical part is of the neo-Hookean, Mooney-Rivlin or Gent form) and of dielectrics exhibiting polarization saturation. Finally we make the link with the classical results of the Hessian electro-mechanical instability criterion and of Euler buckling for an elastic column.

cond-mat.soft↗
arXiv2016

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.

cond-mat.soft↗
arXiv2016

Non-invasive evaluation of skin tension lines with elastic waves

Background: Since their discovery by Karl Langer in the 19th Century, Skin Tension Lines (STLs) have been used by surgeons to decide the location and orientation of an incision. Although these lines are patient-specific, most surgeons rely on generic maps to determine their orientation. Beyond the imprecise pinch test, there remains no accepted method for determining STLs in vivo. Methods: (i) The speed of an elastic motion travelling radially on the skin of canine cadavers was measured with a commercial device called the Reviscometer. (ii) Similar to the original experiments conducted by Karl Langer, circular excisions were made on the skin and the geometric changes to the resulting wounds and excised samples were used to determine the orientation of STLs. Results: A marked anisotropy in the speed of the elastic wave travelling radially was observed. The orientation of the fastest wave was found to correlate with the orientation of the elongated wound (P<0.001, R^2 = 74%). Similarly, the orientation of fastest wave was the same for both in vivo and excised isolated samples, indicating that the STLs have a structural basis. Resulting wounds expanded by an average area of 9% (+16% along STL and -10% across) while excised skin shrunk by an average area of 33% (23% along STL and 10% across). Conclusion: Elastic surface wave propagation has been validated experimentally as a robust method for determining the orientation of STLs non-destructively and non-invasively. This study has implications for the identification of STLs and for the prediction of skin tension levels, both important factors in both human and veterinary reconstructive surgery.

physics.med-ph↗
arXiv2016

Methodical Fitting for Mathematical Models of Rubber-like Materials

A great variety of models can describe the non-linear response of rubber to uni-axial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three steps, which we delineate by relying on a simple formatting of the data, the so-called Mooney transform. First, the small-to-moderate regime, where the polymeric chains unfold easily and the Mooney plot is almost linear. Second, the strain-hardening regime, where blobs of bundled chains unfold to stiffen the response in correspondence to the "upturn" of the Mooney plot. Third, the limiting-chain regime, with a sharp stiffening occurring as the chains extend towards their limit. We provide strain-energy functions with terms accounting for each stage, that (i) give an accurate local and then global fitting of the data; (ii) are consistent with weak non-linear elasticity theory; and (iii) can be interpreted in the framework of statistical mechanics. We apply our method to Treloar's classical experimental data and also to some more recent data. Our method not only provides models that describe the experimental data with a very low quantitative relative error, but also shows that the theory of non-linear elasticity is much more robust that seemed at first sight.

cond-mat.soft↗
arXiv2015

Initial Stress Symmetry and Applications in Elasticity

An initial stress within a solid can arise to support external loads or from processes such as thermal expansion in inert matter or growth and remodelling in living materials. For this reason it is useful to develop a mechanical framework of initially stressed solids irrespective of how this stress formed. An ideal way to do this is to write the free energy density $Ψ= Ψ(\boldsymbol F, \boldsymbol τ)$ in terms of initial stress $\boldsymbol τ$ and the elastic deformation gradient $\boldsymbol F$. In this paper we present a new constitutive condition for initially stressed materials, which we call the initial stress symmetry (ISS). We focus on two consequences of this symmetry. First we examine how ISS restricts the free energy density $Ψ= Ψ(\boldsymbol F, \boldsymbol τ) $ and present two examples of $Ψ(\boldsymbol F, \boldsymbol τ)$ that satisfy ISS. Second we show that the initial stress can be derived from the Cauchy stress and the elastic deformation gradient. To illustrate we take an example from biomechanics and calculate the optimal Cauchy stress within an artery subjected to internal pressure. We then use ISS to derive the optimal target residual stress for the material to achieve after remodelling.

cond-mat.soft↗
arXiv2013

Some results on finite amplitude elastic waves propagating in rotating media

Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity provides such a framework for incompressible solids. Second: how can finite amplitude exact solutions be generated? It is seen that for some finite amplitude transverse waves in rotating incompressible elastic solids with general shear response, the solutions are obtained by reduction of the equations of motion to a system of ordinary differential equations equivalent to the system governing the central motion problem of classical mechanics. In the special case of circularly-polarized harmonic progressive waves, the dispersion equation is solved in closed form for a variety of shear responses, including nonlinear models for rubberlike and soft biological tissues. A fruitful analogy with the motion of a nonlinear string is pointed out.

cond-mat.soft↗
arXiv2013

Influence of Preservation Temperature on the Measured Mechanical Properties of Brain Tissue

The large variability in experimentally measured mechanical properties of brain tissue is due to many factors including heterogeneity, anisotropy, age dependence and post-mortem time. Moreover, differences in test protocols also influence these measured properties. This paper shows that the temperature at which porcine brain tissue is stored or preserved prior to testing has a significant effect on the mechanical properties of brain tissue, even when tests are conducted at the same temperatures. Three groups of brain tissue were stored separately for at least one hour at three different preservation temperatures, i.e., ice cold, room temperature (22C) and body temperature (37C), prior to them all being tested at room temperature (approx. 22C). Significant differences in the corresponding initial elastic shear modulus mu (Pa) (at various amounts of shear, K, i.e., 0-0.2) were observed. The initial elastic moduli were 1043 +/- 271 Pa, 714 +/- 210 Pa and 497 +/- 156 Pa (mean +/- SD) at preservation temperatures of ice cold, 22C and 37C, respectively. Based on this investigation, it is strongly recommended that brain tissue samples must be preserved at an ice-cold temperature prior to testing in order to minimize the difference between the measured in vitro test results and the in vivo properties. A by-product of the study is that simple shear tests allow for large, almost perfectly homogeneous deformation of brain matter.

cond-mat.soft↗
arXiv2013

Finite-amplitude inhomogeneous plane waves of exponential type in incompressible elastic materials

It is proved that elliptically-polarized finite-amplitude inhomogeneous plane waves may not propagate in an isotropic elastic material subject to the constraint of incompressibility. The waves considered are harmonic in time and exponentially attenuated in a direction distinct from the direction of propagation. The result holds whether the material is stress-free or homogeneously deformed.

cond-mat.soft↗
arXiv2013

Shear instability in skin tissue

We propose two toy-models to describe, predict, and interpret the wrinkles appearing on the surface of skin when it is sheared. With the first model, we account for the lines of greatest tension present in human skin by subjecting a layer of soft tissue to a pre-stretch, and for the epidermis by endowing one of the layer's faces with a surface tension. For the second model, we consider an anisotropic model for the skin, to reflect the presence of stiff collagen fibres in a softer elastic matrix. In both cases, we find an explicit bifurcation criterion, linking geometrical and material parameters to a critical shear deformation accompanied by small static wrinkles, with decaying amplitudes normal to the free surface of skin.

cond-mat.soft↗
arXiv2013

The explicit secular equation for surface acoustic waves in monoclinic elastic crystals

The secular equation for surface acoustic waves propagating on a monoclinic elastic half-space is derived in a direct manner, using the method of first integrals. Although the motion is at first assumed to correspond to generalized plane strain, the analysis shows that only two components of the mechanical displacement and of the tractions on planes parallel to the free surface are nonzero. Using the Stroh formalism, a system of two second order differential equations is found for the remaining tractions. The secular equation is then obtained as a quartic for the squared wave speed. This explicit equation is consistent with that found in the orthorhombic case. The speed of subsonic surface waves is then computed for twelve specific monoclinic crystals.

cond-mat.soft↗
arXiv2013

Circularly-polarized plane waves in a deformed Hadamard material

Small amplitude inhomogeneous plane waves propagating in any direction in a homogeneously deformed Hadamard material are considered. Conditions for circular polarization are established. The analysis relies on the use of complex vectors (or bivectors) to describe the slowness and the polarization of the waves. Generally, homogeneous circularly-polarized plane waves may propagate in only two directions, the directions of the acoustic axes, in a homogeneously deformed Hadamard material. For inhomogeneous circularly-polarized plane waves, the number of possibilities is far greater. They include an infinity of "transverse waves", as well as "longitudinal waves", and the superposition of "transverse waves" and "longitudinal waves", where "transverse" and "longitudinal" are used in the bivector sense. Each and every possibility of circular polarization is examined in turn, and explicit examples of solutions are given in every case.

cond-mat.soft↗
arXiv2013

The incompressible limit in linear anisotropic elasticity, with application to surface waves and elastostatics

Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to derive results for incompressible materials from those established for the compressible materials. As an illustration, the explicit secular equation is obtained for surface waves in incompressible monoclinic materials with the symmetry plane at x_3=0. This equation also covers the case of incompressible orthotropic materials. The displacements and stresses for surface waves are often expressed in terms of the elastic stiffnesses, which can be unbounded in the incompressible limit. An alternative formalism in terms of the elastic compliances presented recently by Ting is employed so that surface wave solutions in the incompressible limit can be obtained. A different formalism, also by Ting, is employed to study the solutions to two-dimensional elastostatic problems. In the special case of incompressible monoclinic material with the symmetry plane at x_3=0, one of the three Barnett-Lothe tensors S vanishes while the other two tensors H and L are the inverse of each other. Moreover, H and L are diagonal with the first two diagonal elements being identical. An interesting physical phenomenon deduced from this property is that there is no interpenetration of the interface crack surface in an incompressible bimaterial. When only the inplane deformation is considered, it is shown that the image force due to a line dislocation in a half-space or in a bimaterial depends only on the magnitude, not on the direction, of the Burgers vector.

cond-mat.soft↗
arXiv2013

Small-amplitude inhomogeneous plane waves in a deformed Mooney-Rivlin material

The propagation of small-amplitude inhomogeneous plane waves in an isotropic homogeneous incompressible Mooney--Rivlin material is considered when the material is maintained in a state of finite static homogeneous deformation. Disturbances of complex exponential type are sought and all propagating inhomogeneous solutions to the equations of motion are given, as well as the conditions for linear, elliptical, or circular polarization. % It is seen that a great variety of solutions arises. These include some original solutions, such as circularly-polarized plane waves which propagate with an arbitrary complex scalar slowness, or linearly-polarized waves for which the direction of propagation is not necessarily orthogonal to the direction of attenuation. % Throughout the paper, geometrical interpretations and explicit examples are presented.

cond-mat.soft↗
arXiv2013

Elastic interface acoustic waves in twinned crystals

A new type of Interface Acoustic Waves (IAW) is presented, for single-crystal orthotropic twins bonded symmetrically along a plane containing only one common crystallographic axis. The effective boundary conditions show that the waves are linearly polarized at the interface, either transversally or longitudinally. Then the secular equation is obtained in full analytical form using new relationships for the displacement-traction quadrivector at the interface. For Gallium Arsenide and for Silicon, it is found that the IAWs with transverse (resp. longitudinal) polarization at the interface are of the Stoneley (resp. leaky) type.

cond-mat.soft↗