arXiv subjects

Michel Destrade

Publications and source records attributed to Michel Destrade.

At least 37 records · Page 2Linked to original sources

arXiv2023

Singular travelling waves in soft viscoelastic solids of rate type

We consider shear wave propagation in soft viscoelastic solids of rate type. Based on objective stress rates, the constitutive model accounts for finite strain, incompressibility, as well as stress- and strain-rate viscoelasticity. The theory generalises the standard linear solid model to three-dimensional volume-preserving motions of large amplitude in a physically-consistent way. The nonlinear equations governing shear motion take the form of a one-dimensional hyperbolic system with relaxation. For specific objective rates of Cauchy stress (lower- and upper-convected derivatives), we study the propagation of acceleration waves and shock waves. Then we show that both smooth and discontinuous travelling wave solutions can be obtained analytically. We observe that the amplitude and velocity of steady shocks are very sensitive to variations of the stress relaxation time. Furthermore, the existence of steady shocks is conditional. Extension of these results to the case of multiple relaxation mechanisms and of the Jaumann stress rate is attempted. The analysis of simple shearing motions is more involved in these cases.

cond-mat.soft↗

arXiv2023

An atlas of the heterogeneous viscoelastic brain with local power-law attenuation synthesised using Prony-series

This review addresses the acute need to acknowledge the mechanical heterogeneity of brain matter and to accurately calibrate its local viscoelastic material properties accordingly. Specifically, it is important to compile the existing and disparate literature on attenuation power laws and dispersion to make progress in wave physics of brain matter, a field of research that has the potential to explain the mechanisms at play in diffuse axonal injury and mild traumatic brain injury in general. Currently, viscous effects in the brain are modelled using Prony-series, i.e., a sum of decaying exponentials at different relaxation times. Here we collect and synthesise the Prony-series coefficients appearing in the literature for twelve regions: brainstem, basal ganglia, cerebellum, corona radiata, corpus callosum, cortex, dentate gyrus, hippocampus, thalamus, grey matter, white matter, homogeneous brain, and for eight different mammals: pig, rat, human, mouse, cow, sheep, monkey and dog. Using this data, we compute the fractional-exponent attenuation power laws for different tissues of the brain, the corresponding dispersion laws resulting from causality, and the averaged Prony-series coefficients.

physics.med-ph↗

arXiv2022

Voltage-controlled topological interface states for bending waves in soft dielectric phononic crystal plates

The operating frequency range of passive topological phononic crystals is generally fixed and narrow, limiting their practical applications. To overcome this difficulty, here we design and investigate a one-dimensional soft dielectric phononic crystal (PC) plate system with actively tunable topological interface states via the mechanical and electric loads. We use nonlinear electroelasticity theory and linearized incremental theory to derive the governing equations. First we determine the nonlinear static response of the soft dielectric PC plate subjected to a combination of axial force and electric voltage. Then we study the motion of superimposed incremental bending waves. By adopting the Spectral Element Method, we obtain the dispersion relation for the infinite PC plate and the transmission coefficient for the finite PC plate waveguide. Numerical results show that the low-frequency topological interface state exists at the interface of the finite phononic plate waveguide with two topologically different elements. By simply adjusting the axial force or the electric voltage, an increase or decrease in the frequency of the topological interface state can be realized. Furthermore, applying the electric voltage separately on different elements of the PC plate waveguide is a flexible and smart method to tune the topological interface state in a wide range. These results provide guidance for designing soft smart wave devices with low-frequency tunable topological interface states.

cond-mat.soft↗

arXiv2022

Representing the stress and strain energy of elastic solids with initial stress and transverse texture anisotropy

Real-world solids, such as rocks, soft tissues, and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the `texture anisotropy'. This anisotropy can stem from preferential grain alignment in polycrystalline materials, aligned micro-cracks, or structural reinforcement, such as collagen bundles in biological tissues, steel rods in prestressed concrete and reinforcing fibres in composites. Here we establish a framework for initially stressed solids with transverse texture anisotropy. We consider that the strain energy per unit mass of the reference is an explicit function of the elastic deformation gradient, the initial stress tensor, and the texture anisotropy. We determine the corresponding constitutive relations and develop examples of nonlinear strain energies which depend explicitly on the initial stress and direction of texture anisotropy. As an application, we then employ these models to analyse the stress distribution of an inflated initially stressed cylinder with texture anisotropy, and the tension of a welded metal plate. We also deduce the elastic moduli needed to describe linear elasticity from stress reference with transverse texture anisotropy. As an example we show how to measure the stress with small-amplitude shear waves.

physics.class-ph↗

arXiv2022

Non-destructive mapping of stress, strain and stiffness of thin elastically deformed materials

Knowing the stress within a soft material is of fundamental interest to basic research and practical applications, such as soft matter devices, biomaterial engineering, and medical sciences. However, it is challenging to measure stress fields in situ in a non-invasive way. It becomes even more difficult if the mechanical properties of the material are unknown or altered by the stress. Here we present a robust non-destructive technique capable of measuring in situ stress and strain in elastically deformed thin films without the need to know their material properties. The technique is based on measuring elastic wave speeds, and then using a universal dispersion curve we derived for Lamb wave to predict the local stress and strain. Using optical coherence tomography, we experimentally verified the method for a rubber sheet, a cling film, and the leather skin of a musical instrument.

cond-mat.soft↗

arXiv2021

Wrinkling of soft magneto-active plates

Coupled magneto-mechanical wrinkling has appeared in many scenarios of engineering and biology. Hence, soft magneto-active (SMA) plates buckle when subject to critical uniform magnetic field normal to their wide surface. Here, we provide a systematic analysis of the wrinkling of SMA plates subject to an in-plane mechanical load and a transverse magnetic field?. We consider two loading modes: plane-strain loading and uni-axial loading, and two models of magneto-sensitive plates: the neo-Hookean ideal magneto-elastic model and the neo-Hookean magnetization saturation Langevin model. Our analysis relies on the theory of nonlinear magneto-elasticity and the associated linearized theory for superimposed perturbations. We derive the Stroh formulation of the governing equations of wrinkling, and combine it with the surface impedance method to obtain explicitly the bifurcation equations identifying the onset of symmetric and antisymmetric wrinkles. We also obtain analytical expressions of instability in the thin- and thick-plate limits. For thin plates, we make the link with classical Euler buckling solutions. We also perform an exhaustive numerical analysis to elucidate the effects of loading mode, load amplitude, and saturation magnetization on the nonlinear static response and bifurcation diagrams. We find that antisymmetric wrinkling modes always occur before symmetric modes. Increasing the pre-compression or heightening the magnetic field has a destabilizing effect for SMA plates, while the saturation magnetization enhances their stability. We show that the Euler buckling solutions are a good approximation to the exact bifurcation curves for thin plates.

cond-mat.soft↗

arXiv2021

A hyperbolic framework for shear sound beams in nonlinear solids

In soft elastic solids, directional shear waves are in general governed by coupled nonlinear KZK-type equations for the two transverse velocity components, when both quadratic nonlinearity and cubic nonlinearity are taken into account. Here we consider spatially two-dimensional wave fields. We propose a change of variables to transform the equations into a quasi-linear first-order system of partial differential equations. Its numerical resolution is then tackled by using a path-conservative MUSCL-Osher finite volume scheme, which is well-suited to the computation of shock waves. We validate the method against analytical solutions (Green's function, plane waves). The results highlight the generation of odd harmonics and of second-order harmonics in a Gaussian shear-wave beam.

cond-mat.soft↗

arXiv2021

Acousto-elasticity of Transversely Isotropic Incompressible Soft Tissues: Characterization of Skeletal Striated Muscle

Using shear wave elastography, we measure the changes in the wave speed with the stress produced by a striated muscle during isometric voluntary contraction. To isolate the behaviour of an individual muscle from complementary or antagonistic actions of adjacent muscles, we select the flexor digiti minimi muscle, whose sole function is to extend the little finger. To link the wave speed to the stiffness, we develop an acousto-elastic theory for shear waves in homogeneous, transversely isotropic, incompressible solids subject to uniaxial stress. We then provide measurements of the apparent shear elastic modulus along, and transversely to, the fibre axis for six healthy human volunteers of different age and sex. The results display a great variety across the six subjects. We find that the slope of the apparent shear elastic modulus along the fibre direction changes inversely to the maximum voluntary contraction (MVC) produced by the volunteer. We propose an interpretation of our results by introducing the S (slow) or F (fast) nature of the fibres, which harden the muscle differently and accordingly, produce different MVCs. This work opens the way to measuring the elastic stiffness of muscles in patients with musculoskeletal disorders or neurodegenerative diseases.

cond-mat.soft↗

arXiv2020

Bending control and instability of functionally graded dielectric elastomers

A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each plane parallel to the major surfaces will expand or contract to a different extent. Here we study the voltage-induced bending response of a functionally graded dielectric plate on the basis of the nonlinear theory of electro-elasticity, when both the elastic shear modulus and the electric permittivity change with the thickness coordinate. The theory is illustrated for a neo-Hookean electro-elastic energy function with the shear modulus and permittivity varying linearly across the thickness. We find that in general the bending angle increases with the potential difference provided the Hessian remains positive, but instability can arise as the potential difference increases and the Hessian vanishes. We derive the Hessian criterion for predicting the instability, and show how the material gradients can be tuned to control the bending shape, and to delay or promote the onset of the instability of the elastomer.

cond-mat.soft↗

arXiv2020

On the thermodynamic consistency of Quasi-Linear Viscoelastic models for soft solids

Originating in the field of biomechanics, Fung's model of quasi-linear viscoelasticity (QLV) is one of the most popular constitutive theories employed to compute the time-dependent relationship between stress and deformation in soft solids. It is one of the simplest models of nonlinear viscoelasticity, based on a time-domain integral formulation. In the present study, we consider the QLV model incorporating a single scalar relaxation function. We provide natural internal variables of state, as well as a consistent expression of the free energy to illustrate the thermodynamic consistency of this version of the QLV model. The thermodynamic formulation highlights striking similarities between QLV and the internal-variable models introduced by Holzapfel and Simo. Finally, the dissipative features of compressible QLV materials are illustrated in simple tension.

cond-mat.soft↗

arXiv2020

Straightening wrinkles

We consider the elastic deformation of a circular cylindrical sector composed of an incompressible isotropic soft solid when it is straightened into a rectangular block. In this process, the circumferential line elements on the original inner face of the sector are stretched while those on the original outer face are contracted. We investigate the geometrical and physical conditions under which the latter line elements can be contracted to the point where a localized incremental instability develops. We provide a robust algorithm to solve the corresponding two-point boundary value problem, which is stiff numerically. We illustrate the results with full incremental displacement fields in the case of Mooney-Rivlin materials and also perform an asymptotic analysis for thin sectors

cond-mat.soft↗

arXiv2020

Torsion instability of soft solid cylinders

The application of pure torsion to a long and thin cylindrical rod is known to provoke a twisting instability, evolving from an initial kink to a knot. In the torsional parallel-plate rheometry of stubby cylinders, the geometrical constraints impose zero displacement of the axis of the cylinder, preventing the occurrence of such twisting instability. Under these experimental conditions, wrinkles occur on the cylinder's surface at a given critical angle of torsion. Here we investigate this subclass of elastic instability--which we call torsion instability--of soft cylinders subject to a combined finite axial stretch and torsion, by applying the theory of incremental elastic deformation superimposed on finite strains. We formulate the incremental boundary elastic problem in the Stroh differential form, and use the surface impedance method to build a robust numerical procedure for deriving the marginal stability curves. We present the results for a Mooney-Rivlin material and study the influence of the material parameters on the elastic bifurcation.

cond-mat.soft↗

arXiv2020

Straightening: Existence, uniqueness and stability

One of the least studied universal deformations of incompressible nonlinear elasticity, namely the straightening of a sector of a circular cylinder into a rectangular block, is revisited here and, in particular, issues of existence and stability are addressed. Particular attention is paid to the system of forces required to sustain the large static deformation, including by the application of end couples. The influence of geometric parameters and constitutive models on the appearance of wrinkles on the compressed face of the block is also studied. Different numerical methods for solving the incremental stability problem are compared and it is found that the impedance matrix method, based on the resolution of a matrix Riccati differential equation, is the more precise.

cond-mat.soft↗

arXiv2020

Dominant negative Poynting effect for soft tissues

We identify three distinct shearing modes for simple shear deformations of transversely isotropic soft tissue which allow for both positive and negative Poynting effects (that is, they require compressive and tensile lateral normal stresses, respectively, in order to maintain simple shear). The positive Poynting effect is that usually found for isotropic rubber. Here, specialisation of the general results to three strain-energy functions which are quadratic in the anisotropic invariants, linear in the isotropic strain invariants and consistent with the linear theory suggests that there are two Poynting effects which can accompany the shearing of soft tissue: a dominant negative effect in one mode of shear and a relatively small positive effect in the other two modes. We propose that the relative inextensibility of the fibres relative to the matrix is the primary mechanism behind this large negative Poynting effect.

cond-mat.soft↗

arXiv2020

Gent models for the inflation of spherical balloons

We revisit an iconic deformation of non-linear elasticity: the inflation of a rubber spherical thin shell. We use the 3-parameter Mooney and Gent-Gent (GG) phenomenological models to explain the stretch-strain curve of a typical inflation, as these two models cover a wide spectrum of known models for rubber, including the Varga, Mooney-Rivlin, one-term Ogden, Gent-Thomas and Gent models. We find that the basic physics of inflation exclude the Varga, one-term Ogden and Gent-Thomas models. We find the link between the exact solution of non-linear elasticity and the membrane and Young-Laplace theories often used a priori in the literature. We compare the performance of both models on fitting the data for experiments on rubber balloons and animal bladder. We conclude that the GG model is the most accurate and versatile model on offer for the modelling of rubber balloon inflation.

cond-mat.soft↗

arXiv2020

A robust anisotropic hyperelastic formulation for the modelling of soft tissue

The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility condition is adopted the strain energy Ψof the HGO model is a function of one isotropic and two anisotropic deformation invariants. A compressible form (HGO-C model) is widely used in finite element simulations whereby the isotropic part of Ψis decoupled into volumetric and isochoric parts and the anisotropic part of Ψis expressed in terms of isochoric invariants. Here, by using three simple deformations (pure dilatation, pure shear and uniaxial stretch), we demonstrate that the compressible HGO-C formulation does not correctly model compressible anisotropic material behaviour, because the anisotropic component of the model is insensitive to volumetric deformation due to the use of isochoric anisotropic invariants. In order to correctly model compressible anisotropic behaviour we present a modified anisotropic (MA) model, whereby the full anisotropic invariants are used, so that a volumetric anisotropic contribution is represented. The MA model correctly predicts an anisotropic response to hydrostatic tensile loading, whereby a sphere deforms into an ellipsoid. It also computes the correct anisotropic stress state for pure shear and uniaxial deformation. To look at more practical applications, we developed a finite element user-defined material subroutine for the simulation of stent deployment in a slightly compressible artery. Significantly higher stress triaxiality and arterial compliance are computed when the full anisotropic invariants are used (MA model) instead of the isochoric form (HGO-C model).

cond-mat.soft↗

arXiv2020

Extreme softness of brain matter in simple shear

We show that porcine brain matter can be modelled accurately as a very soft rubber-like material using the Mooney-Rivlin strain energy function, up to strains as high as 60\%. This result followed from simple shear experiments performed on small rectangular fresh samples ($2.5$ cm$^3$ and $1.1$ cm$^3$) at quasi-static strain rates. They revealed a linear shear stress--shear strain relationship ($R^2> 0.97 $), characteristic of Mooney-Rivlin materials at large strains. We found that porcine brain matter is about 30 times less resistant to shear forces than a silicone gel. We also verified experimentally that brain matter exhibits the positive Poynting effect of nonlinear elasticity, and numerically that the stress and strain fields remain mostly homogeneous throughout the thickness of the samples in simple shear.

cond-mat.soft↗

arXiv2020

Morphology of residually-stressed tubular tissues: Beyond the elastic multiplicative decomposition

Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the location of the highest value of the residual hoop stress. We further validate the predictions of the incremental theory with finite element simulations, which allow us to go beyond this threshold and predict the shape, number and amplitude of the resulting creases.

cond-mat.soft↗