arXiv subjects

Michel Destrade

Publications and source records attributed to Michel Destrade.

At least 19 recordsLinked to original sources

arXiv2026

Impact waves in soft bilayer tissues

In this study, we investigate impact-wave propagation in a pre-stressed compressible hyperelastic bilayer resting on a frictionless rigid substrate within the framework of nonlinear elasticity. Semi-analytical solutions for the transient displacement fields induced by localized surface impulses are derived using the Fourier-Laplace transform, and their long-time asymptotic behavior is obtained through the method of stationary phase. Finite element simulations are further performed to validate the theoretical predictions. The results establish a direct connection between characteristic features of the transient displacement fields and the group velocities of the guided-wave modes, revealing how dispersive propagation and modal contributions shape the observed waveforms. Three representative bilayer models corresponding to human articular cartilage, gingiva, and skin are then considered to examine the effects of variations in layer stiffness and thickness. The results show that structural and material variations can substantially modify the spatial distribution, arrival positions, and characteristic velocities of impact waves. In particular, higher-order modes can make significant contributions to the displacement response in certain parameter regimes, such that the dominant features of the wavefield cannot always be characterized by the fundamental mode alone. These findings demonstrate that transient-wave measurements contain mechanical information beyond that captured by a single characteristic surface-wave velocity and provide a theoretical basis for interpreting transient wavefields in multilayered soft materials and for future non-invasive mechanical characterization.

cond-mat.soft↗

arXiv2026

Direct stress imaging from shear wave propagation

Quantitative imaging of stress fields in heterogeneous solids remains challenging because stress is not directly measurable and is typically inferred from deformation using constitutive models. Here we present Acoustoelastic Imaging (AEI), a non-destructive framework for reconstructing stress fields from shear wave propagation. AEI exploits the acoustoelastic effect, whereby pre-existing stress modifies local wave dynamics, and formulates stress recovery as an inverse problem of the governing wave equations. Using full shear waveform inversion with physics-informed learning, AEI reconstructs wave-equation coefficients from full-field wave measurements, enabling estimation of stress magnitude and principal directions without explicit constitutive model specification or material-parameter calibration. We demonstrate sub-wavelength spatial resolution (< 0.28 {\lambda}) and accurate reconstruction of nonuniform stress fields in heterogeneous materials through numerical simulations and ultrasound shear wave elastography experiments. These results establish a general framework for high-resolution stress imaging and provide a route toward non-invasive mapping of internal mechanical states in complex materials and biological tissues.

physics.app-ph↗

arXiv2025

Electro-mechanical wrinkling of soft dielectric films bonded to hyperelastic substrates

Active control of wrinkling in soft film-substrate composites using electric fields is a critical challenge in tunable material systems. Here, we investigate the electro-mechanical instability of a soft dielectric film bonded to a hyperelastic substrate, revealing the fundamental mechanisms that enable on-demand surface patterning. For the linearized stability analysis, we use the Stroh formalism and the surface impedance method to obtain exact and sixth-order approximate bifurcation equations that signal the onset of wrinkles. We derive the explicit bifurcation equations giving the critical stretch and critical voltage for wrinkling, as well as the corresponding critical wavenumber. We look at scenarios where the voltage is kept constant and the stretch changes, and vice versa. We provide the thresholds of the shear modulus ratio $r_{\rm c}^0$ or pre-stretch $\lambda_{\rm c}^0$ below which the film-substrate system wrinkles mechanically, prior to the application of a voltage. These predictions offer theoretical guidance for practical structural design, as the shear modulus ratio $r$ and/or the pre-stretch $\lambda$ can be chosen to be slightly greater than $r_{\rm c}^0$ and/or $\lambda_{\rm c}^0$, so that the film-substrate system wrinkles with a small applied voltage. Finally, we simulate the full nonlinear behavior using the Finite Element method (FEniCS) to validate our formulas and conduct a post-buckling analysis. This work advances the fundamental understanding of electro-mechanical wrinkling instabilities in soft material systems. By enabling active control of surface morphologies via applied electric fields, our findings open new avenues for adaptive technologies in soft robotics, flexible electronics, smart surfaces, and bioinspired systems.

cond-mat.soft↗

arXiv2025

A Gaussian process approach for rapid evaluation of skin tension

Skin tension plays a pivotal role in clinical settings, it affects scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension or its natural pre-stretch. This study aims to utilise modern machine learning (ML) methods to develop a model that uses non-invasive measurements of surface wave speed to predict clinically useful skin properties such as stress and natural pre-stretch. A large dataset consisting of simulated wave propagation experiments was created using a simplified two-dimensional finite element (FE) model. Using this dataset, a sensitivity analysis was performed, highlighting the effect of the material parameters and material model on the Rayleigh and supersonic shear wave speeds. Then, a Gaussian process regression model was trained to solve the ill-posed inverse problem of predicting stress and pre-stretch of skin using measurements of surface wave speed. This model had good predictive performance (R2 = 0.9570) and it was possible to interpolate simplified parametric equations to calculate the stress and pre-stretch. To demonstrate that wave speed measurements could be obtained cheaply and easily, a simple experiment was devised to obtain wave speed measurements from synthetic skin at different values of pre-stretch. These experimental wave speeds agree well with the FE simulations and a model trained solely on the FE data provided accurate predictions of synthetic skin stiffness. Both the simulated and experimental results provide further evidence that elastic wave measurements coupled with ML models are a viable non-invasive method to determine in vivo skin tension.

physics.med-ph↗

arXiv2025

Non-invasive measurement of local stress inside soft materials with programmed shear waves

Mechanical stresses in soft materials across different length scales play a fundamental role in understanding the function of biological systems and in the use of artificial materials for engineering soft machines and biomedical devices. Yet it remains a great challenge to probe local mechanical stresses in situ in a non-invasive, non-destructive manner, in particular when the mechanical properties are unknown. To address this challenge, we propose an acoustoelastic imaging-based method to infer the local mechanical stresses in soft materials by measuring the speed of shear waves induced by custom-programmed acoustic radiation force. Using a medical ultrasound transducer to excite and track the shear waves remotely, we demonstrate the application of the method by imaging uniaxial stress and bending stress in an isotropic hydrogel, and the passive uniaxial stress in a skeletal muscle. These measurements were all done without the knowledge of the constitutive parameters of the materials. These examples indicate that our method will find broad applications, ranging from health monitoring of soft structures and machines, to the diagnosis of diseases that alter stresses in soft tissues.

cond-mat.soft↗

arXiv2025

Analysis of in-vivo skin anisotropy using elastic wave measurements and Bayesian modelling

In vivo skin exhibits viscoelastic, hyper-elastic and non-linear characteristics. It is under a constant non-equibiaxial tension in its natural configuration and is reinforced with oriented collagen fibers, giving rise to anisotropic behaviour. Understanding the complex mechanical behaviour of skin has relevance across many sectors including pharmaceuticals, cosmetics and surgery. However, there is a dearth of quality data characterizing human skin anisotropy in vivo. The available data is usually confined to limited population groups and/or limited angular resolution. Here, we use elastic waves travelling through the skin to obtain measurements from 78 volunteers from 3 to 93 years old. Using a Bayesian framework, we analyse the effect that age, gender and level of skin tension have on the skin anisotropy and stiffness. First, we propose a new measurement of anisotropy based on the eccentricity of angular data and conclude that it is a more robust measurement compared to the classic ``anisotropic ratio". We then find that in vivo skin anisotropy increases logarithmically with age, while the skin stiffness increases linearly along the direction of Langer Lines. We also conclude that gender does not significantly affect the skin anisotropy level, but does affect the overall stiffness, with males having stiffer skin on average. Finally, we find that skin tension significantly affects both the anisotropy and stiffness measurements, indicating that elastic wave measurements have promising applications in determining in vivo skin tension. In contrast to earlier studies, these results represent a comprehensive assessment of the variation of skin anisotropy with age and gender using a sizeable dataset and robust modern statistical analysis. This data has implications for the planning of surgical procedures and the adoption of universal cosmetic surgery practices for young or elderly patients.

physics.bio-ph↗

arXiv2025

The KP equation of plane elastodynamics

The propagation of nonlinear and dispersive waves in various materials can be described by the well-known Kadomtsev-Petviashvili (KP) equation, which is a (2+1)-dimensional partial differential equation. In this paper, we show that the KP equation can be used to describe the in-plane motion of compressible elastic solids with dispersion. Furthermore, a modified KP equation with cubic nonlinearity is obtained in the case of incompressible solids with dispersion. Then, several solutions of these partial differential equations are discussed and computed using a Fourier spectral method. In particular, both equations admit solitary wave solutions.

math-ph↗

arXiv2024

Nonlinear vibration and stability of a dielectric elastomer balloon based on a strain-stiffening model

Limiting chain extensibility is a characteristic that plays a vital role in the stretching of highly elastic materials. The Gent model has been widely used to capture this behaviour, as it performs very well in fitting stress-stretch data in simple tension, and involves two material parameters only. Recently, Anssari-Benam and Bucchi [Int. J. Non. Linear. Mech. 2021, 128, 103626] introduced a different form of generalised neo-Hookean model, focusing on the molecular structure of elastomers, and showed that their model encompasses all ranges of deformations, performing better than the Gent model in many respects, also with only two parameters. Here we investigate the nonlinear vibration and stability of a dielectric elastomer balloon modelled by that strain energy function. We derive the deformation field in spherical coordinates and the governing equations by the Euler-Lagrange method, assuming that the balloon retains its spherical symmetry as it inflates. We consider in turn that the balloon is under two types of voltages, a pure DC voltage and a DC voltage superimposed on an AC voltage. We analyse the dynamic response of the balloon and identify the influential parameters in the model. We find that the molecular structure of the material, as tracked by the number of segments in a single chain, can control the instability and the pull-in/snap-through critical voltage, as well as chaos and quasi-periodicity. The main result is that balloons made of materials exhibiting early strain-stiffening effects are more stable and less prone to generate chaotic nonlinear vibrations than softer materials, such as those modelled by the neo-Hookean strain-energy density function.

nlin.CD↗

arXiv2024

Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models

The Ogden model is often considered as a standard model in the literature for application to the deformation of brain tissue. Here we show that, in some of those applications, the use of the Ogden model leads to non-convexity of the strain-energy function and mis-prediction of the correct concavity of the experimental stress-stretch curves over a range of the deformation domain. By contrast, we propose a family of models which provides a favourable fit to the considered datasets while remaining free from the highlighted shortcomings of the Ogden model. While, as we discuss, those shortcomings might be due to the artefacts of the testing protocols, the proposed family of models proves impervious to such artefacts.

cond-mat.soft↗

arXiv2024

Local and Global Dynamics of a Functionally Graded Dielectric Elastomer Plate

We investigate the nonlinear vibrations of a functionally graded dielectric elastomer plate subjected to electromechanical loads. We focus on local and global dynamics in the system. We employ the Gent strain energy function to model the dielectric elastomer. The functionally graded parameters are the shear modulus, mass density, and permittivity of the elastomer, which are formulated by a common through-thickness power-law scheme. We derive the equation of motion using the Euler-Lagrange equations and solve it numerically with the Runge-Kutta method and a continuation-based method. We investigate the influence of the functionally graded parameters on equilibrium points, natural frequencies, and static/dynamic instability. We also establish a Hamiltonian energy method to detect safe regions of operating gradient parameters. Furthermore, we explore the effect of the functionally graded parameters on chaos and resonance by plotting several numerical diagrams, including time histories, phase portraits, Poincar\'e maps, largest Lyapunov exponent criteria, bifurcation diagram of Poincar\'e maps, and frequency-stretch curves. The results provide a benchmark for developing functionally graded soft smart materials.

cond-mat.soft↗

arXiv2024

Designing necks and wrinkles in inflated auxetic membranes

This article presents the potentiality of inflatable, functionally-graded auxetic membranes to produce wrinkles and necks. We obtain elastic instabilities at desired locations in axisymmetric membranes and with prescribed patterns in square membranes. First, we use an analytical approach to obtain a series of universal results providing insights into the formation of wrinkles and necks in inflated, axisymmetric membranes. For example, we prove analytically that necks and wrinkles may never overlap in pressurized, axially symmetric membranes. Second, we implement the relaxed strain energy of tension field theory into a Finite Element solver (COMSOL). By tuning spatial inhomogeneities of the material moduli, we corroborate our universal results, describe the onset of wrinkling in an averaged way, and also generate non-trivial instabilities at desired locations. This study on membranes with morphing or corrugation on demand has potential applications in Braille reading and haptics.

cond-mat.soft↗

arXiv2024

Wrinkling instability of 3D auxetic bilayers in tension

Bilayers, soft substrates coated with stiff films, are commonly found in nature with examples including skin tissue, vesicles, and organ membranes. They exhibit different types of instabilities when subjected to compression, depending on the contrast in material properties between the two components. In this work, we unravel the mechanisms behind wrinkling instabilities in auxetic bilayer systems under uniaxial tension. We find that a soft bilayer in tension can experience significant lateral contraction, and with sufficient contrast in Poisson ratios, compressive stresses may induce wrinkles aligned with the tensile direction. We analytically model the onset of wrinkles and validate our predictions using Finite Element simulations in ABAQUS. Our findings reveal that wrinkles occur when the Poisson ratio of the substrate is greater than that of the film. As the two Poisson ratios converge to a common value, the critical stretch for instability shoots up rapidly and the wrinkles disappear. We also confirm these results through asymptotic analysis. Using inverse analysis, we design film microstructures to achieve desired effective Poisson ratios and further validate the effective properties with the Finite Element code FEAP. We show that the critical stretch ratio for buckling in auxetic structures with microstructural patterns is in strong agreement with the homogenized model predictions. The proposed method has significant potential for controlling surface patterns in auxetic skin grafts and hydrogel organ patches under mechanical loads. Moreover, the asymptotic expressions for compressible bilayers developed in this work can also be applied under finite strain for buckling-based metrology.

cond-mat.mtrl-sci↗

arXiv2024

The elastic stored energy of initially strained, or stressed, materials: restrictions and third-order expansions

A large variety of materials, widely encountered both in engineering applications and in the biological realm, are characterised by a non-vanishing internal stress distribution, even in the absence of external deformations or applied forces. These initial stresses are due to initial strains or microstructural changes, such as thermal expansion, manufacturing processes, volumetric growth, remodelling, etc. A common constitutive choice for modelling such materials extends the classical approach in the field theory of continuum mechanics to include, explicitly, the initial stress or strain in the elastic stored energy function. Here, we discuss why these energy functions need to satisfy some restrictions to avoid unphysical behaviours, such as non-conservation of energy, {and we derive the required restrictions from the classical assumptions of elasticity.} To illustrate their need, we perform a rigorous asymptotic expansion for proving that these restrictions on stored energy functions that depend on the strain and initial stress are required for consistency with strain energy functions of classical third-order weakly nonlinear elasticity.

cond-mat.soft↗

arXiv2024

The generalised Mooney space for modelling the response of rubber-like materials

Soft materials such as rubbers, silicones, gels and biological tissues have a nonlinear response to large deformations, a phenomenon which in principle can be captured by hyperelastic models. The suitability of a candidate hyperelastic strain energy function is then determined by comparing its predicted response to the data gleaned from tests and adjusting the material parameters to get a good fit, an exercise which can be deceptive because of nonlinearity. Here we propose to generalise the approach of Rivlin and Saunders [Phil Trans A 243 (1951) 251-288] who, instead of reporting the data as stress against stretch, manipulated these measures to create the 'Mooney plot', where the Mooney-Rivlin model is expected to produce a linear fit. We show that extending this idea to other models and modes of deformation (tension, shear, torsion, etc.) is advantageous, not only (a) for the fitting procedure, but also to (b) delineate trends in the deformation which are not obvious from the raw data (and may be interpreted in terms of micro-, meso-, and macro-structures) and (c) obtain a bounded condition number \k{appa} over the whole range of deformation; a robustness which is lacking in other plots and spaces.

cond-mat.soft↗

arXiv2024

Plane-polarised finite-amplitude shear waves in deformed incompressible materials

We investigate how two finite-amplitude, transverse, plane body waves may be superposed to propagate in a deformed hyperelastic incompressible solid. We find that the equations of motion reduce to a well-determined system of partial differential equations, making the motion controllable for all solids. We find that in deformed Mooney-Rivlin materials, they may travel along any direction and be polarised along any transverse direction, an extension of a result by Boulanger and Hayes [Quart. J. Mech. Appl. Math. 45 (1992) 575]. Furthermore, their motion is governed by a linear system of partial differential equations, making the Mooney-Rivlin special in that respect. We select another model to show that for other materials, the equations are nonlinear. We use asymptotic equations to reveal the onset of nonlinearity for the waves, paying particular attention to how close the propagation direction is to the principal axes of pre-deformation.

math.AP↗

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

Models of fractional viscous stresses for incompressible materials

We present and review several models of fractional viscous stresses from the literature, which generalise classical viscosity theories to fractional orders by replacing total strain derivatives in time with fractional time derivatives. We also briefly introduce Prony-type approximations of these theories. Here we investigate the issues of material frame-indifference and thermodynamic consistency for these models and find that on these bases, some are physically unacceptable. Next we study elementary shearing and tensile motions, observing that some models are more convenient to use than others for the analysis of creep and relaxation. Finally, we compute the incremental stresses due to small-amplitude wave propagation in a deformed material, with a view to establish acousto-elastic formulas for prospective experimental calibrations.

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↗