arXiv subjects

Michel Destrade

Publications and source records attributed to Michel Destrade.

At least 55 records · Page 3Linked to original sources

arXiv2020

Influence of initial residual stress on growth and pattern creation for a layered aorta

Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stress-free initial state, is widely used to explain the creation and evolution of growth-induced residual stress and the resulting changes in shape, and to model how growing bio-tissues such as arteries and solid tumors develop a strategy of pattern creation according to geometrical and material parameters. This modelling provides promising avenues for designing and directing some appropriate morphology of a given tissue or organ and achieve some targeted biomedical function. In this paper, we rely on a modified, augmented theory to reveal how we can obtain growth-induced residual stress and pattern evolution of a layered artery by starting from an existing, non-zero initial residual stress state. We use experimentally determined residual stress distributions of aged bi-layered human aortas and quantify their influence by a magnitude factor. Our results show that initial residual stress has a more significant impact on residual stress accumulation and the subsequent evolution of patterns than geometry and material parameters. Additionally, we provide an essential explanation for growth-induced patterns driven by differential growth coupled to an initial residual stress. Finally, we show that initial residual stress is a readily available way to control growth-induced pattern creation for tissues and thus may provide a promising inspiration for biomedical engineering.

cond-mat.soft↗

arXiv2020

Actively controllable topological phase transition in phononic beam systems

Topological insulators, which allow edge or interface waves but forbid bulk waves, have revolutionized our scientific cognition of acoustic/elastic systems. Due to their nontrivial topological characteristics, edge (interface)waves are topologically protected against defects and disorders. This superior and unique characteristic could lead to a wealth of new opportunities in applications of quantum and acoustic/elastic information processing. However, current acoustic/elastic topological insulators are still at an infancy stage where the theory and prediction only work in laboratories and there are still many problems left open before promoting their practical applications. One of the apparent disadvantages is their narrow working frequency range, which is the main concern in this paper. We design a one-dimensional phononic beam system made of a homogeneous epoxy central beam sandwiched by two homogeneous piezoelectric beams, and covered with extremely thin electrodes, periodically and separately placed. These electrodes are connected to external electric circuits with negative capacitors. We show that a topological phase transition can be induced and tuned by changing the values of the negative capacitors. It follows that the working frequency of the topologically protected interface mode can be widely changed, such that the working frequency range of the topological insulator can be considerably `broadened'. This intelligent topological device may also find wide applications in intelligent technologies that need controllable information processing of high precision.

physics.app-ph↗

arXiv2020

Prescribing patterns in growing tubular soft matter by initial residual stress

Initial residual stress is omnipresent in biological tissues and soft matter, and can affect growth-induced pattern selection significantly. Here we demonstrate this effect experimentally by letting soft tubes grow in the presence or absence of initial residual stress and by observing different growth pattern evolutions. These experiments motivate us to model the mechanisms at play when a growing bilayer tubular organ spontaneously displays buckling patterns on its inner surface. We demonstrate that not only differential growth, geometry and elasticity, but also initial residual stress distribution, exert a notable influence on these pattern phenomena. Prescribing an initial residual stress distribution offers an alternative or a more effective way to implement pattern selection for growable bio-tissues or soft matter. The results also show promise for the design of 4D bio-mimic printing protocols or for controlling hydrogel actuators.

cond-mat.soft↗

arXiv2020

Strain energy function for isotropic non-linear elastic incompressible solids with linear finite strain response in shear and torsion

We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion deformations. It is inclusive of the well-known neo-Hookean and the Mooney-Rivlin models, but also can accommodate other terms, as certain arbitrary functions of the principal strain invariants. Effectively, the extra terms can be used to account for several non-linear effects observed experimentally but not captured by the neo-Hookean and Mooney-Rivlin models, such as strain stiffening effects due to limiting chain extensibility.

cond-mat.soft↗

arXiv2020

Electrostatically tunable axisymmetric vibrations of soft electro-active tubes

Due to their unique electromechanical coupling properties, soft electro-active (SEA) resonators are actively tunable, extremely suitable, and practically important for designing the next-generation acoustic and vibration treatment devices. In this paper, we investigate the electrostatically tunable axisymmetric vibrations of SEA tubes with different geometric sizes. We consider both axisymmetric torsional and longitudinal vibrations for an incompressible SEA cylindrical tube under inhomogeneous biasing fields induced by radial electric voltage and axial pre-stretch. We then employ the state-space method, which combines the state-space formalism in cylindrical coordinates with the approximate laminate technique, to derive the frequency equations for two separate classes of axisymmetric vibration of the tube subjected to appropriate boundary conditions. We perform numerical calculations to validate the convergence and accuracy of the state-space method and to illuminate that the axisymmetric vibration characteristics of SEA tubes may be tuned significantly by adjusting the electromechanical biasing fields as well as altering the tube geometry. The reported results provide a solid guidance for the proper design of tunable resonant devices composed of SEA tubes

cond-mat.soft↗

arXiv2020

The effect of an exterior electric field on the instability of dielectric plates

We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem of superimposed, inhomogeneous small-amplitude wrinkles, signalling the onset of instability. We decouple the resulting bifurcation equation into symmetric and antisymmetric modes. For a neo-Hookean dielectric plate, we show that a potential difference between the electrodes can induce a thinning of the plate and thus an increase of its planar area, similar to the scenarios encountered when there is no silicone oil. However, we also find that, depending on the material and geometric parameters, an increasing applied voltage can also lead to a thickening of the plate, and thus a shrinking of its area. In that scenario, Hessian instability and wrinkling bifurcation may then occur spontaneously once some critical voltages are reached.

cond-mat.soft↗

arXiv2020

Wrinkles in the opening angle method

We investigate the stability of the deformation modeled by the opening angle method, often used to give a measure of residual stresses in arteries and other biological soft tubular structures. Specifically, we study the influence of stiffness contrast, dimensions and inner pressure on the onset of wrinkles when an open sector of a soft tube, coated with a stiffer film, is bent into a full cylinder. The tube and its coating are made of isotropic, incompressible, hyperelastic materials. We provide a full analytical exposition of the governing equations and the associated boundary value problem for the large deformation and for the superimposed small-amplitude wrinkles. For illustration, we solve them numerically with a robust algorithm in the case of Mooney-Rivlin materials. We confront the results to experimental data that we collected for soft silicone sectors. We study the influence of axial stretch and inner pressure on the stability of closed-up coated tubes with material parameters comparable with those of soft biological tubes such as arteries and veins, although we do not account for anisotropy. We find that the large deformation described in the opening angle method does not always exist, as it can become unstable for certain combinations of dimensions and material parameters.

cond-mat.soft↗

arXiv2020

Oblique wrinkles

We prove theoretically that when a soft solid is subjected to an extreme deformation, wrinkles can form on its surface at an angle that is oblique to a principal direction of stretch. These oblique wrinkles occur for a strain that is smaller than the one required to obtain wrinkles normal to the direction of greatest compression. We go on to explain why they will probably never be observed in real-world experiments.

cond-mat.soft↗

arXiv2020

Electrothermal equivalent three-dimensional Finite Element Model of a single neuron

Objective: We propose a novel approach for modelling the inter-dependence of electrical and mechanical phenomena in nervous cells, by using electro-thermal equivalences in finite element (FE) analysis so that existing thermo-mechanical tools can be applied. Methods: First, the equivalence between electrical and thermal properties of the nerve materials is established, and results of a pure heat conduction analysis performed in Abaqus CAE Software 6.13-3 are validated with analytical solutions for a range of steady and transient conditions. This validation includes the definition of equivalent active membrane properties that enable prediction of the action potential. Then, as a step towards fully coupled models, electromechanical coupling is implemented through the definition of equivalent piezoelectric properties of the nerve membrane using the thermal expansion coefficient, enabling prediction of the mechanical response of the nerve to the action potential. Results: Results of the coupled electro-mechanical model are validated with previously published experimental results of deformation for the squid giant axon, crab nerve fibre and garfish olfactory nerve fibre. Conclusion: A simplified coupled electro-mechanical modelling approach is established through an electro-thermal equivalent FE model of a nervous cell for biomedical applications. Significance: One of the key findings is the mechanical characterization of the neural activity in a coupled electro-mechanical domain, which provides insights into the electromechanical behaviour of nervous cells, such as thinning of the membrane. This is a first step towards modelling 3D electromechanical alteration induced by trauma at nerve bundle, tissue and organ levels.

physics.app-ph↗

arXiv2020

At least three invariants are necessary to model the mechanical response of incompressible, transversely isotropic materials

The modelling of off-axis simple tension experiments on transversely isotropic nonlinearly elastic materials is considered. A testing protocol is proposed where normal force is applied to one edge of a rectangular specimen with the opposite edge allowed to move laterally but constrained so that no vertical displacement is allowed. Numerical simulations suggest that this deformation is likely to remain substantially homogeneous throughout the specimen for moderate deformations. It is therefore further proposed that such tests can be modelled adequately as a homogenous deformation consisting of a triaxial stretch accompanied by a simple shear. Thus the proposed test should be a viable alternative to the standard biaxial tests currently used as material characterisation tests for transversely isotropic materials in general and, in particular, for soft, biological tissue. A consequence of the analysis is a kinematical universal relation for off-axis testing that results when the strain-energy function is assumed to be a function of only one isotropic and one anisotropic invariant, as is typically the case. The universal relation provides a simple test of this assumption, which is usually made for mathematical convenience. Numerical simulations also suggest that this universal relation is unlikely to agree with experimental data and therefore that at least three invariants are necessary to fully capture the mechanical response of transversely isotropic materials.

cond-mat.soft↗

arXiv2020

Deficiencies in numerical models of anisotropic nonlinearly elastic materials

Incompressible nonlinearly hyperelastic materials are rarely simulated in Finite Element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial Finite Element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a `compressibility parameter' (or `penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a `bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in `Poisson's ratio' close to the perfect incompressibility limit of 1/2 are made.

cond-mat.soft↗

arXiv2020

Counter-intuitive results in acousto-elasticity

We present examples of body wave and surface wave propagation in deformed solids where the slowest and the fastest waves do not travel along the directions of least and greatest stretch, respectively. These results run counter to commonly accepted theory, practice, and implementation of the principles of acousto-elasticity in initially isotropic solids. For instance we find that in nickel and steel, the fastest waves are along the direction of greatest compression, not greatest extension (and vice-versa for the slowest waves), as soon as those solids are deformed. Further, we find that when some materials are subject to a small-but-finite deformations, other extrema of wave speeds appear in non-principal directions. Examples include nickel, steel, polystyrene, and a certain hydrogel. The existence of these ``oblique'', non-principal extremal waves complicates the protocols for the non-destructive determination of the directions of extreme strains.

cond-mat.soft↗

arXiv2020

Electro-mechanical response of a 3D nerve bundle model to mechanical loads leading to axonal injury

Objective: Traumatic brain injuries and damage are major causes of death and disability. We propose a 3D fully coupled electro-mechanical model of a nerve bundle to investigate the electrophysiological impairments due to trauma at the cellular level. Methods: The coupling is based on a thermal analogy of the neural electrical activity by using the finite element software Abaqus CAE 6.13-3. The model includes a real-time coupling, modulated threshold for spiking activation and independent alteration of the electrical properties for each 3-layer fibre within a nerve bundle as a function of strain. Results: Results of the coupled electro-mechanical model are validated with previously published experimental results of damaged axons. Here, the cases of compression and tension are simulated to induce (mild, moderate and severe) damage at the nerve membrane of a nerve bundle, made of four fibres. Changes in strain, stress distribution, and neural activity are investigated for myelinated and unmyelinated nerve fibres, by considering the cases of an intact and of a traumatized nerve membrane. Conclusion: A fully coupled electro-mechanical modelling approach is established to provide insights into crucial aspects of neural activity at the cellular level due to traumatic brain injury. Significance: One of the key findings is the 3D distribution of residual stresses and strains at the membrane of each fibre due to mechanically induced electrophysiological impairments, and its impact on signal transmission.

physics.bio-ph↗

arXiv2020

Effects of nerve bundle geometry on neurotrauma evaluation

Objective: We confirm that alteration of a neuron structure can induce abnormalities in signal propagation for nervous systems, as observed in brain damage. Here, we investigate the effects of geometrical changes and damage of a neuron structure in 2 scaled nerve bundle models, made of myelinated nerve fibers or unmyelinated nerve fibers. Methods: We propose a 3D finite element model of nerve bundles, combining a real-time full electromechanical coupling, a modulated threshold for spiking activation, and independent alteration of the electrical properties for each fiber. We then simulate mechanical compression and tension to induce damage at the membrane of a nerve bundle made of 4 fibers. We examine the resulting changes in strain and neural activity by considering in turn the cases of intact and traumatized nerve membranes. Results: Our results show lower strain and lower electrophysiological impairments in unmyelinated fibers than in myelinated fibers, higher deformation levels in larger bundles, and higher electrophysiological impairments in smaller bundles. Conclusion: We conclude that the insulation sheath of myelin constricts the membrane deformation and scatters plastic strains within the bundle, that larger bundles deform more than small bundles, and that small fibers tolerate a higher level of elongation before mechanical failure.

physics.bio-ph↗

arXiv2020

On anisotropic elasticity and questions concerning its Finite Element implementation

We give conditions on the strain-energy function of nonlinear anisotropic hyperelastic materials that ensure compatibility with the classical linear theories of anisotropic elasticity. We uncover the limitations associated with the volumetric deviatoric separation of the strain energy used, for example, in many Finite Element (FE) codes in that it does not fully represent the behavior of anisotropic materials in the linear regime. This limitation has important consequences. We show that, in the small deformation regime, a FE code based on the volumetric-deviatoric separation assumption predicts that a sphere made of a compressible anisotropic material deforms into another sphere under hydrostatic pressure loading, instead of the expected ellipsoid. For finite deformations, the commonly adopted assumption that fibres cannot support compression is incorrectly implemented in current FE codes and leads to the unphysical result that under hydrostatic tension a sphere of compressible anisotropic material deforms into a larger sphere.

cond-mat.soft↗

arXiv2020

Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis

We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus mu0 varies from 1.8 to 3.2 kPa, the stiffening parameter b of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- (A) and fourth-order (D) constants of weakly nonlinear elasticity from -1.3 to -20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired t-test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

cond-mat.soft↗

arXiv2020

Head-to-nerve analysis of electromechanical impairments of diffuse axonal injury

The aim was to investigate mechanical and functional failure of diffuse axonal injury (DAI) in nerve bundles following frontal head impacts, by finite element simulations. Anatomical changes following traumatic brain injury are simulated at the macroscale by using a 3D head model. Frontal head impacts at speeds of 2.5-7.5 m/s induce mild-to-moderate DAI in the white matter of the brain. Investigation of the changes in induced electromechanical responses at the cellular level is carried out in two scaled nerve bundle models, one with myelinated nerve fibres, the other with unmyelinated nerve fibres. DAI occurrence is simulated by using a real-time fully coupled electromechanical framework, which combines a modulated threshold for spiking activation and independent alteration of the electrical properties for each three-layer fibre in the nerve bundle models. The magnitudes of simulated strains in the white matter of the brain model are used to determine the displacement boundary conditions in elongation simulations using the 3D nerve bundle models. At high impact speed, mechanical failure occurs at lower strain values in large unmyelinated bundles than in myelinated bundles or small unmyelinated bundles; signal propagation continues in large myelinated bundles during and after loading, although there is a large shift in baseline voltage during loading; a linear relationship is observed between the generated plastic strain in the nerve bundle models and the impact speed and nominal strains of the head model. The myelin layer protects the fibre from mechanical damage, preserving its functionalities.

q-bio.TO↗

arXiv2020

A combined experimental and numerical study of stab-penetration forces

The magnitude of force used in a stabbing incident can be difficult to quantify, although the estimate given by forensic pathologists is often seen as `critical' evidence in medico-legal situations. The main objective of this study is to develop a quantitative measure of the force associated with a knife stabbing biological tissue, using a combined experimental and numerical technique. A series of stab-penetration tests were performed to quantify the force required for a blade to penetrate skin at various speeds and using different `sharp' instruments. A computational model of blade penetration was developed using ABAQUS/EXPLICIT, a non-linear finite element analysis (FEA) commercial package. This model, which incorporated element deletion along with a suitable failure criterion, is capable of systematically quantifying the effect of the many variables affecting a stab event. This quantitative data could, in time, lead to the development of a predictive model that could help indicate the level of force used in a particular stabbing incident.

cond-mat.soft↗