Canceling the elastic Poynting effect with geometry.

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).

Experimental assessment of clinical MRI-induced global SAR distributions in head phantoms.

OBJECTIVE: Accurate estimation of SAR is critical to safeguarding vulnerable patients who require an MRI procedure. The increased static field strength and RF duty cycle capabilities in modern MRI scanners mean that systems can easily exceed safe SAR levels for patients. Advisory protocols routinely used to establish quality assurance protocols are not required to advise on the testing of MRI SAR levels and is not routinely measured in annual medical physics quality assurance checks. This study aims to develop a head phantom and protocol that can independently verify global SAR for MRI clinical scanners. METHODS: A four-channel birdcage head coil was used for RF transmission and signal reception. Proton resonance shift thermometry was used to estimate SAR. The SAR estimates were verified by comparing results against two other independent measures, then applied to a further four scanners at field strengths of 1.5 T and 3 T. RESULTS: Scanner output SAR values ranged from 0.42 to 1.52 W/kg. Percentage SAR differences between independently estimated values and those calculated by the scanners differed by 0-2.3%. CONCLUSION: We have developed a quality assurance protocol to independently verify the SAR output of MRI scanners.

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

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. 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 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 4 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 traumatised nerve membrane. 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. 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.

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

Axonal damage is one of the most common pathological features of traumatic brain injury, leading to abnormalities in signal propagation for nervous systems. We present a 3D fully coupled electro-mechanical model of a nerve bundle, made with the finite element software Abaqus 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 the bundle. Compression and tension are simulated to induce damage at the nerve membrane. 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. Results show greater changes in transmitting action potential in the myelinated fibre.

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.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Catastrophic Thinning of Dielectric Elastomers.

We provide an energetic insight into the catastrophic nature of thinning instability in soft electroactive elastomers. This phenomenon is a major obstacle to the development of giant actuators, yet it is neither completely understood nor modeled accurately. In excellent agreement with experiments, we give a simple formula to predict the critical voltages for instability patterns; we model their shape and show that reversible (elastic) equilibrium is impossible beyond their onset. Our derivation is fully analytical, does not require finite element simulations, and can be extended to include prestretch and various material models.

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, R2 =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.

On residual stresses and homeostasis: an elastic theory of functional adaptation in living matter.

Living matter can functionally adapt to external physical factors by developing internal tensions, easily revealed by cutting experiments. Nonetheless, residual stresses intrinsically have a complex spatial distribution, and destructive techniques cannot be used to identify a natural stress-free configuration. This work proposes a novel elastic theory of pre-stressed materials. Imposing physical compatibility and symmetry arguments, we define a new class of free energies explicitly depending on the internal stresses. This theory is finally applied to the study of arterial remodelling, proving its potential for the non-destructive determination of the residual tensions within biological materials.

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 Ψ of 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 Ψ is decoupled into volumetric and isochoric parts and the anisotropic part of Ψ is 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 deformations. 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).

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.

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.

Surface instability of sheared soft tissues.

When a block made of an elastomer is subjected to a large shear, its surface remains flat. When a block of biological soft tissue is subjected to a large shear, it is likely that its surface in the plane of shear will buckle (appearance of wrinkles). One factor that distinguishes soft tissues from rubberlike solids is the presence--sometimes visible to the naked eye--of oriented collagen fiber bundles, which are stiffer than the elastin matrix into which they are embedded but are nonetheless flexible and extensible. Here we show that the simplest model of isotropic nonlinear elasticity, namely, the incompressible neo-Hookean model, suffers surface instability in shear only at tremendous amounts of shear, i.e., above 3.09, which corresponds to a 72 deg angle of shear. Next we incorporate a family of parallel fibers in the model and show that the resulting solid can be either reinforced or strongly weakened with respect to surface instability, depending on the angle between the fibers and the direction of shear and depending on the ratio Emu between the stiffness of the fibers and that of the matrix. For this ratio we use values compatible with experimental data on soft tissues. Broadly speaking, we find that the surface becomes rapidly unstable when the shear takes place "against" the fibers and that as E/mu increases, so does the sector of angles where early instability is expected to occur.

Measuring knife stab penetration into skin simulant using a novel biaxial tension device.

This paper describes the development and use of a biaxial measurement device to analyse the mechanics of knife stabbings. In medicolegal situations it is typical to describe the consequences of a stabbing incident in relative terms that are qualitative and descriptive without being numerically quantitative. Here, the mechanical variables involved in the possible range of knife-tissue penetration events are considered so as to determine the necessary parameters that would need to be controlled in a measurement device. These include knife geometry, in-plane mechanical stress state of skin, angle and speed of knife penetration, and underlying fascia such as muscle or cartilage. Four commonly available household knives with different geometries were used: the blade tips in all cases were single-edged, double-sided and without serrations. Appropriate synthetic materials were used to simulate the response of skin, fat and cartilage, namely polyurethane, compliant foam and ballistic soap, respectively. The force and energy applied by the blade of the knife and the out of plane displacement of the skin were all used successfully to identify the occurrence of skin penetration. The skin tension is shown to have a direct effect on both the force and energy for knife penetration and the depth of out of plane displacement of the skin simulant prior to penetration: larger levels of in-plane tension in the skin are associated with lower penetration forces, energies and displacements. Less force and energy are also required to puncture the skin when the plane of the blade is parallel to a direction of greater skin tension than when perpendicular. This is consistent with the observed behaviour when cutting biological skin: less force is required to cut parallel to the Langer lines than perpendicularly and less force is required to cut when the skin is under a greater level of tension. Finally, and perhaps somewhat surprisingly, evidence is shown to suggest that the quality control processes used to manufacture knives fail to produce consistently uniform blade points in knives that are nominally identical. The consequences of this are that the penetration forces associated with nominally identical knives can vary by as much as 100%.

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 12 specific monoclinic crystals.