The effect of deformation dependent permittivity on the elastic response of a finitely deformed dielectric tube

In this paper, the influence of a radial electric field generated by compliant electrodes on the curved surfaces of a tube of dielectric electroelastic material subject to radially symmetric finite deformations is analyzed within the framework of the general theory of nonlinear electroelasticity. The analysis is illustrated for two constitutive equations based on the neo-Hookean and Gent elasticity models supplemented by an electrostatic energy term with a deformation dependent permittivity

Stability of active muscle tissue

In this discussion, the notion of material stability is examined in the context of active muscle tissue modeling, where the nonlinear constitutive law is dependent on both the physiologically-driven muscle contraction and the finite mechanical deformation. First, the governing equations and constitutive laws for a general active-elastic material are linearized about a homogeneous underlying configuration. In order to obtain mathematical restrictions analogous to those found in elastic materials, stability conditions are derived based on the propagation of homogeneous plane waves with real wave speeds, and the generalized acoustic tensor is obtained. Focusing on 2D motions, and considering a simplified, decoupled transversely isotropic energy function, the restriction on the active acoustic tensor is recast in terms of a generally applicable constitutive law, with specific attention paid to the fiber contribution. The implication of the material stability conditions on material parameters, active contraction, and elastic stretch is investigated for prototype material models of muscle tissue

The effect of residual stress on the stability of a circular cylindrical tube

Residual stresses in an unloaded configuration of an elastic material have a significant influence on the response of the material from that configuration, but the effect of residual stress on the stability of the material, whether loaded or unloaded, has only been addressed to a limited extent. In this paper we consider the level of residual stress that can be supported in a thick-walled circular cylindrical tube of non-linearly elastic material without loss of stability when subjected to fixed axial stretch and either internal or external pressure. In particular, we consider the tube to have radial and circumferential residual stresses, with a simple form of elastic constitutive law that accommodates the residual stress, and incremental deformations restricted to the cross section of the tube. Results are described for a tube subject to a level of (internal or external) pressure characterized by the internal azimuthal stretch. Subject to restrictions imposed by the strong ellipticity condition, the emergence of bifurcated solutions is detailed for their dependence on the level of residual stress and mode number

Waves and vibrations in a finitely deformed electroelastic circular cylindrical tube

In two recent papers, conditions for which axisymmetric incremental bifurcation could arise for a circular cylindrical tube subject to axial extension and radial inflation in the presence of an axial load, internal pressure and a radial electric field were examined, the latter being effected by a potential difference between compliant electrodes on the inner and outer radial surfaces of the tube. The present paper takes this work further by considering the incremental deformations to be time-dependent. In particular, both the axisymmetric vibration of a tube of finite length with appropriate end conditions and the propagation of axisymmetric waves in a tube are investigated. General equations and boundary conditions governing the axisymmetric incremental motions are obtained and then, for purposes of numerical evaluation, specialized for a Gent electroelastic model. The resulting system of equations is solved numerically and the results highlight the dependence of the frequency of vibration and wave speed on the tube geometry, applied deformation and electrostatic potential. In particular, the bifurcation results obtained previously are recovered as a special case when the frequency vanishes. Specification of an incremental potential difference in the present work ensures that there is no incremental electric field exterior to the tube. Results are also illustrated for a neo-Hookean electroelastic model and compared with those previously obtained for the case in which no incremental potential difference (or charge) is specified and an external field is required

Bifurcation of finitely deformed thick-walled electroelastic spherical shells subject to a radial electric field

This paper is concerned with the bifurcation analysis of a pressurized electroelastic spherical shell with compliant electrodes on its inner and outer boundaries. The theory of small incremental electroelastic deformations superimposed on a radially finitely deformed electroelastic thick-walled spherical shell is used to determine those underlying configurations for which the superimposed deformations do not maintain the perfect spherical shape of the shell. Specifically, axisymmetric bifurcations are analyzed, and results are obtained for three different electroelastic energy functions, namely electroelastic counterparts of the neo-Hookean, Gent and Ogden elastic energy functions. For the neo-Hookean energy function it was reported previously that for the purely mechanical case axisymmetric bifurcations are possible under external pressure only, no bifurcation solutions being possible for internally pressurized spherical shells. In the case of an electroelastic neo-Hookean model bifurcation under internal pressure becomes possible when the potential difference between the electrodes exceeds a certain value, which depends on the ratio of inner to outer undeformed radii. Results obtained for the three classes of model are significantly different and are illustrated for a range of fixed values of the potential difference. Although of less practical significance, results are also shown for fixed charges, and these are both different between the models and different from the case of fixed potential difference

Directional Differences in the Biaxial Material Properties of Fascia Lata and the Implications for Fascia Function

Fascia is a highly organized collagenous tissue that is ubiquitous in the body, but whose function is not well understood. Because fascia has a sheet-like structure attaching to muscles and bones at multiple sites, it is exposed to different states of multi- or biaxial strain. In order to measure how biaxial strain affects fascia material behavior, planar biaxial tests with strain control were performed on longitudinal and transversely oriented samples of goat fascia lata (FL). Cruciform samples were cycled to multiple strain levels while the perpendicular direction was held at a constant strain. Structural differences among FL layers were examined using histology and SEM. Results show that FL stiffness, hysteresis, and strain energy density are greater in the longitudinal vs. transverse direction. Increased stiffness in the longitudinal layer is likely due to its greater thickness and greater average fibril diameter compared to the transverse layer(s). Perpendicular strain did not affect FL material behavior. Differential loading in the longitudinal vs. transverse directions may lead to structural changes, enhancing the ability of the longitudinal FL to transmit force, store energy, or stabilize the limb during locomotion. The relative compliance of the transverse fibers may allow expansion of underlying muscles when they contract.Organismic and Evolutionary Biolog

Ray W Ogden: An Appreciation

This special issue of Mathematics and Mechanics of Solids is dedicated to Professor Ray Ogden FRS on the occasion of his 70th birthday. It is a companion volume to another special issue edited by our colleagues Roger Bustamente, Jose Merodio and David Steigmann at the IMA Journal of Applied Mathematics. Ray Ogden’s work has had a major influence in the broad field of solid mechanics, within the context of continuum mechanics. It continues to do so as can be checked by looking at the exponential rise of his citation count, totaling according to Google Scholar more than 15,000 to date, with an h-index of 51. Whatever value we attach to bibliometric indicators, these numbers clearly point to a deep and profound impact. Here, instead of presenting the long list of his achievements, awards and publications (to be found elsewhere), we prefer to highlight three of the themes for which his work has received the most attention. Needless to say, the spectrum of his abilities is far wider

Electroelastic plate instabilities based on the Stroh method in terms of the energy function Ω*(F, DL)

The stability of an electroelastic dielectric elastomer plate with compliant electrodes on its major surfaces under an applied potential difference is examined on the basis of the incremental theory of electroelastic fields. The Stroh method of analysis of the governing equations is used with the material constitutive law given in terms of the energy function Ω*(F, DL), where F is the deformation gradient and DL is the Lagrangian electric displacement field. For a particular class of energy functions, explicit bifurcation equations are obtained for antisymmetric and symmetric modes of instability and the results are illustrated for a Gent electroelastic material model with different values of the Gent parameter. This work confirms previous results obtained in terms of the energy function Ω(F, EL), where EL is the Lagrangian electric field