Statistical field theory of polarizable polymer chains with nonlocal dipolar interactions.

The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. In these models, accounting for the interactions between the induced dipoles on monomers is challenging due to the nonlocality of these interactions. On the other hand, the framework of statistical field theory provides a continuous description of polymer chains that potentially enables a tractable way to account for these interactions. However, prior formulations using this framework have been restricted to the case of weak anisotropy of the monomer polarizability. This paper formulates a general approach based in the framework of statistical field theory to account for the nonlocal nature of the dipolar interactions without any restrictions on the anisotropy or nonlinearity of the polarizability of the monomer. The approach is based on three key elements: (1) the statistical field theory framework, in which the discrete monomers are regularized to a continuous dipole distribution, (2) a replacement of the nonlocal dipole-dipole interactions by the local electrostatics partial differential equation with the continuous dipole distribution as the forcing, and (3) the use of a completely general relation between the polarization and the local electric field. Rather than treat the dipole-dipole interactions directly, the continuous description in the field theory enables the computationally tractable nonlocal-to-local transformation. Further, it enables the use of a realistic statistical-mechanical ensemble wherein the average far-field applied electric field is prescribed, rather than prescribing the applied field at every point in the polymer domain. The model is applied, using the finite element method, to study the electromechanical response of a polymer chain in the ensemble with fixed far-field applied electric field and fixed chain stretch. The nonlocal dipolar interactions are found to increase, over the case where dipole-dipole interactions are neglected, the magnitudes of the polarization and electric field by orders of magnitude as well as significantly change their spatial distributions. Next, the effect of the relative orientation between the applied field and the chain on the local electric field and polarization is studied. The model predicts that the elastic response of the polymer chain is linear, consistent with the Gaussian approximation, and largely unchanged by the orientation of the applied electric field, though the polarization and local electric field distributions are significantly impacted.

Experimental study of muscle permeability under various loading conditions.

The permeability of a few muscle tissues under various loading conditions is characterized. To this end, we develop an experimental apparatus for permeability measurements which is based on the falling head method. We also design a dedicated sample holder which directs the flow through the tissue and simultaneously enables to pre-compress it. Although outside of the scope of this work, we recall that the permeability of the muscle has a crucial role in the pathophysiology of various diseases such as the compartment syndrome. Following the measurements of porcine, beef, chicken and lamb samples, we find that the permeability decreases with the pre-compression of the tissue. Similar decrease is observed following dehydration of the tissue. Remarkably, we find that within a physiological pressure range the permeabilities of the various samples are quite similar. This suggests that the muscle permeability is governed by a common micro-mechanical mechanism in which the blood propagates through the interstitial spaces. Under physiological loading conditions, the muscle permeability is in the range between 80 and 230 [Formula: see text].

The compartment syndrome: is the intra-compartment pressure a reliable indicator for early diagnosis?

Compartment syndrome (CS) occurs when the pressure in an enclosed compartment increases due to tissue swelling or internal bleeding. As the intra-compartmental pressure (ICP) builds up, the blood flow to the tissue or the organ is compromised, resulting in ischemia, necrosis and damage to the nerves and other tissues. At the present there are no established diagnostic procedures, and clinical observations such as pain, paralysis and even compartment pressure monitoring are an unreliable determinant of the presence of the syndrome. Late diagnosis may result in fasciotomy, neurological dysfunctions, amputation and even death. Focusing on the frequently occurring CS of the lower leg, this work is aimed toward introducing a coherent, mechanically motivated analysis of the disease within the framework of poroelasticity. The fascia enclosing the compartment is treated as an inextensible and impermeable layer, and the tissue inside the compartment is represented as a fully saturated poroelastic solid. The model quantitatively predicts the highly non-uniform ICP buildup as a function of both time and location. These findings, which are in good agreement with clinical observations reported in the literature, shed light on the difficulties associated with the identification of the syndrome and may assist in improved diagnostic procedures.

Electromechanical Interplay in Deformable Dielectric Elastomer Networks.

A systematic, statistical-mechanics-based analysis of the response of dielectric elastomers to coupled electromechanical loading is conducted, starting from the monomer level through the polymer chain and ending with closed-form expressions for the polarization and stress fields. It is found that the apparent response at the macrolevel is dictated by four microscopic parameters-the monomer type and polarizability and the chain length and density. Our analysis further reveals a new electrostrictive effect that either reinforces or opposes the polarization-induced deformation. The validity of the results is attested through comparisons with well-established experimental measurements of both the polarization field and the electrostrictive stress.

Towards a physics-based multiscale modelling of the electro-mechanical coupling in electro-active polymers.

Owing to the increasing number of industrial applications of electro-active polymers (EAPs), there is a growing need for electromechanical models which accurately capture their behaviour. To this end, we compare the predicted behaviour of EAPs undergoing homogeneous deformations according to three electromechanical models. The first model is a phenomenological continuum-based model composed of the mechanical Gent model and a linear relationship between the electric field and the polarization. The electrical and the mechanical responses according to the second model are based on the physical structure of the polymer chain network. The third model incorporates a neo-Hookean mechanical response and a physically motivated microstructurally based long-chains model for the electrical behaviour. In the microstructural-motivated models, the integration from the microscopic to the macroscopic levels is accomplished by the micro-sphere technique. Four types of homogeneous boundary conditions are considered and the behaviours determined according to the three models are compared. For the microstructurally motivated models, these analyses are performed and compared with the widely used phenomenological model for the first time. Some of the aspects revealed in this investigation, such as the dependence of the intensity of the polarization field on the deformation, highlight the need for an in-depth investigation of the relationships between the structure and the behaviours of the EAPs at the microscopic level and their overall macroscopic response.

Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues.

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics-motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work, the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting close-form expressions are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method, these predictions are compared with corresponding 3D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations.