On the computational modelling of nonlinear electro-elasticity in heterogeneous bodies at finite deformations

Dielectric elastomer actuators (DEA) have been demonstrated to exhibit a quasi-immediate electro-mechanical actuation response with relatively large deformation capability. The properties of DEA make them suitable to be used in the form of major active components within soft robotics and biomimetic artificial muscles. However, some of the electro-active material properties impose limitations on its applications. Therefore, researchers attempt to modify the structure of the homogeneous DEA material by the incorporation of fillers that possess distinct electro-mechanical properties. This modification of the material’s structure leads to a fabricated inhomogeneous composite. From the point of mathematical material modelling and numerical simulation, we propose a material model and a computational framework using the finite element method, which is capable of emulating nonlinear electro-elastic interactions. We consider a coupled electro-mechanical description with the electric and the electro-mechanical properties of the material assumed to be nonlinearly dependent on the deformation. Furthermore, we demonstrate a coupled ansatz that expresses the electric response as dielectrically quasi-linear with only density-dependent electric permittivity. We couple the electro-mechanical models to the extended tube model, which is a suitable approach for the realistic emulation of the hyperelastic response of rubber-like materials. Thereafter, we demonstrate analytical and numerical solutions of a homogeneous electro-elastic body with the Neo-Hookean material model and the extended tube model to express the hyperelastic response. Finally, we use the finite element method to investigate several heterogeneous configurations consisting of soft DEA matrix filled with spherical stiff inclusions with changing volume fraction and ellipsoidal inclusions with varying aspect ratio.

Elasto-capillary circumferential buckling of soft tubes under axial loading: existence and competition with localised beading and periodic axial modes

We provide an extension to previous analysis of the localised beading instability of soft slender tubes under surface tension and axial stretching. The primary questions pondered here are as follows: under what loading conditions, if any, can bifurcation into circumferential buckling modes occur, and do such solutions dominate localisation and periodic axial modes? Three distinct boundary conditions are considered: in case 1 the tube’s curved surfaces are traction-free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement and surface tension. A linear bifurcation analysis is conducted to determine numerically the existence of circumferential mode solutions. In case 1 we focus on the tensile stress regime given the preference of slender compressed tubes towards Euler buckling over axisymmetric periodic wrinkling. We show that tubes under several loading paths are highly sensitive to circumferential modes; in contrast, localised and periodic axial modes are absent, suggesting that the circumferential buckling is dominant by default. In case 2, circumferential mode solutions are associated with negative surface tension values and thus are physically implausible. Circumferential buckling solutions are shown to exist in case 3 for tensile and compressive axial loads, and we demonstrate for multiple loading scenarios their dominance over localisation and periodic axial modes within specific parameter regimes.

A simple phenomenological approach for myocardial contraction: formulation, parameter sensitivity study and applications in organ level simulations

Contraction in myocardial tissue is the result of a complex process through which chemical energy on the cellular level is converted into the mechanical energy needed to circulate blood throughout the body. Due to its vital role for the organism, myocardial contractility is one of the most intensively investigated subjects in medical research. In this contribution, we suggest a novel phenomenological approach for myocardial contraction that is capable of producing realistic intracellular calcium concentration (ICC) and myocyte shortening graphs, can be easily calibrated to capture different ICC and contraction characteristics and, at the same time, is straightforward to implement and ensures efficient computer simulations. This study is inspired by the fact that existing models for myocardial contractility either contain a number of complex equations and material parameters, which reduce their feasibility, or are very simple and cannot accurately mimic reality, which eventually influences the realm of computer simulations. The proposed model in this manuscript considers first the evolution of the ICC through a logarithmic-type ordinary differential equation (ODE) having the normalized transmembrane potential as the argument. The ICC is further put into an exponential-type ODE which determines the shortening of the myocyte (active stretch). The developed approach can be incorporated with phenomenological or biophysically based models of cardiac electrophysiology. Through examples on the material level, we demonstrate that the shape of the ICC and myocardial shortening curves can be easily modified and accurately fitted to experimental data obtained from rat and mouse hearts. Moreover, the performance of the model in organ level simulations is illustrated through several multi-field initial-boundary value problems in which we show variations in volume-time relations, heterogeneous characteristics of myocardial contraction and application of a drug in a virtual left ventricle model.

Numerical investigation on epi-off crosslinking effects on porcine corneas

Experimental inflation tests, conducted on 90 pig corneas before and after corneal collagen crosslinking (CXL) treatment, are simulated with the finite element method. The experimental sample consists of five groups of corneas treated with different UV-A irradiation times (2.5, 5, 10, 15, and 20 min) at constant irradiance 9 mW/cm2. The linear elastic shell theory is used to estimate the equivalent material stiffness of the corneas, revealing that it increases with the exposure time in CXL corneas. In the view of numerical simulations, a simple mechanical model assuming piecewise constant elastic modulus across the corneal thickness is introduced, to estimate the effective increment of the material stiffness in the anterior stroma and the effective depth of the stiffness increment. The two effective quantities are used in the finite element models to simulate the post-CXL tests. Numerical models are able to describe the mechanical effects of CXL in the cornea. The increment of equivalent material stiffness has to be ascribed to a localized increment of the material stiffness in the anterior layers of the cornea, while the posterior layers preserve the original material stiffness. According to the simplified model, the increment of the material stiffness of the anterior cornea increases with the irradiation dose, while the effective reinforcement depth decreases with the irradiation dose. This trend, predicted by a simple mechanical model by imposing equilibrium and compatibility, has been verified by the numerical calculations that captured the global mechanical response of the corneas in untreated and post-CXL conditions.