Investigation and Validation of a Shape Memory Alloy Material Model Using Interactive Fibre Rubber Composites.

The growing demand for intelligent systems with improved human-machine interactions has created an opportunity to develop adaptive bending structures. Interactive fibre rubber composites (IFRCs) are created using smart materials as actuators to obtain any desired application using fibre-reinforced elastomer. Shape memory alloys (SMAs) play a prominent role in the smart material family and are being used for various applications. Their diverse applications are intended for commercial and research purposes, and the need to model and analyse these application-based structures to achieve their maximum potential is of utmost importance. Many material models have been developed to characterise the behaviour of SMAs. However, there are very few commercially developed finite element models that can predict their behaviour. One such model is the Souza and Auricchio (SA) SMA material model incorporated in ANSYS, with the ability to solve for both shape memory effect (SME) and superelasticity (SE) but with a limitation of considering pre-stretch for irregularly shaped geometries. In order to address this gap, Woodworth and Kaliske (WK) developed a phenomenological constitutive SMA material model, offering the flexibility to apply pre-stretches for SMA wires with irregular profiles. This study investigates the WK SMA material model, utilizing deformations observed in IFRC structures as a reference and validating them against simulated models using the SA SMA material model. This validation process is crucial in ensuring the reliability and accuracy of the WK model, thus enhancing confidence in its application for predictive analysis in SMA-based systems.

A fully implicit finite element method for bidomain models of cardiac electromechanics.

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes.

Accuracy of Devereaux and Teichholz formulas for left ventricular mass calculation in different geometric patterns: comparison with cardiac magnetic resonance imaging.

Left ventricular (LV) myocardial mass is important in the evaluation of cardiac remodeling and requires accurate assessment when performed on linear measurements in two-dimensional echocardiography (Echo). We aimed to compare the accuracy of the Devereaux formula (DEV) and the Teichholz formula (TEICH) in calculating LV myocardial mass in Echo using cardiac magnetic resonance (CMR) as the reference method. Based on preceding mathematical calculations, we identified primarily LV size rather than wall thickness as the main source of bias between DEV and TEICH in a retrospective derivation cohort (n = 1276). Although LV mass from DEV and TEICH were correlated with CMR, TEICH did not show a proportional bias as did DEV (- 2 g/m2 vs. + 22 g/m2). This could be validated in an independent prospective cohort (n = 226) with symptomatic non-ischemic heart failure. DEV systematically overestimated LV mass in all tiers of LV remodeling as compared to TEICH. In conclusion, the TEICH method accounts for the changes in LV geometry with increasing LV mass and thus better reflects the different pattern of LV remodeling than the DEV method. This has important clinical implications, as TEICH may be more appropriate for use in clinical practice, rather than DEV, currently recommended.

Balancing conduction velocity error in cardiac electrophysiology using a modified quadrature approach.

Conduction velocity error is often the main culprit behind the need for very fine spatial discretizations and high computational effort in cardiac electrophysiology problems. In light of this, a novel approach for simulating an accurate conduction velocity in coarse meshes with linear elements is suggested based on a modified quadrature approach. In this approach, the quadrature points are placed at arbitrary offsets of the isoparametric coordinates. A numerical study illustrates the dependence of the conduction velocity on the spatial discretization and the conductivity when using different quadrature rules and calculation approaches. Additionally, examples using the modified quadrature in coarse meshes for wave propagation demonstrate the improved accuracy of the conduction velocity with this method. This novel approach possesses great potential in reducing the computational effort required but remains limited to specific linear elements and experiences a reduction in accuracy for irregular meshes and heterogeneous conductivities. Further research can focus on developing an adaptive quadrature and extending the approach to other element formulations in order to make the approach more generally applicable.

Computational modelling of mechano-electric feedback and its arrhythmogenic effects in human ventricular models.

The current study aims to investigate the role of mechano-electric feedback (MEF) in healthy cardiac cycles and in cardiac arrhythmia using human ventricular models. The numerical formulation of stretch-activated channels (SACs) in terms of the fibre stretch of the myocardium is incorporated into the modified Hill model that describes the myocardium as an electro-visco-active material. Additionally, we propose models of SACs formulated in terms of the rate of stretch along fibre direction and the stretch along sheet direction. We analyze the effect of the three different models for SACs and different material properties on the regular cycles by using electrocardiogram and volume-time curves, and show that the each model of SACs has regionally different influences on the heart model. Moreover, we simulate 'commotio cordis' and 'precordial thump' and demonstrate that MEF plays a major role in the occurrence of fibrillation and defibrillation in the absence of the structural cardiac damage. Furthermore, we study the role of MEF in premature ventricular contraction when the blood pressure is disturbed.

Thermo-Electro-Mechanical Simulation of Electro-Active Composites.

In this contribution, a computational thermo-electro-mechanical framework is considered, to simulate coupling between the mechanical, electrical and thermal fields, in nonhomogeneous electro-active materials. A thermo-electro-mechanical material model and a mixed Q1P0 finite element framework are described and used for the simulations. Finite element simulations of the response of heterogeneous structures consisting of a soft matrix and a stiff incluison are considered. The behavior of the composite material is studied for varying initial temperatures, different volume fractions and various aspect ratios of the inclusion. For some of the examples, the response of the structure beyond a limit point of electro-mechanical instability is traced. Regarding the soft matrix of the composite, thermal properties of silicone rubber at normal conditions have been obtained by molecular dynamics (MD) simulations. The material parameters obtained by MD simulations are used within the finite element simulations.

A numerical study on the effects of spatial and temporal discretization in cardiac electrophysiology.

Millions of degrees of freedom are often required to accurately represent the electrophysiology of the myocardium due to the presence of discretization effects. This study seeks to explore the influence of temporal and spatial discretization on the simulation of cardiac electrophysiology in conjunction with changes in modeling choices. Several finite element analyses are performed to examine how discretization affects solution time, conduction velocity and electrical excitation. Discretization effects are considered along with changes in the electrophysiology model and solution approach. Two action potential models are considered: the Aliev-Panfilov model and the ten Tusscher-Noble-Noble-Panfilov model. The solution approaches consist of two time integration schemes and different treatments for solving the local system of ordinary differential equations. The efficiency and stability of the calculation approaches are demonstrated to be dependent on the action potential model. The dependency of the conduction velocity on the element size and time step is shown to be different for changes in material parameters. Finally, the discrepancies between the wave propagation in coarse and fine meshes are analyzed based on the temporal evolution of the transmembrane potential at a node and its neighboring Gauss points. Insight obtained from this study can be used to suggest new methods to improve the efficiency of simulations in cardiac electrophysiology.

Increasing the Fatigue Resistance of Strain-Hardening Cement-Based Composites (SHCC) by Experimental-Virtual Multi-Scale Material Design.

Strain-hardening cement-based composites are a promising class of materials for a wide variety of applications due to their considerable tensile strength and pronounced ductility caused by the development of multiple fine cracks. Nevertheless, the safe use of such composites requires sound knowledge of their mechanical behaviour under different types of loading, particularly under fatigue loading, while considering distinct influences like initial crack width and fibre orientation. To deepen this knowledge, single-fibre pull-out tests on PVA-fibres from a cementitious matrix were carried out to gain information about the micro-mechanical and degradation processes of the fibre. It could be shown that the fibres tend to rupture instead of being pulled out under quasi-static loading. When changing the loading regime to alternating loading, this failure mechanism shifts to pull-out. By varying the experimental parameters such as initial crack width, inclination angle or compressive-force level a clear influence on the fibre's crack bridging capacity could be observed associated with effects on the degradation processes. Based on the data obtained, a micro-mechanical numerical model was developed to support the assumptions and observations from single-fibre pull-out tests and to enable predictions of the performance of the material on the microscale under cyclic loading.

Thermo-Electro-Mechanical Characterization of PDMS-Based Dielectric Elastomer Actuators.

The present contribution aims towards a thermo-electro-mechanical characterization of dielectric elastomer actuators (DEA) based on polydimethylsiloxane (PDMS). To this end, an experimental setup is proposed in order to evaluate the PDMS-based DEA behavior under the influence of various rates of mechanical loading, different ambient temperatures, and varying values of an applied electric voltage. To obtain mechanical, electro-mechanical and thermo-mechanical experimental data, the passive behavior of the material, as well as the material's response when electrically activated, was tested. The influence of the solid electrode on the dielectric layer's surface was also examined. Moreover, this work focuses on the production of such DEA, the experimental setup and the interpretation and evaluation of the obtained mechanical hysteresis loops. Finite element modeling approaches were used in order to model the passive and the electro-mechanically active response of the material. A comparison between experimental and simulation results was performed.

Numerical Mesoscale Analysis of Textile Reinforced Concrete.

This contribution presents a framework for Numerical Material Testing (NMT) of textile reinforced concrete based on the mesomechanical analysis of a Representative Volume Element (RVE). Hence, the focus of this work is on the construction of a proper RVE representing the dominant mechanical characteristics of Textile Reinforced Concrete (TRC). For this purpose, the RVE geometry is derived from the periodic mesostructure. Furthermore, sufficient constitutive models for the individual composite constituents as well as their interfacial interactions are considered, accounting for the particular mechanical properties. The textile yarns are modeled as elastic transversal isotropic unidirectional layers. For the concrete matrix, an advanced gradient enhanced microplane model is utilized considering the complex plasticity and damage behavior at multiaxial loading conditions. The mechanical interactions of the constituents are modeled by an interface formulation considering debonding and friction as well as contact. These individual constitutive models are calibrated by corresponding experimental results. Finally, the damage mechanisms as well as the load bearing behavior of the constructed TRC-RVE are analyzed within an NMT procedure based on a first-order homogenization approach. Moreover, the effective constitutive characteristics of the composite at macroscale are derived. The numerical results are discussed and compared to experimental results.

Modelling of High Velocity Impact on Concrete Structures Using a Rate-Dependent Plastic-Damage Microplane Approach at Finite Strains.

Concrete is known as a quasi-brittle material and the microplane model has been proven to be a powerful method to describe its constitutive features. For some dynamic cases, however, numerous microplane models used successfully at small strains are not sufficient to predict the nonlinear behaviour of damaged concrete due to large deformations. In this contribution at hand, a combined plasticity-damage microplane model extended to the finite strain framework is formulated and regularised using implicit gradient enhancement to achieve mesh insensitivity and to obtain more stable finite element solutions. A modified smooth three surface Drucker-Prager yield function with caps is introduced within the compression-tension split. Moreover, a viscoplastic consistency formulation is implemented to deliver rate dependency at dynamic cases. In case of penetration into concrete materials, the proposed model is equipped with an element erosion procedure to yield a better approximation of crack patterns. Numerical examples on impact cases are performed to challenge the capability of the newly proposed model to existing experimental data.

A Biomimetic Fish Fin-Like Robot Based on Textile Reinforced Silicone.

The concept of merging pre-processed textile materials with tailored mechanical properties into soft matrices is so far rarely used in the field of soft robotics. The herein presented work takes the advantages of textile materials in elastomer matrices to another level by integrating a material with highly anisotropic bending properties. A pre-fabricated textile material consisting of oriented carbon fibers is used as a stiff component to precisely control the mechanical behavior of the robotic setup. The presented robotic concept uses a multi-layer stack for the robot's body and dielectric elastomer actuators (DEAs) on both outer sides of it. The bending motion of the whole structure results from the combination of its mechanically adjusted properties and the force generation of the DEAs. We present an antagonistic switching setup for the DEAs that leads to deflections to both sides of the robot, following a biomimetic principle. To investigate the bending behavior of the robot, we show a simulation model utilizing electromechanical coupling to estimate the quasi-static deflection of the structure. Based on this model, a statement about the bending behavior of the structure in general is made, leading to an expected maximum deflection of 10 mm at the end of the fin for a static activation. Furthermore, we present an electromechanical network model to evaluate the frequency dependent behavior of the robot's movement, predicting a resonance frequency of 6.385 Hz for the dynamic switching case. Both models in combination lead to a prediction about the acting behavior of the robot. These theoretical predictions are underpinned by dynamic performance measurements in air for different switching frequencies of the DEAs, leading to a maximum deflection of 9.3 mm located at the end of the actuators. The herein presented work places special focus on the mechanical resonance frequency of the robotic setup with regard to maximum deflections.

An orthotropic viscoelastic material model for passive myocardium: theory and algorithmic treatment.

This contribution presents a novel constitutive model in order to simulate an orthotropic rate-dependent behaviour of the passive myocardium at finite strains. The motivation for the consideration of orthotropic viscous effects in a constitutive level lies in the disagreement between theoretical predictions and experimentally observed results. In view of experimental observations, the material is deemed as nearly incompressible, hyperelastic, orthotropic and viscous. The viscoelastic response is formulated by means of a rheological model consisting of a spring coupled with a Maxwell element in parallel. In this context, the isochoric free energy function is decomposed into elastic equilibrium and viscous non-equilibrium parts. The baseline elastic response is modelled by the orthotropic model of Holzapfel and Ogden [Holzapfel GA, Ogden RW. 2009. Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos Trans Roy Soc A Math Phys Eng Sci. 367:3445-3475]. The essential aspect of the proposed model is the account of distinct relaxation mechanisms for each orientation direction. To this end, the non-equilibrium response of the free energy function is constructed in the logarithmic strain space and additively decomposed into three anisotropic parts, denoting fibre, sheet and normal directions each accompanied by a distinct dissipation potential governing the evolution of viscous strains associated with each orientation direction. The evolution equations governing the viscous flow have an energy-activated nonlinear form. The energy storage in the Maxwell branches has a quadratic form leading to a linear stress-strain response in the logarithmic strain space. On the numerical side, the algorithmic aspects suitable for the implicit finite element method are discussed in a Lagrangian setting. The model shows excellent agreement compared to experimental data obtained from the literature. Furthermore, the finite element simulations of a heart cycle carried out with the proposed model show significant deviations in the strain field relative to the elastic solution.

A fully implicit finite element method for bidomain models of cardiac electrophysiology.

This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential Φ(i)-Φ(e) and the extracellular potential Φ(e) are treated as independent variables. To this end, the respective reaction-diffusion equations are recast into weak forms via a conventional isoparametric Galerkin approach. The resultant nonlinear set of residual equations is consistently linearised. The method results in a symmetric set of equations, which reduces the computational time significantly compared to the conventional solution algorithms. The proposed method is inherently modular and can be combined with phenomenological or ionic models across the cell membrane. The efficiency of the method and the comparison of its computational cost with respect to the simplified monodomain models are demonstrated through representative numerical examples.

Optimal applicator placement in hepatic radiofrequency ablation on the basis of rare data.

In this paper, a numerical procedure to determine an optimal applicator placement for hepatic radiofrequency ablation incorporating uncertain material parameters is presented. The main focus is set on the treatment of subjective and rare data-based information. For this purpose, we employ the theory of fuzzy sets and model uncertain parameters as fuzzy quantities. While fuzzy modelling has been established in structural engineering in the recent past, it is novel in biomedical engineering. Incorporating fuzzy quantities within an optimisation task is basically innovative. In our context, fuzzy modelling allows us to determine an optimal applicator placement that maximises the therapy success under the given uncertainty conditions. The applicability of our method is demonstrated by means of an example case.