Muscle Constitutive Model With a Tangent Modulus Approximation: Ansys Implementation and Verification.

Sophisticated muscle material models are required to perform detailed finite element simulations of soft tissue; however, state-of-the-art muscle models are not among the built-in materials in popular commercial finite element software packages. Implementing user-defined muscle material models is challenging for two reasons: deriving the tangent modulus tensor for a material with a complex strain energy function is tedious and programing the algorithm to compute it is error-prone. These challenges hinder widespread use of such models in software that employs implicit, nonlinear, Newton-type finite element methods. We implement a muscle material model in Ansys using an approximation of the tangent modulus, which simplifies its derivation and implementation. Three test models were constructed by revolving a rectangle (RR), a right trapezoid (RTR), and a generic obtuse trapezoid (RTO) around the muscle's centerline. A displacement was applied to one end of each muscle, holding the other end fixed. The results were validated against analogous simulations in FEBio, which uses the same muscle model but with the exact tangent modulus. Overall, good agreement was found between our Ansys and FEBio simulations, though some noticeable discrepancies were observed. For the elements along the muscle's centerline, the root-mean-square-percentage error in the Von Mises stress was 0.00%, 3.03%, and 6.75% for the RR, RTR, and RTO models, respectively; similar errors in longitudinal strain were observed. We provide our Ansys implementation so that others can reproduce and extend our results.

Analysis of mechanical deformation effect on the voltage generation of a vertical contact mode triboelectric generator.

One of the associated factors that controls the performance of a triboelectric generator (TEG) is the mechanical deformation of the dielectric layer. Therefore, a good contact model can be a prominent tool to find a more realistic and efficient way of determining the relationships between the contact and electrical output of the generator. In this study, experiments are conducted on a vertical contact mode triboelectric generator under an MTS machine. The open-circuit voltages are measured at different loads imposed by the MTS by controlling the cyclic displacement of the top tribo layer of the generator. A finite-element-based theoretical model is developed to explain the behavior of the generator during the experiments. The 2D-contact problem of the micro-structured tribo layers is simulated and then the contact results are integrated into 3D to find the actual contact area between the two surfaces. These numerical contact results improve the existing theoretical model by evaluating the correct surface charge density and contact area as a function of the input parameters. The excellent agreement between our experimental and theoretical results illustrates that theoretical modeling could be used as a robust approach to predict the mechanical and electrical performance of TEGs. In addition, some parametric studies of the harvester are presented here for different geometrical parameters of the microstructures.

A generic physics-informed neural network-based constitutive model for soft biological tissues.

Constitutive modeling is a cornerstone for stress analysis of mechanical behaviors of biological soft tissues. Recently, it has been shown that machine learning (ML) techniques, trained by supervised learning, are powerful in building a direct linkage between input and output, which can be the strain and stress relation in constitutive modeling. In this study, we developed a novel generic physics-informed neural network material (NNMat) model which employs a hierarchical learning strategy by following the steps: (1) establishing constitutive laws to describe general characteristic behaviors of a class of materials; (2) determining constitutive parameters for an individual subject. A novel neural network structure was proposed which has two sets of parameters: (1) a class parameter set for characterizing the general elastic properties; and (2) a subject parameter set (three parameters) for describing individual material response. The trained NNMat model may be directly adopted for a different subject without re-training the class parameters, and only the subject parameters are considered as constitutive parameters. Skip connections are utilized in the neural network to facilitate hierarchical learning. A convexity constraint was imposed to the NNMat model to ensure that the constitutive model is physically relevant. The NNMat model was trained, cross-validated and tested using biaxial testing data of 63 ascending thoracic aortic aneurysm tissue samples, which was compared to expert-constructed models (Holzapfel-Gasser-Ogden, Gasser-Ogden-Holzapfel, and four-fiber families) using the same fitting and testing procedure. Our results demonstrated that the NNMat model has a significantly better performance in both fitting (R2 value of 0.9632 vs 0.9019, p=0.0053) and testing (R2 value of 0.9471 vs 0.8556, p=0.0203) than the Holzapfel-Gasser-Ogden model. The proposed NNMat model provides a convenient and general methodology for constitutive modeling.

Impact of hypertension and arterial wall expansion on transport properties and atherosclerosis progression.

This study explored the impact of hypertension on atheroma plaque formation through a mechanobiological model. The model incorporates blood flow via the Navier-Stokes equation. Plasma flow through the endothelium is determined by Darcy's law and the Kedem-Katchalsky equations, which consider the three-pore model utilized for substance flow across the endothelium. The behaviour of these substances within the arterial wall is described by convection-diffusion-reaction equations, while the arterial wall itself is modelled as a hyperelastic material using Yeoh's model. To accurately evaluate hypertension's influence, adjustments were made to incorporate wall compression-induced wall compaction by radial compression. This compaction impacts three key variables of the transport phenomena: diffusion, porosity, and permeability. Based on the obtained findings, we can conclude that hypertension significantly augments plaque growth, leading to an over 400% increase in plaque thickness. This effect persists regardless of whether wall mechanics are considered. Tortuosity, arterial wall permeability, and porosity have minimal impact on atheroma plaque growth under normal arterial pressure. However, the atheroma plaque growth changes dramatically in hypertensive cases. In such scenarios, the collective influence of all factors-tortuosity, permeability, and porosity-results in nearly a 20% increase in plaque growth. This emphasizes the importance of considering wall compression due to hypertension in patient studies, where elevated blood pressure and high cholesterol levels commonly coexist.

Finite-element modelling of interactions of needle with tympanic membrane and middle ear.

The tympanic membrane (TM) is one of the most common routes to access the middle ear and inner ear for the treatment of hearing and balance pathologies. Since the TM is a soft thin biological tissue with small dimensions, using needles seems to be among the most practical interventional approaches. In this study, we proposed a finite-element (FE) analysis of needle-TM interactions that combines a 3D model of the TM and other main middle-ear structures in gerbil, and a 2D model of needle insertion into the TM based on the cohesive zone method (CZM). The TM was modelled using a 1st-order Ogden hyperelastic material and its properties were obtained by fitting to the experimental force-displacement plots of large deformation in the TM under needle indentation. The cohesive parameters were also acquired by calibrating the puncture force against the experimental data of needle insertion into the TM. These FE models were then used to obtain the deformation behaviour of the TM and other middle-ear structures due to the insertion force applied at different locations on the TM. Moreover, we investigated the effect of the TM thickness, the geometry of the needle (i.e., diameter and tip angle), and needle material on the insertion of needles into the TM. We also studied the penetration success of deformable needles.

Soft-Rigid Hybrid Revolute and Prismatic Joints Using Multilayered Bellow-Type Soft Pneumatic Actuators: Design, Characterization, and Its Application as Soft-Rigid Hybrid Gripper.

Despite the exponentially expanding capabilities of robotic systems with the introduction of soft robotics, the lack of practical considerations in designing and integrating soft robotic components hinders the widespread application of newly developed technology in real life. This study investigates the development and performance evaluation of soft-rigid hybrid (SRH) robotic systems employing multilayered bellow-shaped soft pneumatic actuators (MBSPAs) to overcome the common challenges exclusively exhibited in soft robotics. Specifically, we introduce a unique SRH revolute joint enabled by a single thermoplastic polyurethane-MBSPA and rigid components to tackle the limitations of existing soft pneumatic actuators (SPAs), such as restricted payload capacity, vulnerability to external damages, and lack of resilience against outdoor environment. The proposed SRH system entails rigid components encapsulating to protect the MBSPA throughout the entirety of the desired range of motion, and demonstrates improved displacement efficiency, force output, and resilience against external loads. The rigid components also help to stabilize the axis of motion, fostering high durability and repeatable motion. We also extend this concept to a one-degree of freedom SRH prismatic joint. Finite element method modeling is used to estimate the general actuator performance, facilitating the design of MBSPA with limited material information and bypassing trial and error. The wider application of this research targets delicate object handling in industries such as agriculture, encouraging safe and efficient automated harvesting. The article includes thorough actuator performance characterization including displacement, frequency response, durability with life cycle testing up to 25,000 cycles, force output, stiffness, and power density. Performance comparisons with other SPA are provided. A proof of concept 3-point gripper enabled by the proposed SRH joints is capable of gripping objects of various sizes and shapes, with detailed workspace analysis and demonstration showing the gripper's versatility. The SRH system presented here lays a robust foundation for the ongoing advancement of soft robotic technology toward real-life applications, unveiling the potential for a future in which robots operate efficiently in the targeted applications, aiming to integrate seamlessly into workflows with human workers.

Visco-hyperelastic material model fitting to experimental stress-strain curves using a genetic algorithm and its application to soft tissue simulants.

Ballistic impacts on human thorax without penetration can produce severe injuries or even death of the carrier. Soft tissue finite element models must capture the non-linear elasticity and strain-rate dependence to accurately estimate the dynamic human mechanical response. The objective of this work is the calibration of a visco-hyperelastic model for soft tissue simulants. Material model parameters have been calculated by fitting experimental stress-strain relations obtained from the literature using genetic algorithms. Several parametric analyses have been carried out during the definition of the optimization algorithm. In this way, we were able to study different optimization strategies to improve the convergence and accuracy of the final result. Finally, the genetic algorithm has been applied to calibrate two different soft tissue simulants: ballistic gelatin and styrene-ethylene-butylene-styrene. The algorithm is able to calculate the constants for visco-hyperelastic constitutive equations with high accuracy. Regarding synthetic stress-strain curves, a short computational time has been shown when using the semi-free strategy, leading to high precision results in stress-strain curves. The algorithm developed in this work, whose code is included as supplementary material for the reader use, can be applied to calibrate visco-hyperelastic parameters from stress-strain relations under different strain rates. The semi-free relaxation time strategy has shown to obtain more accurate results and shorter convergence times than the other strategies studied. It has been also shown that the understanding of the constitutive models and the complexity of the stress-strain objective curves is crucial for the accuracy of the method.

Hyperelastic material models for simulating deformation of silicone ring pessaries.

Pessaries are removable gynecological prosthetic devices that provide mechanical support for temporary or long-term symptom relief of pelvic floor disorders, such as pelvic organ prolapse and stress urinary incontinence. To date, limited mechanical tests have been performed on physical pessary designs to characterize their behaviour under load; however, custom pessary manufacturing is expensive and time consuming. As an alternative, finite element (FE) modeling can provide detailed numerical insight into the response of a pessary design under load but to date has seen limited application, with little data available for pessary silicone materials. This study aimed to identify hyperelastic material models for two silicone materials used in custom pessary cocoon moulded manufacturing towards FE analysis of ring with support (RWS) pessaries. It was hypothesized that hyperelastic material models could be identified to capture the force and deformation response of multiple RWS sizes under different boundary conditions and silicone materials (Shore 60A and 40A). To understand the material characteristics of pessary silicone, uniaxial tension and compression tests were performed then the experimental data was fit with Mooney-Rivlin (MR) material models. To ensure the material models characterize the pessary behaviour, data from mechanical tests representing the RWS pessary folding and modified 3-point bending were compared to FE recreations (FEBio) of the same tests with the MR materials applied to the pessaries. The FE model results demonstrated good agreement in the force-displacement response for the fold and 3-point bending models for different pessary sizes and silicone stiffnesses. This work demonstrates the hyperelastic material models' efficacy and will enable future studies to improve biomechanical analysis of silicone pessary designs.

Storage-induced mechanical changes of porcine lenses assessed with optical coherence elastography and inverse finite element modeling.

Introduction: In an effort of gaining a better understanding of the lens mechanics, ex vivo lenses samples are often used. Yet, ex vivo tissue might undergo important postmortem changes depending on the unavoidable preservation method employed. The purpose of this study was to assess how various storage conditions and the removal of the lens capsule affect the mechanical properties of ex vivo porcine lens samples. Methods: A total of 81 freshly enucleated porcine eyes were obtained and divided into six groups and preserved differently. In the first three groups, the lens within the intact eye was preserved for 24 h by: (i) freezing at -80°C (n = 12), (ii) freezing at -20°C (n = 12), and (iii) refrigeration at +8°C (n = 12). In the remaining groups, the lenses were immediately extracted and treated as follows: (iv) kept intact, no storage (n = 12), (v) decapsulated, no storage (n = 21), and (vi) immersed in Minimum Essential Medium (MEM) at +8°C (n = 12) for 24 h. Frozen lenses were thawed at room temperature. Each lens was compressed between two glass lamella and subjected, first to a period of relaxation during which the compression force was recorded and second to an oscillating micro-compression while the deformation was recorded with a total of 256 subsequent B-scans via optical coherence tomography. The corresponding axial strain was retrieved via phase-sensitive image processing and subsequently used as input for an inverse finite element analysis (iFEA) to retrieve the visco-hyperelastic material properties of the lenses. Results: After freezing at temperatures of -80°C and -20°C, the cortical strains increased by 14% (p = 0.01) and 34% (p < 0.001), and the nuclear strains decreased by 17% (p = 0.014) and 36% (p < 0.001), compared to the lenses tested immediately after postmortem, respectively. According to iFEA, this resulted from an increased ratio of the nuclear: cortical E-modulus (4.06 and 7.06) in -80°C and -20°C frozen lenses compared to fresh lenses (3.3). Decapsulation had the largest effect on the material constant C10, showing an increase both in the nucleus and cortex. Preservation of the intact eye in the refrigerator induced the least mechanical alterations in the lens, compared to the intact fresh condition. Discussion: Combining iFEA with optical coherence elastography allowed us to identify important changes in the lens mechanics induced after different preserving ex vivo methods.

An in-silico study on the mechanical behavior of colorectal cancer cell lines in the micropipette aspiration process.

Cancer alters the structural integrity and morphology of cells. Consequently, the cell function is overshadowed. In this study, the micropipette aspiration process is computationally modeled to predict the mechanical behavior of the colorectal cancer cells. The intended cancer cells are modeled as an incompressible Neo-Hookean visco-hyperelastic material. Also, the micropipette is assumed to be rigid with no deformation. The proposed model is validated with an in-vitro study. To capture the equilibrium and time-dependent behaviors of cells, ramp, and creep tests are respectively performed using the finite element method. Through the simulations, the effects of the micropipette geometry and the aspiration pressure on the colorectal cancer cell lines are investigated. Our findings indicate that, as the inner radius of the micropipette increases, despite the increase in deformation rate and aspirated length, the time to reach the equilibrium state increases. Nevertheless, it is obvious that increasing the tip curvature radius has a small effect on the change of the aspirated length. But, due to the decrease in the stress concentration, it drastically reduces the equilibrium time and increases the deformation rate significantly. Interestingly, our results demonstrate that increasing the aspiration pressure somehow causes the cell stiffening, thereby reducing the upward trend of deformation rate, equilibrium time, and aspirated length. Our findings provide valuable insights for researchers in cell therapy and cancer treatment and can aid in developing more precise microfluidic.

Energetically stable curve fitting to hyperelastic models based on uniaxial and biaxial tensile tests.

Hyperelastic constitutive laws in biomechanics are used to model soft tissues, and material model parameters are often determined by performing curve fitting on data from uniaxial or biaxial tensile tests. The strain energy function of the applied constitutive law must to be energetically stable; however, this condition is not inherently provided by most currently available models. This study provides a procedure to determine stable strain energy functions in a biaxial strain space based on either uniaxial or biaxial tensile tests. Instead of conservative, strain-independent conditions, a stability region is defined in the strain space based on the sample's tensile tests, thus allowing optimisation within a wider parameter space, resulting in better approximations. An extension of the Levenberg-Marquardt algorithm incorporating user-defined stability constraints is proposed, and the constrained optimisation algorithm is applied to isotropic and anisotropic models. The uniqueness of solutions of the Fung model is also discussed. The material model parameters of stable solutions for soft tissue measurements from various literature sources are determined to demonstrate the proposed procedure. Applying appropriate constraints in the optimisation algorithm resulted in stable and physically permissible constrained solutions for the strain energy function, in contrast to the results of most unconstrained optimisation cases.

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements.

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

Interpretable data-driven modeling of hyperelastic membranes.

We proposed an approach for interpretable data-driven modeling of an isotropic incompressible hyperelastic membrane deformation. The approach is based on the response functions in terms of the Laplace stretch and the finite element method, where response functions are partial derivatives of a hyperelastic potential with respect to the chosen strain measure. The Laplace stretch as the strain measure allows us to recover directly the response functions from experimental data and construct automatically data-driven constitutive relations. All needed formulas were obtained explicitly. We tested our approach for membrane inflation with data-driven constitutive relations based on the perforated membrane extension tests.

On implementation of fibrous connective tissues' damage in Abaqus software.

Connective fibrous tissues, such as tendons and ligaments, in humans and animals exhibit hyperelastic behaviour. The constitution of the material of these tissues is anisotropic due to the presence of the collagen fibres, where one family of fibres is the typical case. Traumatic events and/or aging may sometimes lead to the damage of the tissue. The study of motion of affected joints or limbs is usually not permitted in vivo. This is where finite element method (FEM) becomes useful as a premise for general analysis, surgical planning or designing of implants and medical treatment. One of the most often used FEM commercial programs is the field of the biomechanics is Abaqus. The present study discusses the potential of user subroutine UANISOHYPER_INV in this code to analyse response of transversely isotropic tissue with damage in quasi-static range. This subroutine requires providing the material energy function and its derivatives only. The stress tensor and constitutive matrix are computed by the software automatically. To the best of the Authors' knowledge this procedure provides the easiest way to simulate the anisotropic hyperelastic material behaviour in Abaqus. In this study its usage is extended onto the damage response simulation. The verification of the approach and its validation against experimental data indicates its efficiency.

Experimental study on a bending type soft pneumatic actuator for minimizing the ballooning using chamber-reinforcement.

Soft robotics is an emerging area of research due to its safe interaction with humans; it also has exciting applications, such as wearable soft medical devices for rehabilitation, prosthetics, etc. Soft robots require soft actuators for performing desired movements, including bending, expansion, contraction, and twisting. This work focuses on bending-type multi-chambered extra-soft actuators actuated by pneumatic pressure. The corrugated design of a multi-chambered soft pneumatic actuator (SPA) is analyzed experimentally to observe the radial, longitudinal, and lateral expansions of different chambers, i.e., ballooning of the chambers under the application of air pressure. From the experimental study, it is observed that the ballooning mainly occurs at the free end of the actuator in a cantilever-type boundary condition, which could not be demonstrated by the computational solution using the finite element analysis (FEA). Moreover, it is observed that the effect of ballooning also disturbs the constant curvature profile of SPA. Therefore, a chamber-reinforcement solution is provided for minimizing the ballooning and ensuring the uniform bending of a SPA.

A Biomechanical Simulation of Forearm Flexion Using the Finite Element Approach.

Upper limb movement is vital in daily life. A biomechanical simulation of the forearm with consideration of the physiological characteristics of the muscles is instrumental in gaining deeper insights into the upper limb motion mechanisms. In this study, we established a finite element model of the forearm, including the radius, biceps brachii, and tendons. We simulated the motion of the forearm resulting from the contraction of the biceps brachii by using a Hill-type transversely isotropic hyperelastic muscle model. We adjusted the contraction velocity of the biceps brachii muscle in the simulation and found that a slower muscle contraction velocity facilitated forearm flexion. Then, we changed the percentage of fast-twitch fibers, the maximum muscle strength, and the neural excitation values of the biceps brachii muscle to investigate the forearm flexion of elderly individuals. Our results indicated that reduced fast-twitch fiber percentage, maximum muscle strength, and neural excitation contributed to the decline in forearm motion capability in elderly individuals. Additionally, there is a threshold for neural excitation, below which, motion capability sharply declines. Our model aids in understanding the role of the biceps brachii in forearm flexion and identifying the causes of upper limb movement disorders, which is able to provide guidance for enhancing upper limb performance.

The biomechanical effects of different membrane layer structures and material constitutive modeling on patient-specific cerebral aneurysms.

The prevention, control and treatment of cerebral aneurysm (CA) has become a common concern of human society, and by simulating the biomechanical environment of CA using finite element analysis (FEA), the risk of aneurysm rupture can be predicted and evaluated. The target models of the current study are mainly idealized single-layer linear elastic cerebral aneurysm models, which do not take into account the effects of the vessel wall structure, material constitution, and structure of the real CA model on the mechanical parameters. This study proposes a reconstruction method for patient-specific trilaminar CA structural modeling. Using two-way fluid-structure interaction (FSI), we comparatively analyzed the effects of the differences between linear and hyperelastic materials and three-layer and single-layer membrane structures on various hemodynamic parameters of the CA model. It was found that the numerical effects of the different CA membrane structures and material constitution on the stresses and wall deformations were obvious, but does not affect the change in its distribution pattern and had little effect on the blood flow patterns. For the same material constitution, the stress of the three-layer membrane structure were more than 10.1% larger than that of the single-layer membrane structure. For the same membrane structure, the stress of the hyperelastic material were more than 5.4% larger than that of the linear elastic material, and the displacement of the hyperelastic material is smaller than that of the linear elastic material by about 20%. And the maximum value of stress occurred in the media, and the maximum displacement occurred in the intima. In addition, the upper region of the tumor is the maximum rupture risk region for CA, and the neck of the tumor and the bifurcation of the artery are also the sub-rupture risk regions to focus on. This study can provide data support for the selection of model materials for CA simulation and analysis, as well as a theoretical basis for clinical studies and subsequent research methods.

Hyperelastic Modeling and Validation of Hybrid-Actuated Soft Robot with Pressure-Stiffening.

Soft robots have gained popularity, especially in intraluminal applications, because their soft bodies make them safer for surgical interventions than flexures with rigid backbones. This study investigates a pressure-regulating stiffness tendon-driven soft robot and provides a continuum mechanics model for it towards using that in adaptive stiffness applications. To this end, first, a central single-chamber pneumatic and tri-tendon-driven soft robot was designed and fabricated. Afterward, the classic Cosserat's rod model was adopted and augmented with the hyperelastic material model. The model was then formulated as a boundary-value problem and was solved using the shooting method. To identify the pressure-stiffening effect, a parameter-identification problem was formulated to identify the relationship between the flexural rigidity of the soft robot and internal pressure. The flexural rigidity of the robot at various pressures was optimized to match theoretical deformation and experiments. The theoretical findings of arbitrary pressures were then compared with the experiment for validation. The internal chamber pressure was in the range of 0 to 40 kPa and the tendon tensions were in the range of 0 to 3 N. The theoretical and experimental findings were in fair agreement for tip displacement with a maximum error of 6.40% of the flexure's length.

Parameters Identification of Rubber-like Hyperelastic Material Based on General Regression Neural Network.

In this study, we present a systematic scheme to identify the material parameters in constitutive model of hyperelastic materials such as rubber. This approach is proposed based on the combined use of general regression neural network, experimental data and finite element analysis. In detail, the finite element analysis is carried out to provide the learning samples of GRNN model, while the results observed from the uniaxial tensile test is set as the target value of GRNN model. A problem involving parameters identification of silicone rubber material is described for validation. The results show that the proposed GRNN-based approach has the characteristics of high universality and good precision, and can be extended to parameters identification of complex rubber-like hyperelastic material constitutive.

Phase and group velocities for shear wave propagation in an incompressible, hyperelastic material with uniaxial stretch.

Objective.Determining elastic properties of materials from observations of shear wave propagation is difficult in anisotropic materials because of the complex relations among the propagation direction, shear wave polarizations, and material symmetries. In this study, we derive expressions for the phase velocities of the SH and SV propagation modes as a function of propagation direction in an incompressible, hyperelastic material with uniaxial stretch.Approach.Wave motion is included in the material model by adding incremental, small amplitude motion to the initial, finite deformation. Equations of motion for the SH and SV propagation modes are constructed using the Cauchy stress tensor derived from the strain energy function of the material. Group velocities for the SH and SV propagation modes are derived from the angle-dependent phase velocities.Main results.Sample results are presented for the Arruda-Boyce, Mooney-Rivlin, and Isihara material models using model parameters previously determined in a phantom.Significance.Results for the Mooney-Rivlin and Isihara models demonstrate shear splitting in which the SH and SV propagation modes have unequal group velocities for propagation across the material symmetry axis. In addition, for sufficiently large stretch, the Arruda-Boyce and Isihara material models show cusp structures with triple-valued group velocities for the SV mode at angles of roughly 15° to the material symmetry axis.