Hyperelastic Material Model Research Articles

Constrained neural network training and its application to hyperelastic material modeling

Neural networks (NN) have been studied and used widely in the field of computational mechanics, especially to approximate material behavior. One of their disadvantages is the large amount of data needed for the training process. In this paper, a new approach to enhance NN training with physical knowledge using constraint optimization techniques is presented. Specific constraints for hyperelastic materials are introduced, which include energy conservation, normalization and material symmetries. We show, that the introduced enhancements lead to better learning behavior with respect to well known issues like a small number of training samples or noisy data. The NN is used as a material law within a finite element analysis and its convergence behavior is discussed with regard to the newly introduced training enhancements. The feasibility of NNs trained with physical constraints is shown for data based on real world experiments. We show, that the enhanced training outperforms state-of-the-art techniques with respect to stability and convergence behavior within FE simulations.

Experimental investigation on sphere pig movement in multiple thickness pipe

In the petroleum industry, using pipelines is the safest and most reliable method for crude oil or product transportation. Pipeline pigging is crucial for safe and reliable pipeline operation. The driver pressure of a pig is an important parameter of this operation. Thus, it should be known in advance. In the present survey, an experimental setup has been built to investigate the driver pressure for sphere pig motion for various material hardness as well as oversize ratios. Three spheres have been produced from 55, 65, and 75 Shore-A hardness polyurethane and they have been launched into a six-inch test spool, containing four pipes with different wall thicknesses, equipped with a reciprocating pump as well as a digital pressure measurement system. Then the driver pressures have been measured for all test cases. The uniaxial tension test results of each material along with the test spool and sphere geometries were imported into the simulation software, ABAQUS. The predicted pressure difference values by the simulation had no similar manner to the experimental results when a fixed friction coefficient has been employed. A modification of the simulation scheme is presented here, which is the use of contact pressure dependent frictional behavior in finite element simulations, as the main novelty of the work. This correction leads to close matching of the experimental and numerical results with less than 10% deviation which is an acceptable estimation in the pigging operation. Thus, the pressure-dependent coefficient of friction along with the proper hyperelastic material model can successfully evaluate the differential pressure needed for ball pig motion in a pipe. As the experimental tests are time consuming and expensive for larger pipeline pigs, this method provides a fast and economic tool for driver pressure prediction in larger pipes, based on FEM simulation.

Methodology to Calibrate the Dissection Properties of Aorta Layers from Two Sets of Experimental Measurements

Aortic dissection is a prevalent cardiovascular pathology that can have a fatal outcome. However, the mechanisms that trigger this disease and the mechanics of its progression are not fully understood. Computational models can help understand these issues, but they need a proper characterisation of the tissues. Therefore, we propose a methodology to obtain the dissection parameters of all layers in aortic tissue via the computational modelling of two different delamination tests: the peel and mixed tests. Both experimental tests have been performed in specimens of porcine aorta, where the intima-media and media-adventitia interfaces, as well as the medial layer, were dissected. These two tests have been modelled using a cohesive zone formulation for the separating interface and a hyperelastic anisotropic material model via an implicit static analysis. The dissection properties of each interface have been calibrated by reproducing the force-displacement curves obtained in the experimental tests. The values of peak and mean force of the experiments were fitted with an error below 10%. With this methodology, we intend to contribute to the development of reliable numerical tools for simulating aortic dissection and aortic aneurysm rupture.

Skeletal muscle: Modeling the mechanical behavior by taking the hierarchical microstructure into account

Skeletal muscles ensure the mobility of mammals and are complex natural fiber–matrix–composites with a hierarchical microstructure. In this work, we analyze the muscle’s mechanical behavior on the level of fascicles and muscle fibers. We introduce continuum mechanics hyperelastic material models for the connective tissue endomysium and the embedded muscle fibers. The coupled electrical, chemical and mechanical processes taking place in activated contracting muscle fibers are captured including the temporal change of the activation level and the spatial propagation of the activation potential in fibers. In our model, we investigate the material behavior of fascicle, fiber and endomysium in the fiber direction and examine interactions between muscle fiber and endomysium by considering the temporal and spatial change of muscle fiber activation. In addition, a loading case of normal and shear forces is applied to analyze the fiber lifting force and the lifting height of unipennate muscles with different pennation angles. Moreover, the development of local stresses and strains in fibers and endomysium for different strains are studied. The simulation results allow to identify regions in high risk of damage. Optimal arrangements of unipennate muscle microstructure are found for either very small or very large pennation angles.

Association of diameter and wall stresses of tricuspid aortic valve ascending thoracic aortic aneurysms

ObjectiveAscending thoracic aortic aneurysms carry a risk of acute type A dissection. Elective repair guidelines are designed around size thresholds, but the 1-dimensional parameter of maximum diameter cannot predict acute events in small aneurysms. Biomechanically, dissection can occur when wall stress exceeds strength. Patient-specific ascending thoracic aortic aneurysm wall stresses may be a better predictor of dissection. Our aim was to compare wall stresses in tricuspid aortic valve–associated ascending thoracic aortic aneurysms based on diameter. MethodsPatients with tricuspid aortic valve–associated ascending thoracic aortic aneurysm and diameter 4.0 cm or greater (n = 221) were divided into groups by 0.5-cm diameter increments. Three-dimensional geometries were reconstructed from computed tomography images, and finite element models were developed taking into account prestress geometries. A fiber-embedded hyperelastic material model was applied to obtain longitudinal and circumferential wall stress distributions under systolic pressure. Median stresses with interquartile ranges were determined. The Kruskal–Wallis test was used for comparisons between size groups. ResultsPeak longitudinal wall stresses for tricuspid aortic valve–associated ascending thoracic aortic aneurysm were 290 (265-323) kPa for size 4.0 to 4.4 cm versus 330 (296-359) kPa for 4.5 to 4.9 cm versus 339 (320-373) kPa for 5.0 to 5.4 cm versus 318 (293-351) kPa for 5.5 to 5.9 cm versus 373 (363-449) kPa for 6.0 cm or greater (P = 8.7e-8). Peak circumferential wall stresses were 460 (421-543) kPa for size 4.0 to 4.4 cm versus 503 (453-569) kPa for 4.5 to 4.9 cm versus 549 (430-588) kPa for 5.0 to 5.4 cm versus 540 (471-608) kPa for 5.5 to 5.9 cm versus 596 (506-649) kPa for 6.0 cm or greater (P = .0007). ConclusionsCircumferential and longitudinal wall stresses are higher as diameter increases, but size groups had large overlap of stress ranges. Wall stress thresholds based on aneurysm wall strength may be a better predictor of patient-specific risk of dissection than diameter in small ascending thoracic aortic aneurysms.

Sensitivity of material model parameters on finite element models of infant head impacts.

Finite element (FE) models of human infant heads can be used in forensic investigations to infer whether a given pattern of head injuries could have resulted from a hypothetical scenario. This requires accurate models of the behaviour of the head tissues. Material models for human infant head tissues have been developed using experimental data from both infant and adult tissues. Experimental data for infants are scarce due to ethical considerations. To guide future experimental work, a sensitivity analysis of the material model parameters was conducted on a FE model of an infant occipital head impact. A simplified head geometry, consisting of the scalp, skull, suture and brain, was impacted onto a rigid anvil at a speed equivalent to a drop height of 0.3m. The scalp, suture and brain were represented using hyperelastic material models, while an isotropic elastic model was used for the skull. Three hundred simulations were performed, with the material model parameters varied in each. Spearman's rank correlation was used to determine the influence of each parameter on selected outputs which predict injury level. The elastic modulus and Poisson's ratio for the skull were the most important parameters, followed by the hyperelastic constants for the brain, scalp and suture. It is recommended that future research prioritises increasing experimental datasets of skull elastic modulus, especially at higher loading rates, followed by obtaining data for the skull Poisson's ratio. The results from this sensitivity analysis can ensure that future experimental work makes the best use of scarce tissues.

Effect of axonal fiber architecture on mechanical heterogeneity of the white matter—a statistical micromechanical model

A diffusion tensor imaging (DTI) -based statistical micromechanical model was developed to study the effect of axonal fiber architecture on the inter- and intra-regional mechanical heterogeneity of the white matter. Three characteristic regions within the white matter, i.e., corpus callosum, brain stem, and corona radiata, were studied considering the previous observations of locations of diffuse axonal injury. The embedded element technique was used to create a fiber-reinforced model, where the fiber was characterized by a Holzapfel hyperelastic material model with variable dispersion of axonal orientations. A relationship between the fractional anisotropy and the dispersion parameter of the hyperelastic model was used to introduce the statistical DTI data into the representative volume element. The FA-informed statistical micromechanical models of three characteristic regions of white matter were developed by deriving the corresponding probabilistic measures of FA variations. Comparison of the model predictions and experimental data indicated a good agreement, suggesting that the model could reasonably capture the inter-regional heterogeneity of white matter. Moreover, the standard deviations of experimental results correlated well with the model predictions, suggesting that the model could capture the intra-regional mechanical heterogeneity for different regions of white matter.

Comparison of two different surface for rolling airless tire by finite element method

Drum testing was carried out to determine rolling tire performance. The finite element method was used to model the drum testing instead. In order to yield accurate results, the generalized Maxwell’s viscoelastic material model with hyperelastic material model was employed to simulate the drum testing on the airless tire. However, it consumed a lot of simulation time because of the contact surface between tire and drum was difficult to compute by using a finite element method. The finite element model of rolling an airless tire on a flat surface was developed. The contact patch and spoke deformation were carried out to investigate the surface effects. The spoke deformation of rolling an airless tire on a flat surface was found to be in accord with the curvature surface of the drum. The flat surface showed little difference in the contact area against the drum. Particularly, it was found that the analysis time of rolling an airless tire on a flat surface was less than the drum 10.13 times.

A Spatiotemporal Analysis of a Fluid Structure Interaction Model of the Left Coronary Artery

Coronary artery disease is the second leading cause of death in the United States. Models of coronary arteries have been widely used to understand the hemodynamic drivers of the disease. Fluid-Structure Interaction (FSI) modeling of the coronary arteries provides information on both the forces that are created by the blood and the forces distributed into the artery wall. A better understanding of the artery health and markers of disease progression may be discernable by performing a spatiotemporal analysis of the coronary artery hemodynamics and solid mechanics. The goals of this investigation were: 1) to create a three-dimensional (3D) FSI model of the left anterior descending coronary artery and 2) to evaluate disease progression using multiple mechanical descriptors in both space and time domains using COMSOL Multiphysics. The 3D geometry reconstruction was based on a patient's computer tomography angiography (CTA) data. The fluid domain representing the blood volume and solid domain representing the artery wall were fully coupled. The artery wall was modeled using a 5-parameter hyperelastic Mooney-Rivlin material model. We assessed time averaged wall shear stress, wall shear stress gradient, and oscillatory shear index (OSI) along the fluid-structure interface. Artery wall strain (along the three principal directions) and Von-Mises stress were assessed within regions of the solid (i.e., the vascular wall). A virtual calculation of the Fractional Flow Reserve (vFFR), which is used for clinical diagnosis of cardiac ischemia, was performed. These analyses were collected from three different regions along the artery, proximal to, at, and distal to an area of narrowing in the artery throughout the cardiac cycle. Clear differences were observed between the regions. The distal region to the narrowing had variable OSI and high time averaged wall shear stress, but the lowest average Von-Mises stress. The vFFR was 0.96 which is comparable to the average FFR in the left anterior descending artery. This type of model reconstruction and analysis can be used to evaluate plaque vulnerabilities. It may also have clinical implications when assessing the patient's specific coronary artery mechanical environment that may lead to plaque development and instability.

In-plane shear response of a composite hexagonal honeycomb core under large deformation – A numerical and experimental study

In the present work, experimental shear tests using a custom-built picture-frame shear fixture have been conducted to investigate the in-plane pure-shear response of an HRP-C fiberglass/phenolic hexagonal honeycomb core under large deformation. Three-dimensional digital image correlation was used during the quasi-static tests to measure the homogenized surface strain fields in the core specimen. A new hyperelastic orthotropic material model was developed to capture the in-plane finite strain behavior of the honeycomb core. The picture-frame shear test on the core was simulated numerically using the homogenized material model, and predictions were compared with test data. Unlike the Hookean orthotropic material model, which exhibited softer responses in comparison to test data, good agreement was observed between the hyperelastic orthotropic model predictions and test results.

Material Modelling of Fabric Deformation in Forming Simulation of Fiber-Metal Laminates – A Review on Modelling Fabric Coupling Mechanisms

During forming of complex fiber-metal laminates (FML), compressive stress zones occur. In pure textile forming, these compressive stresses typically lead to extensive wrinkling. In FML forming, however, wrinkling is partly hindered by the metal layers. Thus, combined stress states occur, where compression influences the deformation. In forming simulation, these compressive stresses can lead to erroneous formation of shear bands within the fabric layer, if the deformation behavior is not modelled correctly. Simple fabric models neither consider interactions between roving directions nor model interactions between membrane strains and shear strains. More advanced invariant-based hyperelastic material models are able to capture these interactions, but only consider tension and shear, while disregarding compression. A common assumption is to set the fabric compression stiffness close to zero. Experimentally, the in-plane fabric compression stiffness has not been determined so far. However, in FML forming, the compression stiffness and the combined compression-tension-shear behavior becomes relevant. In this article, the authors summarize and analyze the capacity of state-of-the-art fabric material models to predict the deformation behavior of fabrics under combined loading. Based on these findings, conclusions are drawn for a new macroscopic modeling approach for woven fabrics, including coupling of tension, compression and shear.

The importance of intervertebral disc material model on the prediction of mechanical function of the cervical spine

BackgroundLinear elastic, hyperelastic, and multiphasic material constitutive models are frequently used for spinal intervertebral disc simulations. While the characteristics of each model are known, their effect on spine mechanical response requires a careful investigation. The use of advanced material models may not be applicable when material constants are not available, model convergence is unlikely, and computational time is a concern. On the other hand, poor estimations of tissue’s mechanical response are likely if the spine model is oversimplified. In this study, discrepancies in load response introduced by material models will be investigated.MethodsThree fiber-reinforced C2-C3 disc models were developed with linear elastic, hyperelastic, and biphasic behaviors. Three different loading modes were investigated: compression, flexion and extension in quasi-static and dynamic conditions. The deformed disc height, disc fluid pressure, range of motion, and stresses were compared.ResultsResults indicated that the intervertebral disc material model has a strong effect on load-sharing and disc height change when compression and flexion were applied. The predicted mechanical response of three models under extension had less discrepancy than its counterparts under flexion and compression. The fluid-solid interaction showed more relevance in dynamic than quasi-static loading conditions. The fiber-reinforced linear elastic and hyperelastic material models underestimated the load-sharing of the intervertebral disc annular collagen fibers.ConclusionThis study confirmed the central role of the disc fluid pressure in spinal load-sharing and highlighted loading conditions where linear elastic and hyperelastic models predicted energy distribution different than that of the biphasic model.

Tendon constrained inflatable architecture: rigid axial load bearing design case

Inflatables can provide advanced functionality such as structural support, controlled compliance, posability, self-actuation, etc when they are architecturally constrained. Unfortunately, some of the key benefits of inflatables, including their low architectural complexity and high deploy-and-stow capability, are typically adversely affected as functionalities become more sophisticated. A new architectural approach, a tendon constrained inflatable (TCI), is introduced to decouple functionality from deploy-and-stow capability. A TCI is a structure composed of a soft inflatable bladder with rigid end caps connected by inextensible internal constraint tendons. When a TCI is inflated, the tendons under pure tension impose constraints on the inflatable by pre-tensioning the TCI to be able to resist external loads, but when not pressurized, the soft bladder and flexible tendons collapse and provide a compact stow. This paper develops the fundamental case of TCI functionality, rigid axial load bearing, by providing predictive models, validation experiments, design space plots, and a design case study. A model predicting the rigid load-bearing capacity as a function of pressure for varying TCI architectural design parameters is derived through (a) an unconstrained inflation model, based on an axisymmetric nonlinear membrane deformation model and a hyperelastic material model, and (b) a constraint model that bounds specific inflation directions depending on the applied constraint. This axial rigid load-bearing TCI performance model is validated through experiments measuring TCI deformation due to pressure and external load. This model serves as the basis to develop versatile design space plots that provide various views of the design parameter dependencies. These plots are demonstrated in the context of a deployable modular support design case study. The insights gained enable the design of TCIs with rigid load-bearing functionality in a deployable and stowable package as well as setting the foundation to develop more sophisticated architecture with decoupled functionality and deploy-and-stow capability.

Numerical investigation on the sensitivity of endplate design and gas diffusion material models in quantifying localized interface and bulk electrical resistance

A localized non-intuitive relationship between electrical interface contact resistance and bulk properties such as bulk electrical resistance and permeability in the fuel cell gas diffusion layer (GDL) is reported. A numerical method is adopted to investigate contact pressure and hence the interface contact resistance at the interfaces of bipolar plate (BPP)|GDL and GDL|Polymer electrolyte membrane (PEM). The results are observed to be sensitive to GDL material models as well as endplate designs. This means, endplates designed to improve the electrical contact resistance or contact pressure at the BPP|GDL interface may not necessarily assure an improvement in bulk properties, in fact, it is observed in this study that these properties are inversely related. Further, a differential deformation in GDL along with consolidation effect is predicted with compressible version of hyperelastic material model. More importantly, it is revealed that the selection of material models plays a significant role in the deformation behaviour of the GDLs irrespective of the clamping design adopted.

A novel material point method (MPM) based needle-tissue interaction model

Needle-tissue interaction model is essential to tissue deformation prediction, interaction force analysis and needle path planning system. Traditional FEM based needle-tissue interaction model would encounter mesh distortion or continuous mesh subdivision in dealing with penetration, in which the computational instability and poor accuracy could be introduced. In this work, a novel material point method (MPM) is applied to establish the needle-tissue interaction model which is suitable to handle the discontinuous penetration problem. By integrating a hyperelastic material model, the tissue deformation and interaction force can be solved simultaneously and independently. A testbed of needle insertion into a Polyvinyl alcohol (PVA) hydrogel phantom was constructed to validate both tissue deformation and interaction force. The results showed the experimental data agrees well with the simulation results of the proposed model.

Three-Dimensional Quantification of Collagen Microstructure During Tensile Mechanical Loading of Skin.

Skin is a heterogeneous tissue that can undergo substantial structural and functional changes with age, disease, or following injury. Understanding how these changes impact the mechanical properties of skin requires three-dimensional (3D) quantification of the tissue microstructure and its kinematics. The goal of this study was to quantify these structure-function relationships via second harmonic generation (SHG) microscopy of mouse skin under tensile mechanical loading. Tissue deformation at the macro- and micro-scale was quantified, and a substantial decrease in tissue volume and a large Poisson’s ratio was detected with stretch, indicating the skin differs substantially from the hyperelastic material models historically used to explain its behavior. Additionally, the relative amount of measured strain did not significantly change between length scales, suggesting that the collagen fiber network is uniformly distributing applied strains. Analysis of undeformed collagen fiber organization and volume fraction revealed a length scale dependency for both metrics. 3D analysis of SHG volumes also showed that collagen fiber alignment increased in the direction of stretch, but fiber volume fraction did not change. Interestingly, 3D fiber kinematics was found to have a non-affine relationship with tissue deformation, and an affine transformation of the micro-scale fiber network overestimates the amount of fiber realignment. This result, along with the other outcomes, highlights the importance of accurate, scale-matched 3D experimental measurements when developing multi-scale models of skin mechanical function.

Machine learning model predict stress-strain plot for Marlow hyperelastic material design

Machine Learning (ML), a subset of Artificial Intelligence (AI), is a study of computer algorithms that detect useful patterns in a multitude of experimental data sets. ML uses patterns for the prediction of values, classification of entities into specific categories, etc. Herein, we have presented a general workflow that exhibits the step-by-step process required to predict the properties of the ionic thermoplastic elastomer (Ionic-TPEs) sample. The workflow consists of five distinct steps; (a) acquisition of experimental data, (b) preprocessing of data and formation of structured data set, (c) selection and training of right ML model, (d) evaluation of the performance of the trained model, and (e) communication of the results. For this purpose, three different regression ML models have been selected and compared among them to find out the best performing ML model. A virtual stress-strain plot, created by the trained regression model for the ionic TPE sample, has been compared with the actual experimental data. Statistical parameters such as coefficient of determination (R2 score), mean absolute error (MAE), and mean squared error (MSE) has been evaluated, which suggests how well the regression models have been able to predict the values with reference to the actual experimental data. Physical properties such as tensile strength, elongation at break, hardness (Shore A), and tear strength has been predicted and compared against the actual experimental data for the particular ionic TPE sample. Furthermore, we demonstrate the Marlow hyperelastic material modeling using the virtual stress-strain plot constructed by the RF regression model.

A constitutive model for linear hyperelastic materials with orthotropic inclusions by use of quaternions

An approximated theoretical model for linear hyperelastic materials with orthotropic inclusions is presented based on a mixture approach and orientation averaging of mechanical properties. In many modern composites, particle inclusions are used to achieve the desired properties. The properties of the resulting composite depend on the material, inclusion-density and also the shape and orientation of the particles. This paper discusses different methods to describe the orientation of the particles and formulate an orientation density distribution function. In particular, the use of quaternions is compared to Cardan angles for orientation averaging. The proposed approximating material model can be applicable to a composite made of a matrix material that contains biaxial particles or a material that is composed of particles of an orthotropic material. An example for the former could be fiber concrete with hooked-end fibers and an example for the latter could be particle boards, as wood is an orthotropic material.

Palpation Sensitivity of an Embedded Nodule Using the Finite Element Method

Abstract A physician palpates a tissue to detect an embedded tumor nodule by sensing an increase in local tissue stiffness and nodule size. The Hertz contact model, however, is unable to predict the material or physical properties of a tumor nodule embedded in a healthy tissue of finite thickness. In this study, utilizing a hyperelastic material model, we propose a general methodology to analyze the extent to which the stiffness, size, and depth of a nodule embedded in a tissue affect its detectability. Using dimensional analysis, we generate simple power-law relations to predict physical and material properties of tumor nodules embedded in healthy tissue during indentation. Our results indicate that indenter radius and indentation depth are critical parameters in nodule detection and a thin indenter and large indentation depth increase detection sensitivity of an embedded tumor nodule. Our results also show that anisotropic material properties of either a tissue or an embedded nodule render the embedded tumor nodule undetectable using indentation. We define palpation sensitivity maps that can be used to predict material and physical properties of tumor nodules in healthy tissues. The analysis and results presented in this study might increase accuracy and precision in instrumented probe-based laparoscopic or robotic surgeries.

Numerical Determination of the Circumferential Residual Stress of Porcine Aorta by Pulling-Back Method

Residual stress is very important for the study of cardiovascular-relevant issues, such as assessing the vulnerability of atherosclerosis and aneurysm. In this paper, the circumferential residual stress of porcine aorta was characterized by combining ex vivo experiments with numerical studies. In the experiments, porcine aortic rings were prepared and cut open, and the cross sections of the opened aortic rings were extracted to construct finite element models. The 5-parameter Mooney–Rivlin model was chosen to describe the tensile mechanical behavior of the aorta. In numerical studies, based on the finite element models and hyperelastic material model, a pulling-back displacement was applied to reclose the models of the opened aortic rings, and the equivalent circumferential residual stress to the pre-opened aorta was analyzed. The results showed that the circumferential residual stress of the aorta generally decreased from the proximal to the distal ends, and the residual stresses of the aortic rings close to the distal end did not show a great difference. This work provides an improved understanding of the residual stress distribution in aorta and may be used as a more realistic initial condition for future stress analysis of the arterial tissue.