Nonlinear Hyperelastic Material Research Articles

Characterizing atherosclerotic tissues: in silico analysis of mechanical properties using intravascular ultrasound and inverse finite element methods.

Atherosclerosis is a prevalent cause of acute coronary syndromes that consists of lipid deposition inside the artery wall, creating an atherosclerotic plaque. Early detection may prevent the risk of plaque rupture. Nowadays, intravascular ultrasound (IVUS) is the most common medical imaging technology for atherosclerotic plaque detection. It provides an image of the section of the coronary wall and, in combination with new techniques, can estimate the displacement or strain fields. From these magnitudes and by inverse analysis, it is possible to estimate the mechanical properties of the plaque tissues and their stress distribution. In this paper, we presented a methodology based on two approaches to characterize the mechanical properties of atherosclerotic tissues. The first approach estimated the linear behavior under particular pressure. In contrast, the second technique yielded the non-linear hyperelastic material curves for the fibrotic tissues across the complete physiological pressure range. To establish and validate this method, the theoretical framework employed in silico models to simulate atherosclerotic plaques and their IVUS data. We analyzed different materials and real geometries with finite element (FE) models. After the segmentation of the fibrotic, calcification, and lipid tissues, an inverse FE analysis was performed to estimate the mechanical response of the tissues. Both approaches employed an optimization process to obtain the mechanical properties by minimizing the error between the radial strains obtained from the simulated IVUS and those achieved in each iteration. The second methodology was successfully applied to five distinct real geometries and four different fibrotic tissues, getting median R 2 of 0.97 and 0.92, respectively, when comparing the real and estimated behavior curves. In addition, the last technique reduced errors in the estimated plaque strain field by more than 20% during the optimization process, compared to the former approach. The findings enabled the estimation of the stress field over the hyperelastic plaque tissues, providing valuable insights into its risk of rupture.

Transfer-learning-based strategy for enhancing prediction accuracy and computational efficiency of nonlinear mechanical properties in composite materials

In modern composite design, superior macroscopic mechanical properties can be achieved by optimizing the microstructures of materials. However, the direct prediction of the microstructure–property relationship under nonlinear conditions through numerical methods can be inefficient or imprecise. In this study, a transfer learning strategy based on the reduced order model (ROM) was proposed, offering an enhanced and rapid prediction of the mechanical responses of composite materials under nonlinear conditions. Initially, an extensive training dataset was generated by applying the ROM, used to pre-train the neural network model. Following this, a few data calculated from full-order finite element models were leveraged to fine-tune the network parameters. This approach exploits the efficient data generation capability of the ROM, with its potential computational inaccuracies in nonlinear scenarios mitigated, leading to an improvement in the accuracy and efficiency of the surrogate model. Numerical examples of a nonlinear hyper-elastic material with inclusions were examined, revealing that the computational cost in the offline stage of the transfer learning method is only half that of traditional neural network models, and it enable near real-time predictions in the online stage. Notably, it was shown that the accuracy loss of the developed surrogate model in scenarios of strong non-linearity is significantly less than that of the ROM. This method presents an innovative pathway for the swift and accurate evaluation of the effective mechanical properties of composite structures, with the potential to offer valuable insights for related methodological research.

A clustering-enhanced potential-based reduced order homogenization framework for nonlinear heterogeneous materials

This paper proposes a data-driven approach to improve the efficiency of computational homogenization for nonlinear hyperelastic materials with different microstructures in a small strain context. By combining clustering analysis and Proper Orthogonal Decomposition (POD) with efficient sampling, a reduced order model is established to accurately predict elastoplasticity under monotonic loadings. The microscopic RVE is spatially divided into multiple clusters using the k-means clustering algorithm during the offline phase. As suggested in Kunc and Fritzen (2019a), the reduced order model is constructed using reduced bases of deformation gradient fluctuations on the microscale. In contrast to the conventional displacement-based approach, deformation gradient fluctuations are employed to generate the POD snapshots. To improve the prediction accuracy and reduce the cost of offline computation, the energy minimum point set generation method proposed by Kunc and Fritzen (2019b) is employed. Numerical results show a acceleration factor in the order of 10-100 compared to a purely POD-based model can be archived, which significantly improves the applicability for structural analysis, while maintaining a sufficient accuracy level.

Developing failure criteria for laceration injury of dermal tissue

Despite its importance, there is a poor understanding of human injury tolerance to trauma generally, and more specifically understanding of the mechanics of skin penetration or laceration. The objective of this analysis is to determine the failure criteria that will allow the evaluation of the laceration risk of blunt-tipped edges within a computational modeling environment. An axisymmetric tissue finite element model was set up in Abaqus 2021 to match the experimental set-up from a previous study. The model simulated the pressing of penetrometer geometries into dermal tissue, and stress and strain outputs were evaluated at the experimental failure force. Two separate nonlinear hyperelastic material models were calibrated for the dermis to data from the literature (high and low stiffness models). For both the high-stiffness and low-stiffness skin models, the failure force appears to occur near a local maximum in the principal strain. All failures occurred after the maximum strain near or at the top surface is or above 59%, with mid-thickness strain at a similar level. The strain energy density is concentrated near the edge tip for each configuration, indicating highly localized material damage at the point of loading, and increases rapidly prior to the approximate failure force. As the edge is further compressed into the tissue, the stress triaxiality near the edge contacting point decreases towards zero. This study has identified general failure criteria for skin laceration which can be implemented in a computational model. A higher risk for laceration would be indicated with strain energy density larger than 60 mJ/mm3, dermal strain larger than 55%, and stress triaxiality below 0.1. These findings were largely insensitive to the dermal stiffness and broadly applicable across different indenter geometries. It is expected that this framework may be implemented to evaluate hazardous forces for product edges, interactions with robots, and interfaces with medical and drug delivery devices.

Large deformation frictional contact formulations for isogeometric Kirchhoff–Love shell

The large deformation frictional contact between shell structures is commonplace in engineering applications like the sheet metal forming process. Due to the specific assumptions of shell structures, the numerical calculation of shell contact is more complicated than the computation of contact between normal two or three dimensional solids. In recent years, the Kirchhoff–Love shell has become one of the most popular mathematical shell models under the context of isogeometric analysis. In this paper, we detailedly formulate the frictional contact contributions for Kirchhoff–Love shell structures considering both stick and slide states. The variation and linearization of contact variables considered to be sophisticated are explicitly derived and plainly organized. The general nonlinear hyperelastic materials are utilized to describe the constitutive relations of shell structures undergoing large deformation. The normal and tangential contact constraints are enforced using the classical penalty method. Based on the precise representation of shell structures using NURBS functions, we developed an effective contact detection algorithm to accurately capture the contact areas between shells. A computation framework for solving Kirchhoff–Love shell frictional contact problems is established in the context of NURBS-based isogeometric analysis. Several shell contact examples are calculated, and the obtained results are compared with those of the classical finite element method. The convergence and accuracy of the presented method are verified in these examples.

Two-phase model of compressive stress induced on a surrounding hyperelastic medium by an expanding tumour.

In vitro experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an externally-supplied, diffusible nutrient (e.g., oxygen), affect the tumour's growth dynamics. In this article, we present a mathematical model that describes these in vitro experiments. We use the model to understand how tumour growth generates mechanical deformations in the hydrogel and how these deformations in turn influence the tumour's growth. The hydrogel is viewed as a nonlinear hyperelastic material and the tumour is modelled as a two-phase mixture, comprising a viscous tumour cell phase and an isotropic, inviscid interstitial fluid phase. Using a combination of numerical and analytical techniques, we show how the tumour's growth dynamics change as the mechanical properties of the hydrogel vary. When the hydrogel is soft, nutrient availability dominates the dynamics: the tumour evolves to a large equilibrium configuration where the proliferation rate of nutrient-rich cells on the tumour boundary balances the death rate of nutrient-starved cells in the central, necrotic core. As the hydrogel stiffness increases, mechanical resistance to growth increases and the tumour's equilibrium size decreases. Indeed, for small tumours embedded in stiff hydrogels, the inhibitory force experienced by the tumour cells may be so large that the tumour is eliminated. Analysis of the model identifies parameter regimes in which the presence of the hydrogel drives tumour elimination.

Numerical simulation of viscoelastic fluid–structure interaction benchmarks and their application to the human eye

We present a numerical solution method for time-dependent viscoelastic fluid–structure interaction employing the arbitrary Lagrangian Eulerian framework. The derived monolithic variational formulation is discretized in time using the shifted Crank–Nicolson scheme and in space using the finite element method. For the linearisation we employ Newton’s method with exact Jacobians. The viscoelastic fluid is modelled either using the Oldroyd-B or a Burgers-type model. The elastic structures are non-linear hyperelastic materials. We validate the implementation on benchmark problems and numerically analyse the convergence for global mesh refinement and adaptive mesh refinement using the dual-weighted residual method. Furthermore we numerically analyse the influence of the viscoelasticity of the fluid on typical goal functionals like the drag, the lift and the displacement. The derived numerical solution method is applied to ophthalmology where we analyse the interaction of the viscoelastic vitreous with its surrounding elastic structures.

Simulation of the female pelvic mobility and vesical pressure changes employing fluid-structure interaction method.

This study aims to develop a fluid-structural interaction (FSI) method to pinpoint the effects of pressure changes inside the bladder and their impact on the supporting structure and the urethra mobility. A physiological model of the nulliparous female pelvis, including the organs, supportive structures, and urine, was developed based on magnetic resonance images. Soft tissues with nonlinear hyperelastic material characteristics were modeled. The Navier-Stokes equations governing the fluid flow within the computational domain (urine) were solved. The urine and soft tissue interactions were simulated by the FSI method. The vesical pressure and its impact on the urethral mobility and supportive structures were investigated during the Valsalva maneuver. Moreover, the simulation results were validated by comparing with a urodynamic test and other research. The results demonstrated that the vesical pressure simulated by the FSI method could predict the nonlinear behavior of the urodynamic test pressure. The urethra retropubic bladder neck and the bladder neck-pubic bone angle changed 58.92% and -55.76%, respectively. The retropubic urethral length distance changed by -48.74%. The error compared to the statistical results of other research is < 5%. The total deformation and mobility of the urethra predicted by the FSI model were consistent with clinical observations in a subject. The urethra supports dependence on the tissues' mechanical properties, interaction between the tissues, and effect of urine fluid inside the bladder. This simulation effectively depicts the patterns of urethra mobility, which provides a better understanding of the behavior of the pelvic floor.

Characterization and modeling of a thermoplastic elastomer tissue simulant under uniaxial compression loading for a wide range of strain rates

Characterization and modeling of the mechanical behavior of biological tissues are critical to many biomedical related applications. For research and development, various soft materials have often been used as a tissue substitute. Among them, the mineral oil-based synthetic polymer styrene-ethylene-butylene-styrene (SEBS) gel has gained some popularity due to its superior mechanical and physical properties. Tissue materials or their simulants are often characterized with quasi-static loading and are treated and modeled as a nonlinear hyperelastic material. As tissues are often subjected to loadings with a wide range of strain rates, understanding of the mechanical behavior and development a predictive capability for such loadings are essential. In this work, a comprehensive study of the mechanical behavior of SEBS gels with different chemical compositions and polymer concentrations was conducted under uniaxial compression loadings over a wide range of strain rates, from 1×10−3/s to 6×103/s. In addition to experiments, a comprehensive but simple visco-pseudo-hyperelasticity model was developed. The model was demonstrated to be able to capture all the material features observed in the experiments, such as rate sensitivity, strain-induced softening, and permanent deformation after unloading. Because of its simple functional form, the model can be conveniently used for practical applications such as prediction of the rate dependence of the shear modulus.

Topology optimization of soft compressible phononic laminates for widening the mechanically tunable band gaps

Active tuning of frequency bandgaps has received significant attention in the recent past. To this end, soft compressible phononic composites have indicated great promise owing to their capability to undergo large reversible deformations and deformation dependent constitutive properties. In this investigation, we present an optimization framework for arriving at the optimum topology of a two-phase soft compressible phononic composite for maximizing the frequency gap between the first four consecutive frequency bands of longitudinal wave propagation. The laminate is subjected simultaneously to an equal biaxial pre-stretch in the plane perpendicular to the direction of wave propagation and a prestress in the direction of wave propagation. The nonlinear hyperelastic neo-Hookean material model is employed for characterizing the constitutive behavior of the soft compressible laminate phases. The finite element method with Bloch–Floquet theory is employed for finding the band-structure of the infinitely periodic soft laminate. A gradient-based method of moving asymptotes is used to solve the underlying topology optimization problem. In particular, we present the optimum unit cell designs for two separate problems involving maximization of the absolute width of the band gap and that of the relative width of the band gap when compared to that in the un-deformed laminate. Test cases are presented to highlight the effects of the levels of biaxial prestretch and the longitudinal prestress. Our results indicate that a compressional longitudinal prestress and a lateral prestretch have a favorable impact on widening of the frequency band-gaps. The numerical framework and the inferences reported here can find their potential use in the optimal design of soft compressible composites used in acoustic applications.

Effect of Displacement Degree of Distal Chevron Osteotomy on Metatarsal Stress: A Finite Element Method.

Simple SummaryIn this study, the finite element method was used to explore the effect of distal chevron osteotomy displacement on metatarsal stress. For the subjects used in this study, the metatarsal stress was minimized by moving 4 mm. For the displacement of chevron osteotomy, both postoperative stability and stress distribution of metatarsal should be considered. The most appropriate distance is suggested to be obtained by combining HVA, IMA, age, body weight, and metatarsal width. The finite element method can be used for preoperative estimation of chevron osteotomy and guide the operation.Background: The stress of foot bone can effectively evaluate the functional damage caused by foot deformity and the results of operation. In this study, the finite element method was used to investigate the degree of displacement of distal chevron osteotomy on metatarsal stress and metatarsophalangeal joint load; Methods: Four finite element models of displacement were established by using the CT images of a patient with moderate hallux valgus (hallux valgus angle and intermetatarsal angle were 26.74° and 14.09°, respectively), and the validity of the model was verified. Each finite element model consisted of bones and various cartilage structures, ligaments, and plantar fascia, as well as encapsulated soft tissue. Except for soft tissue, the material properties of other parts were isotropic linear elastic material, and the encapsulated soft tissue was set as nonlinear hyperelastic material. The mesh was tetrahedral mesh. Link elements were used in ligament and plantar fascia. A ground reaction force with a half-body weight was applied at the bottom of the floor to simulate the ground reaction when standing. The upper surfaces of the encapsulated soft tissue, distal tibia, and distal fibula were fixed. The stress distribution of metatarsals and the stress of cartilage of the first metatarsophalangeal joint were compared and analyzed; Results: Compared with the hallux valgus without osteotomy, the stress of the first metatarsals and second metatarsals of 2–4 mm decreased, and the stress of the interarticular cartilage of the first metatarsophalangeal joint with 4 mm was reduced. In the case of 6 mm, the stress value between the first metatarsal and the first metatarsophalangeal joint increased, and 4 mm was the most suitable distance; Conclusions: Compared with the hallux valgus without osteotomy, the stress of the first metatarsals and second metatarsals of 2–4 mm decreased, and the stress of the interarticular cartilage of the first metatarsophalangeal joint with 4 mm was reduced. In the case of 6 mm, the stress value between the first metatarsal and the first metatarsophalangeal joint increased, and 4 mm was the most suitable distance. For the degree of displacement of the distal chevron osteotomy, the postoperative stability and the stress distribution of metatarsal bone should be considered. Factors such as hallux valgus angle, intermetatarsal angle, patient’s age, body weight, and metatarsal width should be considered comprehensively. The factors affecting osteotomy need to be further explored. The degree of displacement of osteotomy can be evaluated by FE method before the operation, and the most suitable distance can be obtained.

Nonlinear material identification of heterogeneous isogeometric Kirchhoff–Love shells

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for describing incompressible material behavior as well as initially curved shells. The material distribution is discretized by bilinear elements such that the nodal values are the design variables to be identified. Independent FE analysis and material discretization, as well as flexible incorporation of experimental data, offer high robustness and control. Three elementary test cases and one application example, which exhibit large deformations and different challenges, are considered: uniaxial tension, pure bending, sheet inflation, and abdominal wall pressurization. Experiment-like results are generated from high-resolution simulations with the subsequent addition of up to 4% noise. Local optimization based on the trust-region approach is used. The results show that with a sufficient number of experimental measurements, design variables and analysis elements, the algorithm is capable to reconstruct material distributions with high precision even in the presence of large noise. The proposed formulation is very general, facilitating its extension to other material models, optimization algorithms and meshing approaches. Adapted material discretizations allow for an efficient and accurate reconstruction of material discontinuities by avoiding overfitting due to superfluous design variables. For increased computational efficiency, the analytical sensitivities and Jacobians are provided.

An inverse method for mechanical characterization of heterogeneous diseased arteries using intravascular imaging

The increasing prevalence of finite element (FE) simulations in the study of atherosclerosis has spawned numerous inverse FE methods for the mechanical characterization of diseased tissue in vivo. Current approaches are however limited to either homogenized or simplified material representations. This paper presents a novel method to account for tissue heterogeneity and material nonlinearity in the recovery of constitutive behavior using imaging data acquired at differing intravascular pressures by incorporating interfaces between various intra-plaque tissue types into the objective function definition. Method verification was performed in silico by recovering assigned material parameters from a pair of vessel geometries: one derived from coronary optical coherence tomography (OCT); one generated from in silico-based simulation. In repeated tests, the method consistently recovered 4 linear elastic (0.1 ± 0.1% error) and 8 nonlinear hyperelastic (3.3 ± 3.0% error) material parameters. Method robustness was also highlighted in noise sensitivity analysis, where linear elastic parameters were recovered with average errors of 1.3 ± 1.6% and 8.3 ± 10.5%, at 5% and 20% noise, respectively. Reproducibility was substantiated through the recovery of 9 material parameters in two more models, with mean errors of 3.0 ± 4.7%. The results highlight the potential of this new approach, enabling high-fidelity material parameter recovery for use in complex cardiovascular computational studies.

NUMERICAL SIMULATION FOR FLUID-STRUCTURE INTERACTION OF A BLOOD FLOW WITH THE AORTIC VALVE USING THE FEM MONOLITHIC FORMULATION

The paper aims to present a numerical simulation for fluid-structure interaction (FSI) of a blood flow over the aortic valve. The finite element discretization is adopted both for fluid and solid domains. The monolithic scheme is used for the strong coupling of fluid and structure to satisfy kinematic and dynamic equilibrium conditions at the interface. The Navier-Stokes equations of an incompressible flow are solved by using the integrated method based on the ALE formula for the moving grid, and the total Lagrangian formulation is used for the non-linear hyper-elastic material of the aortic valve with the Mooney-Rivlin material model adopted as a constitutive equation for the solid domain. The monolithic FEM method is validated by solving a 3D pressure wave problem and the results are compared to the previous solutions. And then, the present method is employed to investigate blood flow through the aortic valve with a complex geometry. The simulation results can be used for predicting the risk of aortic valve diseases…

Considerations for analysis of endothelial shear stress and strain in FSI models of atherosclerosis

Atherosclerosis is a lipid driven chronic inflammatory disease that is characterized by the formation of plaques at predilection sites. These predilection sites (side branches, curved segments, and bifurcations) have often been associated with disturbed shear stress profiles. However, in addition to shear stress, endothelial cells also experience artery wall strain that could contribute to atherosclerosis progression. Herein, we describe a method to accurately obtain these shear stress and strain profiles.We developed a fluid–structure interaction (FSI) framework for modelling arteries within a commercially available package (Abaqus, version 6.14) that included known prestresses (circumferential, axial and pressure associated). In addition, we co-registered 3D histology to a micro-CT-derived 3D reconstruction of an atherosclerotic carotid artery from a cholesterol-fed ApoE−/− mouse to include the spatial distribution of lipids within a subject-specific model. The FSI model also incorporated a nonlinear hyperelastic material model with regionally-varying properties that distinguished between healthy vessel wall and plaque.FSI predicted a lower shear stress than CFD (~−12%), but further decreases in plaque regions with softer properties (~-24%) were dependent on the approach used to implement the prestresses in the artery wall. When implemented with our new hybrid approach (zero prestresses in regions of lipid deposition), there was significant heterogeneity in endothelial shear stress in the atherosclerotic artery due to variations in stiffness and, in turn, wall strain.In conclusion, when obtaining endothelial shear stress and strain in diseased arteries, a careful consideration of prestresses is necessary. This paper offers a way to implement them.

Biomechanical Effects of Deep Anterior Lamellar Keratoplasty and Penetrating Keratoplasty for Keratoconus: A Finite Element Analysis.

PurposeTo theoretically compare corneal displacement and the von Mises (VM) stress distribution of deep anterior lamellar keratoplasty (DALK) and penetrating keratoplasty (PK) for keratoconus (KC) and to evaluate the effects of residual stromal thickness (RST) and intraocular pressure (IOP) on postoperative corneal biomechanics.MethodsWe performed DALK and PK simulations using Ansys by employing anisotropic nonlinear hyperelastic corneal material properties. We analyzed corneal displacement and VM stress in DALK and PK models under IOPs of 10, 15, 20, and 25 mmHg. We established two DALK models: The ideal-type DALK ensured that postoperative central corneal thickness was constant at 560 µm and the corneal graft thickness varied with RST. The clinical-type DALK ensured that corneal grafts had the same thickness (500 µm) regardless of RST. Then we analyzed the effects of RST and IOP on postoperative corneal displacement and VM stress.ResultsCorneal displacement and VM stress were lower in the DALK than in the PK model. In the ideal-type DALK model, an increase in RST was associated with increased deformation and decreased VM stress in the healing zone, except for a RST of 0 µm. In the clinical-type DALK model, deformation and VM stress in the healing zone decreased with an increase in RST, except for a RST of 0 µm.ConclusionsDALK showed more stability than PK. For the ideal-type DALK model, an increase in RST resulted in decreased postoperative corneal biomechanics in the healing zone. For the clinical-type DALK model, corneal deformation and VM stress decreased with an increase in RST, which provides numerical evidence for the design of corneal transplantation for patients with KC.Translational RelevanceIn this computational modeling study, we first theoretically compared corneal biomechanics between DALK and PK for KC. Then, the effects of RST and IOP on postoperative corneal biomechanics were investigated. Our findings provide novel insights into the optimal design for corneal transplantation for patients with KC.

An open-source FEniCS-based framework for hyperelastic parameter estimation from noisy full-field data: Application to heterogeneous soft tissues

We introduce a finite-element-model-updating-based open-source framework to identify mechanical parameters of heterogeneous hyperelastic materials from in silico generated full-field data which can be downloaded here https://github.com/aflahelouneg/inverse_identification_soft_tissue. The numerical process consists in simulating an extensometer performing in vivo uniaxial tensile experiment on a soft tissue. The reaction forces and displacement fields are respectively captured by force sensor and Digital Image Correlation techniques. By means of a forward nonlinear FEM model and an inverse solver, the model parameters are estimated through a constrained optimization function with no quadratic penalty term. As a case study, our Finite Element Model Updating (FEMU) tool has been applied on a model composed of a keloid scar surrounded by healthy skin. The results show that at least 4 parameters can be accurately identified from an uniaxial test only. The originality of this work lies in two major elements. Firstly, we develop a low-cost technique able to characterize the mechanical properties of heterogeneous nonlinear hyperelastic materials. Secondly, we explore the model accuracy via a detailed study of the interplay between discretization error and the error due to measurement uncertainty. Next steps consist in identifying the real parameters and so finding the matching preferential directions of keloid scars growth.

Modeling of multiwall carbon nanotubes reinforced natural rubber for soft robotic applications – A comprehensive presentation

Soft materials like rubbers, polymers and elastomers are non-linear hyper elastic materials or visco-elastic materials that show the large deformation under loading. One of the nonlinear material model is to be used in the simulation of soft mechanism. Mooney-Rivlin, Ogden, Polynomial, Arruda-Boyce, Yeoh, and Neo-Hookean and Extended Tube are some nonlinear hyperelastic material models existing in the practice. The objexctive of the current research is to present comprehensively the nonlinear material constants of the multiwall nanocarbon (MWCNT) reinforced natural rubber (NR) composites. NR/MWCNT composites with 5%, 10%, 20% and 30% weight fractions of MWCNTs are prepared through compression molding. The uniaxial tensile test was conducted on dumb bell specimens of ASTM D412-06a standard. The respective strain–stress data from uni-axial tensile tests are further curve fitted into existing popular nonlinear hyperelastic models. The nonlinear constants of respective model are comprehensively tabulated, which designers can use in the component design and analysis. Finite element contact analysis of a cylindrical soft finger pressed against a rigid plate is conducted and presented.

Modeling of the elastic properties of compressed expanded graphite - A material used in spiral wound gaskets

The paper presents the method of modeling the elastic deformations of expanded graphite, a material used as flexible filling in spiral wound gaskets. Five methods (from A to E) were proposed, by means of which the mean values of the effective elasticmodulus were determined on the basis of the experimentally determined stress-strain characteristics of expanded graphite. The values determined in this way constituted the data set into the isotropic material model, reflecting the elastic properties of the expanded graphite tape in the numerical spiral wound gasket model. A different way of modeling the graphite's elastic properties using the numerical model was method F, in which a nonlinear hyperelastic material model proposed by Blatz-Ko was adapted. The basic purpose of the numerical calculations was to determine both the compression curve of the gasket and the stress distribution in the gasket's windings. The obtained numerical results of the gasket's compression were compared with the experimental test, which allowed the assumptions of the numerical models to be validated. The best way to reflect the elastic behavior of expanded graphite in the gasket's numerical model turned out to be the nonlinear material model presented in method F.

A membrane theory for circular graphene sheets, based on a hyperelastic material model for large deformations

Large deflections relevant for suspended circular graphene sheets with simply supported boundaries are computed by a theory for 2D membranes subjected to several types of vertical axisymmetric forces, based on the principle of virtual power (PVP). Corresponding stress–strain relations are provided in the form of a nonlinear hyperelastic material model for graphene. When approximating the deflections through Fourier series, the PVP yields a nonlinear algebraic system of equations, which is solved by the iterative Newton–Raphson procedure. The new computational efficient method is validated through comparison of the numerical results it provides, with predictions obtained from experimental nanoindentaion measurements.