Nonlinear Hyperelastic Material Research Articles

Mechanical response comparison in an implant overdenture retained by ball attachments on conventional regular and mini dental implants: a finite element analysis

This study investigates the bone/implant mechanical responses in an implant overdenture retained by ball attachments on two conventional regular dental implants (RDI) and four mini dental implants (MDI) using finite element (FE) analysis. Two FE models of overdentures retained by RDIs and MDIs for a mandibular edentulous patient with validation within 6% variation errors were constructed by integrating CT images and CAD system. Bone grafting resulted in 2 mm thickness at the buccal side constructed for the RDIs-supported model to mimic the bone augmentation condition for the atrophic alveolar ridge. Nonlinear hyperelastic material and frictional contact element were used to simulate characteristic of the ball attachment-retained overdentures. The results showed that a denture supported by MDIs presented higher surrounding bone strains than those supported by RDIs under different load conditions. Maximum bone micro strains were up to 6437/2987 and 13323/5856 for MDIs/RDIs under single centric and lateral contacts, respectively. Corresponding values were 4429/2579 and 9557/5774 under multi- centric and lateral contacts, respectively. Bone micro strains increased 2.06 and 1.96-folds under single contact, 2.16 and 2.24-folds under multiple contacts for MDIs and RDIs when lateral to axial loads were compared. The maximum RDIs and MDIs implant stresses in all simulated cases were found by far lower than their yield strength. Overdentures retained using ball attachments on MDIs in poor edentulous bone structure increase the surrounding bone strain over the critical value, thereby damaging the bone when compared to the RDIs. Eliminating the occlusal single contact and oblique load of an implant-retained overdenture reduces the risk for failure.

Large Deformation Properties of Red Blood Cell Membrane Based on a Higher Order Gradient Quasi-continuum Model.

Based on the proposed higher order gradient quasi-continuum model, the numerical investigations of the basic mechanical properties and deformation behaviors of human red blood cell (RBC) membrane under large deformation at room temperature (i.e., 300 K) are carried out in the present paper. The results show that RBC membrane is a nonlinear hyperelastic material. The mechanical properties of RBC membrane is dominated by isotropic nature at the stage of initial deformation, however, its anisotropic material properties emerge clearly with the loading increasing. The out-of-plane wrinkling of RBC membrane upon shear loading can be reproduced numerically. With the use of the so-called higher order Cauchy-Born rule as the kinematic description, the bending stiffness of RBC membrane can be considered conveniently.

Predicting pressure distribution between transfemoral prosthetic socket and residual limb using finite element analysis

A static implicit nonlinear finite element model (FEM) was created and analysed to determine the pressure distribution between the residual limb and the prosthetic socket of a transfemoral amputee. This analysis was performed in an attempt to develop a process allowing healthcare providers and engineers to simulate the fit and comfort of transfemoral prosthetics to reduce the number of re-fittings. The FEM considered the effects of donning and body weight and included geometric nonlinearity due to large deflections, nonlinear contacts due to friction, and nonlinear hyper-elastic material properties for the residual limb's soft tissue. The results attained can provide prosthetic fitting clinicians customised information on where the prosthetic fits too tight, and how stress concentrations would change as a result of geometric modifications to the prosthetic. This knowledge can improve patients' comfort levels by providing well targeted and more accurate modifications to the prosthetic, minimising the need for numerous refittings.

Measurement of the axial and circumferential mechanical properties of rat skin tissue at different anatomical locations.

Skin tissue is not only responsible for thermoregulation but also for protecting the human body from mechanical, bacterial, and viral insults. The mechanical properties of skin tissue may vary according to the anatomical locations in the body. However, the linear elastic and nonlinear hyperelastic mechanical properties of the skin in different anatomical regions and at different loading directions (axial and circumferential) so far have not been determined. In this study, the mechanical properties during tension of the rat abdomen and back were calculated at different loading directions using linear elastic and nonlinear hyperelastic material models. The skin samples were subjected to a series of tensile tests. The elastic modulus and maximum stress of the skin tissues were measured before the incidence of failure. The nonlinear mechanical behavior of the skin tissues was also computationally investigated through a constitutive equation. Hyperelastic strain energy density function was calibrated using the experimental data. The results revealed the anisotropic mechanical behavior of the abdomen and the isotropic mechanical response of the back skin. The highest elastic modulus was observed in the abdomen skin under the axial direction (10 MPa), while the lowest one was seen in the back skin under axial loading (5 MPa). The Mooney-Rivlin material model closely addressed the nonlinear mechanical behavior of the skin at different loading directions, which can be implemented in the future biomechanical models of skin tissue. The results might have implications not only for understanding of the isotropic and anisotropic mechanical behavior of skin tissue at different anatomical locations but also for providing more information for a diversity of disciplines, including dermatology, cosmetics industry, clinical decision making, and clinical intervention.

Эффективная конечно-элементная модель для расчета индентирования сэндвич-панели

Computationally effective finite element model of composite material was developed to predict the strength and energy absorption at lowvelocity impact. Object of research – a sandwich panel, consisting of two layers of randomly–reinforced fiberglass plastic and cellularcore Divinycell ™ P100. Mechanical characteristics of fiberglass skin for the numerical model have been determined from experiments on tension, bending and shear. Porous core was considered as a solid nonlinear hyperelastic material model Ogden Foam (first order). The constants of the model were determined from the corresponding curves under uniaxial and biaxial tension/compression, pure shear, and triaxial tension/compression for evaluating volume change. Since the carry out of such experiments is difficult, necessary strain diagrams were obtained from the calculation of the elementary Kelvin cell (tetrakaidodekaedr) suitable for describing the structure of a regular core. Cell Kelvin is a recurring form, space-filling without voids, with a minimum ratio of surface area to volume. The calculation results of the local deformation of a three-layer sandwich panel with using a model hyperelastic material Ogden Foam satisfactorily reflected the observed non-linearity diagrams in experiments and show the full energy equivalence until the destruction of skin by the shear. Thus, the developed finite element model can be used to predict the strength and energy absorption limit in low velocity impact loading studies.

A biphasic finite element study on the role of the articular cartilage superficial zone in confined compression

The aim of this study was to investigate the role of the superficial zone on the mechanical behavior of articular cartilage. Confined compression of articular cartilage was modeled using a biphasic finite element analysis to calculate the one-dimensional deformation of the extracellular matrix (ECM) and movement of the interstitial fluid through the ECM and articular surface. The articular cartilage was modeled as an inhomogeneous, nonlinear hyperelastic biphasic material with depth and strain-dependent material properties. Two loading conditions were simulated, one where the superficial zone was loaded with a porous platen (normal test) and the other where the deep zone was loaded with the porous platen (upside down test). Compressing the intact articular cartilage with 0.2MPa stress reduced the surface permeability by 88%. Removing the superficial zone increased the rate of change for all mechanical parameters and decreased the fluid support ratio of the tissue, resulting in increased tissue deformation. Apparent permeability linearly increased after superficial removal in the normal test, yet it did not change in the upside down test. Orientation of the specimen affected the time-dependent biomechanical behavior of the articular cartilage, but not equilibrium behavior. The two tests with different specimen orientations resulted in very different apparent permeabilities, suggesting that in an experimental study which quantifies material properties of an inhomogeneous material, the specimen orientation should be stated along with the permeability result. The current study provides new insights into the role of the superficial zone on mechanical behavior of the articular cartilage.

Systematic Integration of Finite Element Methods Into Multibody Dynamics Considering Hyperelasticity and Plasticity

This study proposes a systematic extension of a multiflexible-body dynamics (MFBD) formulation that is based on a recursive formulation for rigid body dynamics. It is extended to include nonlinear plastic and hyperelastic material models for the flexible bodies. The flexible bodies in the existing MFBD formulation use a finite element formulation based on corotational elements. The rigid bodies and flexible bodies are coupled using the method of Lagrange multipliers. The extensions to add plasticity and hyperelasticity are outlined. A solid, brick-type element and a shell element are adapted from the literature for use with the plastic material, and a constant volume constraint is introduced to enforce the approximation of incompressibility with the hyperelastic materials. A brief overview of the MFBD formulation and the details required to extend the formulation to incorporate these nonlinear material models are presented. Numerical examples are presented to demonstrate the feasibility of the model.

Free-vibration acoustic resonance of nonlinear hyperelastic materials

The free-vibration acoustic resonance (FVAR) of nonlinear hyperelastic materials was investigated within the framework of nonlinear elasticity and the calculus of variations. Variational analysis revealed that displacement due to FVAR satisfies the following conditions: time reversal symmetry, time periodicity, periodic vanishing of displacement velocity, and surface traction-free conditions. Numerical analysis of two-dimensional St. Venant–Kirchhoff hyperelastic materials revealed the existence and structure of the color symmetry embedded therein. The nonlinear FVAR modes showed non-monotonic amplitude dependence of resonance frequency. The symmetries of three-dimensional nonlinear FVAR modes for triclinic, monoclinic, and orthorhombic elastic media are shown on the basis of the magnetic point groups. This classification shows excellent agreement with that obtained by the overtone analysis of molecular vibration.

A theory for deformation dependent evolution of continuous fibre distribution applicable to collagen remodelling

This work explores the implications of a constitutive framework that introduces a particular remodelling process for materials having a continuous distribution of fibre directions. It is assumed that the matrix constituent is unaffected and that fibres remodel by a process of dissolution and reassembly. Dissolution results from a time dependent chemical kinetic process that is influenced by fibre stretch. Two possibilities for the reassembly of the fibres are considered: (1) fibres reassemble in a stress-free state or (2) fibres assemble in a pre-strained state matching that of the surrounding matrix. The composite is treated as a non-linear hyperelastic material. The constitutive framework accounts for the time dependent redistribution of fibre orientation and density. A directional fibre orientation density function is defined that combines fibre dissolution, reassembly and their dependence on deformation history. Expressions for the time dependence of this function are developed for the two fibre reassembly assumptions and different deformation histories. Numerical results for uniaxial extension are presented in the form of polar plots that illustrate fibre orientation density at different times and fibre density versus time plots that show evolution at different orientations.

Magnetic Resonance Imaging (MRI) Based Finite Element Modeling for Analyzing the Influence of Material Properties on Menisci Responses

To investigate the importance of the meniscal non-linear behaviour on knee joint finite element analysis (FEA) study, the aim of this study was to compare linear elastic and nonlinear hyperelastic material models on the pressure distribution of meniscus. For this purpose, a 3D finite element (FE) knee model of a healthy living subject was constructed from magnetic resonance imaging (MRI) to simulate contact pressure under axial compressive loading. Differences in meniscal contact pressures were observed between linear elastic and nonlinear hyperelastic models. These findings emphasize the importance of accounting the nonlinear material behaviour of the menisci in knee joint FEA studies.

Emergence of colour symmetry in free-vibration acoustic resonance of a nonlinear hyperelastic material

We investigated free-vibration acoustic resonance (FVAR) of two-dimensional St Venant-Kirchhoff-type hyperelastic materials and revealed the existence and structure of colour symmetry embedded therein. The hyperelastic material is isotropic and frame indifferent and includes geometrical nonlinearity in its constitutive equation. The FVAR state is formulated using the principle of stationary action with a subsidiary condition. Numerical analysis based on the Ritz method revealed the existence of four types of nonlinear FVAR modes associated with the irreducible representations of a linearized system. Projection operation revealed that the FVAR modes can be classified on the basis of a single colour (black or white) and three types of bicolour (black and white) magnetic point groups: [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. These results demonstrate that colour symmetry naturally arises in the finite amplitude nonlinear FVAR modes, and its vibrational symmetries are explained in terms of magnetic point groups rather than the irreducible representations that have been used for linearized systems. We also predicted a grey colour nonlinear FVAR mode which cannot be derived from a linearized system.

Dynamic non-linear energy absorbers based on properly stretched in-plane elastomer structures

Traditionally, elastomers are considered to be one of the best material candidates for the design of energy absorbing devices, due to their remarkable visco-elastic and extensibility material properties. This capability can be further enhanced by the design of appropriate Dielectric Elastomer Generators (DEGs). The present paper proceeds to another alternative direction, which consists of the design of appropriate elastomer structures with enhanced energy absorption capabilities, are attributed more to the appropriate non-linear design of the elastomer structure itself, than to the hyperelastic material properties of the elastomer members. For this reason, a simple chi-shaped in-plane elastic structure is considered, comprising one proof mass with four elastomer members attached to it, placed in a chi-shaped configuration, and being properly stretched. A systematic analysis is carried out, with respect to the variation of two basic structure design properties on the dynamic behavior: the orientation angle of the members and their initial pre-stress. The obtained results show that the variation of just these two basic parameters of the structure may lead to a quite rich and interesting non-linear dynamic behavior. More specifically, the traditional always-in-tension concept leads to a linear dynamic system response, even though the elastomer members are considered to have been made of a non-linear hyper-elastic material. Alternatively, a new partially-loose-member operating concept is analyzed. This concept suggests that some individual elastomer members be allowed to become loose for some period of the operating cycle, (but not all of them simultaneously), strongly enhancing the broadband energy absorbing capability of the structure itself.

A Multiscale Finite Element Simulation of Human Aortic Heart Valve

Some of the heart valve diseases can be treated by surgical replacement with either a mechanical or bioprosthetic heart valve (BHV). Recently, tissue-engineered heart valves (TEHVs) have been proposed to be the ultimate solution for treating valvular heart disease. In order to improve the durability and design of artificial heart valves, recent studies have focused on quantifying the biomechanical interaction between the organ, tissue, and cellular –level components in native heart valves. Such data is considered fundamental to designing improved BHVs. Mechanical communication from the larger scales affects active biomechanical processes. For instance any organ-scale motion deforms the tissue, which in turn deforms the interstitial cells (ICs). Therefore, a multiscale solution is required to study the behavior of human aortic valve and to predict local cell deformations. The proposed multiscale finite element approach takes into account large deformations and nonlinear anisotropic hyperelastic material models. In this simulation, the organ scale motion is computed, from which the tissue scale deformation will be extracted. Similarly, the tissue deformation will be transformed into the cell scale. Finally, each simulation is verified against a number of experimental measures.

In vivo determination of elastic properties of the human aorta based on 4D ultrasound data

Computational analysis of the biomechanics of the vascular system aims at a better understanding of its physiology and pathophysiology. To be of clinical use, however, these models and thus their predictions, have to be patient specific regarding geometry, boundary conditions and material. In this paper we present an approach to determine individual material properties of human aortae based on a new type of in vivo full field displacement data acquired by dimensional time resolved three dimensional ultrasound (4D-US) imaging. We developed a nested iterative Finite Element Updating method to solve two coupled inverse problems: The prestrains that are present in the imaged diastolic configuration of the aortic wall are determined. The solution of this problem is integrated in an iterative method to identify the nonlinear hyperelastic anisotropic material response of the aorta to physiologic deformation states. The method was applied to 4D-US data sets of the abdominal aorta of five healthy volunteers and verified by a numerical experiment. This non-invasive in vivo technique can be regarded as a first step to determine patient individual material properties of the human aorta.

Conmutación temporal entre técnicas numéricas implícita y explícita para simulación de estructuras no lineales inestables

Simulation problems involving non-linear materials imply in numerous cases divergence of the implicit method which use return mapping algorithms for modelling of the nonlinear response. A switching implicit-explicit numerical technique in the context of Finite Element Methods is presented in this paper. Implicit/explicit mesh partitions are not considered whatsoever. Formulation for application to nonlinear hyperelastic materials and nonlinear elastic-plastic materials is provided. Furthermore, the response of the solid subjected to large deformations is presented and is embedded in the proposed technique. Numerical tests for nonlinear problems (geometric and/or material) showed the accurateness of the technique.

자동차 그로멧의 유한요소해석 및 노화시험에 대한 연구

Grommet is one of the Automotive rubber components and is made from EPDM(Ethylene Propylene Diene monomer M-class) rubber and the nonlinear hyperelastic material properties of rubber are important to predict the behavior of rubber product. In this study, the stable stress-strain relations were obtained from the uni-axial tension test and the equi-biaxial tension test. Finite element analysis for grommet was carried out and heat aging test for the lifetime prediction of grommet was introduced.

Goal-oriented error estimation for fluid–structure interaction problems

In this work, we present an adaptive finite element method for the numerical simulation of stationary fluid–structure interaction problems. The coupled system is given in a variational and monolithic Arbitrary Lagrangian Eulerian framework. We derive methods for goal-oriented error estimation and mesh adaptation with the dual weighted residual method. Key to applying this error estimator is the underlying canonic variational formulation of the fluid–structure interaction problem by mapping the flow problem to ALE coordinates. The developed method is applied to two and three dimensional stationary benchmark problems coupling the incompressible Navier–Stokes equations with a nonlinear hyper-elastic material law.

Numerical and experimental investigation of vascular suture closure

In order to optimize the performance of the suture for tissue closure, it is essential to develop strategies for devising new and improved techniques that can visualize and compare various suturing techniques. This paper describes an experimental and numerical investigation on the performance of sutured tissue. In the experiments, two pieces of glutaraldehyde cross-linked bovine pericardium were sutured together through simple running suture and tensioned to study the performance of the sutured tissue. During testing, the tension load and the total displacement of the specimen were recorded. The strain field of the specimen was simultaneously captured using two high speed cameras and post processed using its associated image processing software. In addition, nonlinear hyperelastic material models for Shelhigh patch and cryopreserved human aorta were derived through least-square fitting into the tensile testing data. Three dimensional finite element models were developed to replicate the behavior of wound closure. The effect of tissue material mismatch, and stiffness of the suture thread on the mechanical behavior of sutured tissue was examined. The stain distributions obtained from simulation agrees with the captured surface strain map from experiments. A relative softer suture thread could reduce the peak stress concentrations at the knotting location. The mechanical performance of sutured tissue depends on the level of mismatch in material stiffness between the native tissue and the replacement material

Preliminary analysis of the sacroiliac joint in the hyperlordotic spine, a finite element model

Preliminary analysis of the sacroiliac joint in the hyperlordotic spine, a finite element model

Analyzing the propagation of a quadratic nonlinear hyperelastic cylindrical wave

The perturbation method (small-parameter method) is used to analyze the propagation of a cylindrical wave in a quadratic nonlinear hyperelastic material described by the classical Murnaghan model. The exact representation of the first-order solution in terms of squared Hankel functions of zero and first orders and their product is derived. A simplification of the new solution is considered