Journal articles: 'Hyperelastic anisotropic material'

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Gurvich, Mark R. "On Characterization of Anisotropic Elastomeric Materials for Structural Analysis." Rubber Chemistry and Technology 77, no. 1 (March 1, 2004): 115–30. http://dx.doi.org/10.5254/1.3547805.

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Abstract Existing efforts in constitutive modeling of elastomers are primarily focused on isotropic materials. On the other hand, anisotropic elastic models were successfully developed for traditional composites with relatively small strains, where geometrical non-linearity of deformation may be ignored. There are, however, certain materials where neither large deformation and incompressibility nor anisotropy of material stiffness may be neglected. This study proposes a general constitutive approach to model both hyperelasticity (including incompressibility) and full anisotropy of material deformation in structural analysis. According to the proposed approach, an original hyperelastic anisotropic body is modeled as a combination of two hypothetical components (hyperelastic isotropic and elastic anisotropic ones). The proposed approach shows simplicity and convenience of practical application along with high accuracy of analysis. It may be easily implemented in computational analysis of 2- and 3-D problems using commercially available FEA codes without additional programming efforts. Analytical and computational implementation of the approach is considered on representative examples of elastomeric structures and rubber-based composites. Analytical solutions are shown for examples of biaxial tension of composites and inflation of a toroidal anisotropic tube. FEA solutions are discussed on examples of an inflated anisotropic sphere and non-uniform deformation of a composite layer. Obtained results are discussed to emphasize benefits of the proposed approach. Finally, a methodology to evaluate material parameters using corresponding test results is considered according to the proposed approach.

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Chanda, Arnab, Subhodip Chatterjee, and Vivek Gupta. "Soft composite based hyperelastic model for anisotropic tissue characterization." Journal of Composite Materials 54, no. 28 (June 23, 2020): 4525–34. http://dx.doi.org/10.1177/0021998320935560.

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Soft tissues are complex anisotropic composite systems comprising of multiple differently oriented layers of fiber embedded within a soft matrix. To date, soft tissues have been mainly characterized using simplified linear elastic material models, isotropic viscoelastic and hyperelastic models, and transversely isotropic models. In such models, the effect of fiber volume fraction (FVF), fiber orientation, and fiber-matrix interactions are missing, inhibiting accurate characterization of anisotropic tissue properties. The current work addresses this literature gap with the development of a novel soft composite based material framework to model tissue anisotropy. In this model, the fiber and matrix are considered as separate hyperelastic materials, and fiber-matrix interaction is modeled using multiplicative decomposition of the deformation gradient. The effect of the individual contribution of the fibers and matrix are introduced into the numerical framework for a single soft composite layer, and fiber orientation effects are incorporated into the strain energy functions. Also, strain energy formulations are developed for multiple soft composite layers with varying fiber orientations and contributions, describing the biomechanical behavior of an entire anisotropic tissue block. Stress-strain relationships were derived from the strain energy equations for a uniaxial mechanical test condition. To validate the model parameters, experimental models of soft composites tested under uniaxial tension were characterized using the novel anisotropic hyperelastic model (R2 = 0.983). To date, such a robust anisotropic hyperelastic composite framework has not been developed, which would be indispensable for experimental characterization of tissues and for improving the fidelity of computational biological models in future.

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Ansari, Mohd Zahid, Sang Kyo Lee, and Chong Du Cho. "Hyperelastic Muscle Simulation." Key Engineering Materials 345-346 (August 2007): 1241–44. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.1241.

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Biological soft tissues like muscles and cartilages are anisotropic, inhomogeneous, and nearly incompressible. The incompressible material behavior may lead to some difficulties in numerical simulation, such as volumetric locking and solution divergence. Mixed u-P formulations can be used to overcome incompressible material problems. The hyperelastic materials can be used to describe the biological skeletal muscle behavior. In this study, experiments are conducted to obtain the stress-strain behavior of a solid silicone rubber tube. It is used to emulate the skeletal muscle tensile behavior. The stress-strain behavior of silicone is compared with that of muscles. A commercial finite element analysis package ABAQUS is used to simulate the stress-strain behavior of silicone rubber. Results show that mixed u-P formulations with hyperelastic material model can be used to successfully simulate the muscle material behavior. Such an analysis can be used to simulate and analyze other soft tissues that show similar behavior.

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Cudny, Marcin, and Katarzyna Staszewska. "A hyperelastic model for soils with stress-induced and inherent anisotropy." Acta Geotechnica 16, no. 7 (March 5, 2021): 1983–2001. http://dx.doi.org/10.1007/s11440-021-01159-z.

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AbstractIn this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to introduce constant inherent cross-anisotropic component. A convenient feature of the new model is low number of material constants directly related to the parameters commonly used in the literature. The proposed description can be incorporated as a small strain elastic core in the development of some more sophisticated hyperelastic-plastic models of overconsolidated soils. It can also be used as an independent model in analyses involving small strain problems, such as dynamic simulations of the elastic wave propagation. Various options and features of the proposed anisotropic hyperelastic model are investigated. The directional model response is compared with experimental data available in the literature.

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Nam, Tran Huu. "Using FEM for large deformation analysis of inflated air-spring cylindrical shell made of rubber-textile cord composite." Vietnam Journal of Mechanics 28, no. 1 (April 17, 2006): 10–20. http://dx.doi.org/10.15625/0866-7136/28/1/5474.

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An orthotropic hyperelastic constitutive model is presented for large deformation analysis of the nonlinear anisotropic hyperelastic material of the cylindrical air-spring shell used in vibroisolation of driver's seat. Nonlinear hyperelastic constitutive equations of orthotropic composite material are incorporated into the finite strain analysis by finite element method (FEM). The results of deformation analysis of the inflated air-spring shell made of composite with rubber matrix reinforced by textile cords are given. Obtained numerical results of deformation corresponding to the experimentally measured deformation of the inflated cylindrical air-spring.

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Chanda, Arnab, and Christian Callaway. "Tissue Anisotropy Modeling Using Soft Composite Materials." Applied Bionics and Biomechanics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/4838157.

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Soft tissues in general exhibit anisotropic mechanical behavior, which varies in three dimensions based on the location of the tissue in the body. In the past, there have been few attempts to numerically model tissue anisotropy using composite-based formulations (involving fibers embedded within a matrix material). However, so far, tissue anisotropy has not been modeled experimentally. In the current work, novel elastomer-based soft composite materials were developed in the form of experimental test coupons, to model the macroscopic anisotropy in tissue mechanical properties. A soft elastomer matrix was fabricated, and fibers made of a stiffer elastomer material were embedded within the matrix material to generate the test coupons. The coupons were tested on a mechanical testing machine, and the resulting stress-versus-stretch responses were studied. The fiber volume fraction (FVF), fiber spacing, and orientations were varied to estimate the changes in the mechanical responses. The mechanical behavior of the soft composites was characterized using hyperelastic material models such as Mooney-Rivlin’s, Humphrey’s, and Veronda-Westmann’s model and also compared with the anisotropic mechanical behavior of the human skin, pelvic tissues, and brain tissues. This work lays the foundation for the experimental modelling of tissue anisotropy, which combined with microscopic studies on tissues can lead to refinements in the simulation of localized fiber distribution and orientations, and enable the development of biofidelic anisotropic tissue phantom materials for various tissue engineering and testing applications.

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Sokolova, M. Yu, and D. V. Khristich. "FINITE STRAINS OF NONLINEAR ELASTIC ANISOTROPIC MATERIALS." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 70 (2021): 103–16. http://dx.doi.org/10.17223/19988621/70/9.

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Anisotropic materials with the symmetry of elastic properties inherent in crystals of cubic syngony are considered. Cubic materials are close to isotropic ones by their mechanical properties. For a cubic material, the elasticity tensor written in an arbitrary (laboratory) coordinate system, in the general case, has 21 non-zero components that are not independent. An experimental method is proposed for determining such a coordinate system, called canonical, in which a tensor of elastic properties includes only three nonzero independent constants. The nonlinear model of the mechanical behavior of cubic materials is developed, taking into account geometric and physical nonlinearities. The specific potential strain energy for a hyperelastic cubic material is written as a function of the tensor invariants, which are projections of the Cauchy-Green strain tensor into eigensubspaces of the cubic material. Expansions of elasticity tensors of the fourth and sixth ranks in tensor bases in eigensubspaces are determined for the cubic material. Relations between stresses and finite strains containing the second degree of deformations are obtained. The expressions for the stress tensor reflect the mutual influence of the processes occurring in various eigensubspaces of the material under consideration.

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Vladimirov, Ivaylo N., Michael P. Pietryga, Yalin Kiliclar, Vivian Tini, and Stefanie Reese. "Failure modelling in metal forming by means of an anisotropic hyperelastic-plasticity model with damage." International Journal of Damage Mechanics 23, no. 8 (January 16, 2014): 1096–132. http://dx.doi.org/10.1177/1056789513518953.

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In metal forming, formability is limited by the evolution of ductile damage in the work piece. The accurate prediction of material failure requires, in addition to the description of anisotropic plasticity, the inclusion of damage in the finite element simulation. This paper discusses the application of an anisotropic hyperelastic-plasticity model with isotropic damage to the numerical simulation of fracture limits in metal forming. The model incorporates plastic anisotropy, nonlinear kinematic and isotropic hardening and ductile damage. The constitutive equations of the proposed model are numerically integrated both implicitly and explicitly, and the model is implemented as a user material subroutine UMAT in the commercial solvers ABAQUS/Standard and LS-DYNA, respectively. The numerical examples investigate the potential of the constitutive framework regarding the prediction of failure in metal forming processes such as, e.g. cross-die deep drawing. In particular, simulations of the Nakazima stretching test with varying specimen geometry are utilized to simulate the forming limit diagram at fracture and the numerical results are compared to experimental data for aluminium alloy sheets.

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Hashemi, Sanaz S., Masoud Asgari, and Akbar Rasoulian. "An experimental study of nonlinear rate-dependent behaviour of skeletal muscle to obtain passive mechanical properties." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 234, no. 6 (March 5, 2020): 590–602. http://dx.doi.org/10.1177/0954411920909705.

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Accurate modelling of biological tissues has been a significant need for analysis of the human body. In this article, a comprehensive in vitro experimental study has been done on the fresh bovine skeletal muscle before the onset of rigour mortis in order to provide an experimental description of passive skeletal muscle properties in three dimensions. Different situations including various deformation modes, different loading rates and loading directions are tested to consider all features of skeletal muscle behaviour. Based on the nonlinear continuum mechanics, a three-dimensional visco-hyperelastic model is introduced which considers all aspects of skeletal muscle’s features such as nonlinear hyperelastic, time-dependent behaviour, anisotropy and quasi-incompressibility. Visco-hyperelastic material constants are obtained for passive behaviour of the muscle based on genetic algorithm optimization method via comparing the theoretical and experimental results. Experiments show that the rate of loading affects the configuration of experimental curves considerably. It could be also concluded that compression–tension asymmetry, as well as anisotropic behaviour, of the muscle is due to fibres orientation. Obtained experimental results help to achieve a better understanding of mechanical properties and nonlinear behaviour of the skeletal muscles.

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Chatelin, Simon, Caroline Deck, and Rémy Willinger. "An anisotropic viscous hyperelastic constitutive law for brain material finite-element modeling." Journal of Biorheology 27, no. 1-2 (December 6, 2012): 26–37. http://dx.doi.org/10.1007/s12573-012-0055-6.

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Nam, Tran Huu. "Identification parameters of material model and large deformation analysis of inflated air-spring shell made of rubber-textile cord composite." Vietnam Journal of Mechanics 27, no. 2 (July 1, 2005): 118–28. http://dx.doi.org/10.15625/0866-7136/27/2/5721.

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In the paper an orthotropic hyperelastic constitutive model is presented which can be applied to numerical simulation for the response of biological soft tissue and of the nonlinear anisotropic hyperelastic material of the cylindrical air-spring shell used in vibroisolation of driver's seat. The parameters of strain energy function of the proposed constitutive model are fitted to the experimental results by the nonlinear least squares method. The deformation of the inflated cylindrical air-spring shell is calculated by solving the system of five first-order ordinary differential equations with the material constitutive law and proper boundary conditions. Numerical results of principal stretches and deformed profiles of the inflated cylindrical air-spring shell obtained by numerical deformation analysis are compared with experimental ones.

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Qu, Zhipeng, Wei He, Mingyun Lv, and Houdi Xiao. "Large-Strain Hyperelastic Constitutive Model of Envelope Material under Biaxial Tension with Different Stress Ratios." Materials 11, no. 9 (September 19, 2018): 1780. http://dx.doi.org/10.3390/ma11091780.

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This paper reports the biaxial tensile mechanical properties of the envelope material through experimental and constitutive models. First, the biaxial tensile failure tests of the envelope material with different stress ratio in warp and weft directions are carried out. Then, based on fiber-reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model on envelope material with different stress ratio is developed. A strain energy function that characterizes the anisotropic behavior of the envelope material is decomposed into three parts: fiber, matrix and fiber–fiber interaction. The fiber–matrix interaction is eliminated in this model. A new simple model for fiber–fiber interaction with different stress ratio is developed. Finally, the results show that the constitutive model has a good agreement with the experiment results. The results can be used to provide a reference for structural design of envelope material.

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Djeridi, Rachid, and Mohand Ould Ouali. "Numerical Implementation and Finite Element Analysis of Anisotropic Hyperelastic Biomaterials - Influence of Fibers Orientation." Key Engineering Materials 554-557 (June 2013): 2414–23. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.2414.

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Modeling anisotropic behavior of fiber reinforced rubberlike materials is actually of a great interest in many industrials sectors. Indeed, accurately description of the mechanical response and damage of such materials allows the increase of the lifecycle of these materials which generally evolve under several environment conditions. In this paper theoretical study and finite element analysis of anisotropic biomaterials is presented. The mechanical model adopted to achieve this study has been implemented into the finite element code Abaqus using an implicit scheme. This constitutive law has been utilized to perform some numerical simulations. The material parameters of the model have been determined by numerical calibration. One fiber family is considered in this work. Effects of the fiber orientation on the mechanical response and stiffness change of biomaterial is studied. Both the compressible and incompressible states have been taken into account. The results show firstly the capability of the model to reproduce the known results and that optimal fiber orientation can be found.

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Suda, Masaki, and Akihiro Matsuda. "902 Development of an anisotropic hyperelastic material model which is considering stress softening." Proceedings of Ibaraki District Conference 2013.21 (2013): 17–18. http://dx.doi.org/10.1299/jsmeibaraki.2013.21.17.

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Diani, Julie, Mathias Brieu, and Pierre Gilormini. "Observation and modeling of the anisotropic visco-hyperelastic behavior of a rubberlike material." International Journal of Solids and Structures 43, no. 10 (May 2006): 3044–56. http://dx.doi.org/10.1016/j.ijsolstr.2005.06.045.

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Vu, Ngoc-Hung, Xuan-Tan Pham, Vincent François, and Jean-Christophe Cuillière. "Characterization of multilayered carbon-fiber–reinforced thermoplastic composites for assembly process." Journal of Thermoplastic Composite Materials 32, no. 5 (May 1, 2018): 673–89. http://dx.doi.org/10.1177/0892705718772878.

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The aim of this research work is to characterize the mechanical behavior of multilayered carbon-fiber–reinforced polyphenylene sulfide composites with the application to assembly process of nonrigid parts. Two anisotropic hyperelastic material models were investigated and implemented in Abaqus as a user-defined material. An inverse characterization method was applied to identify the parameters of these material models. Finite element simulations at finite strains of a flexible composite sheet were carried out. Numerical results of sheet deformation were compared with the experimental results in order to evaluate the appropriateness of the material models developed for this application.

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Puso, M. A., and J. A. Weiss. "Finite Element Implementation of Anisotropic Quasi-Linear Viscoelasticity Using a Discrete Spectrum Approximation." Journal of Biomechanical Engineering 120, no. 1 (February 1, 1998): 62–70. http://dx.doi.org/10.1115/1.2834308.

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The objective of this work was to develop a theoretical and computational framework to apply the finite element method to anisotropic, viscoelastic soft tissues. The quasi-linear viscoelastic (QLV) theory provided the basis for the development. To allow efficient and easy computational implementation, a discrete spectrum approximation was developed for the QLV relaxation function. This approximation provided a graphic means to fit experimental data with an exponential series. A transversely isotropic hyperelastic material model developed for ligaments and tendons was used for the elastic response. The viscoelastic material model was implemented in a general-purpose, nonlinear finite element program. Test problems were analyzed to assess the performance of the discrete spectrum approximation and the accuracy of the finite element implementation. Results indicated that the formulation can reproduce the anisotropy and time-dependent material behavior observed in soft tissues. Application of the formulation to the analysis of the human femur-medial collateral ligament–tibia complex demonstrated the ability of the formulation to analyze large three-dimensional problems in the mechanics of biological joints.

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Azarov, Daniil. "Mechanical-Geometrical Modeling Of The Hyperelastic Materials At Uniaxial Stretching." Journal of Physics: Conference Series 2131, no. 5 (December 1, 2021): 052017. http://dx.doi.org/10.1088/1742-6596/2131/5/052017.

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Abstract Hyperelastic materials, such as rubber, occupy an important place in the design and operation of various technological equipment and machines. The article analyzed the deformation behavior of hyperelastic materials using a mechanical-geometric model. The method of mechanical-geometric modeling is a new method for obtaining constitutive relations and strain energy density functions for nonlinear elastic solids. It is based on physically and geometrically consistent prerequisites. The resulting models can describe broad classes of nonlinear elastic materials (both isotropic and anisotropic) depending on the mechanical and geometric properties “embedded” in them at the first stages of design. This paper discusses two basic types of models based on different initial geometry. The mechanical parameters of the models are constants, and the models themselves are considered in a statement corresponding to isotropic hyperelastic materials. The article presents the most common diagrams of deformation of artificial and natural rubbers, as well as steel. Hyperelastic materials, depending on the task, can be described in the nonlinear theory of elasticity as ideal incompressible, or as weakly compressible. Parameters of expressions of strain energy density functions of mechanical-geometric models obtained for cases of incompressible and weakly compressible continuous solids were identified. Stretch diagrams and diagrams of the transverse deformation function of the obtained mechanical-geometric models for the two cases mentioned above are plotted. The extension diagram for the model with parameters corresponding to the classic structural material of the steel type is also shown. Comments are given on the possibility of further paths of developing the method of mechanical-geometric modeling to obtain results not only in the field of nonlinear theory of elasticity, but also viscoelasticity.

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Ndlovu, Zwelihle, Dawood Desai, Thanyani Pandelani, Harry Ngwangwa, and Fulufhelo Nemavhola. "Biaxial Estimation of Biomechanical Constitutive Parameters of Passive Porcine Sclera Soft Tissue." Applied Bionics and Biomechanics 2022 (February 28, 2022): 1–11. http://dx.doi.org/10.1155/2022/4775595.

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This study assesses the modelling capabilities of four constitutive hyperelastic material models to fit the experimental data of the porcine sclera soft tissue. It further estimates the material parameters and discusses their applicability to a finite element model by examining the statistical dispersion measured through the standard deviation. Fifteen sclera tissues were harvested from porcine’ slaughtered at an abattoir and were subjected to equi-biaxial testing. The results show that all the four material models yielded very good correlations at correlations above 96%. The polynomial (anisotropic) model gave the best correlation of 98%. However, the estimated material parameters varied widely from one test to another such that there would be need to normalise the test data to avoid long optimisation processes after applying the average material parameters to finite element models. However, for application of the estimated material parameters to finite element models, there would be need to consider normalising the test data to reduce the search region for the optimisation algorithms. Although the polynomial (anisotropic) model yielded the best correlation, it was found that the Choi-Vito had the least variation in the estimated material parameters, thereby making it an easier option for application of its material parameters to a finite element model and requiring minimum effort in the optimisation procedure. For the porcine sclera tissue, it was found that the anisotropy was more influenced by the fiber-related properties than the background material matrix-related properties.

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Peng, X. Q., Z. Y. Guo, and B. Moran. "An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus." Journal of Applied Mechanics 73, no. 5 (May 16, 2005): 815–24. http://dx.doi.org/10.1115/1.2069987.

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Based on fiber reinforced continuum mechanics theory, an anisotropic hyperelastic constitutive model for the human annulus fibrosus is developed. A strain energy function representing the anisotropic elastic material behavior of the annulus fibrosus is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber-matrix shear interaction, respectively. Taking advantage of the laminated structure of the annulus fibrosus with one family of aligned fibers in each lamella, interlamellar fiber-fiber interaction is eliminated, which greatly simplifies the constitutive model. A simple geometric description for the shearing between the fiber and the matrix is developed and this quantity is used in the representation of the fiber-matrix shear interaction energy. Intralamellar fiber-fiber interaction is also encompassed by this interaction term. Experimental data from the literature are used to obtain the material parameters in the constitutive model and to provide model validation. Determination of the material parameters is greatly facilitated by the partition of the strain energy function into matrix, fiber and fiber-matrix shear interaction terms. A straightforward procedure for computation of the material parameters from simple experimental tests is proposed.

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Yao, Yuan, Xiaoshuang Huang, Xiongqi Peng, Pengfei Liu, and Gong Youkun. "An anisotropic hyperelastic constitutive model for plain weave fabric considering biaxial tension coupling." Textile Research Journal 89, no. 3 (December 20, 2017): 434–44. http://dx.doi.org/10.1177/0040517517748495.

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A nonlinear anisotropic hyperelastic constitutive model is developed for plain weave fabrics by considering biaxial tensile coupling. The strain energy function is decomposed into two parts to represent tensile energy, including the biaxial tensile coupling effect from fiber elongation and shearing energy from relative rotation between warp and weft yarns. A simple and efficient material parameter identification method is proposed. The model is exemplified on a balanced plain weave glass fabric. Experimental data from the literature are used to identify material parameters in the constitutive model. Model validation is implemented by comparing numerical results with various experimental data, including biaxial tension tests under different stretch ratios and the picture frame shearing test. The developed constitutive model is applied to numerical simulation of a double-dome stamping of the plain weave fabric. The influences of binder force and initial fiber yarn orientation on forming are investigated. Numerical results demonstrated that the biaxial tensile coupling effect could not be neglected in forming simulation. The developed constitutive model is suitable to characterize the nonlinear behavior of plain weave fabrics under large deformation.

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Gong, Youkun, Dongxiu Yan, Yuan Yao, Ran Wei, Hongling Hu, Peng Xu, and Xiongqi Peng. "An Anisotropic Hyperelastic Constitutive Model with Tension–Shear Coupling for Woven Composite Reinforcements." International Journal of Applied Mechanics 09, no. 06 (September 2017): 1750083. http://dx.doi.org/10.1142/s1758825117500831.

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An anisotropic hyperelastic constitutive model with tension–shear coupling was developed for woven composite reinforcements based on fiber reinforced continuum mechanics theory. The strain energy of the model was additively decomposed into two parts nominally representing the fiber stretches and fiber–fiber interaction considering shear–tension coupling, respectively. Experimental data were used to identify material parameters orderly and simply in the constitutive model for a specific balanced plain woven carbon fabric. The developed model was validated by comparing numerical results with picture-frame shear tests under different pre-stretch ratios, and was then applied to the simulation of a hemispherical stamping experiment, demonstrating that the developed constitutive model is highly suitable to characterize the nonlinear and anisotropic mechanical behaviors of woven composite reinforcements under large deformation. The proposed model establishes a theoretical foundation for more accurate forming simulation and processing optimization of woven fabric composites.

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BHAT, SUBRAYA KRISHNA, NORIYUKI SAKATA, and HIROSHI YAMADA. "IDENTIFICATION OF UNIAXIAL DEFORMATION BEHAVIOR AND ITS INITIAL TANGENT MODULUS FOR ATHEROMATOUS INTIMA IN THE HUMAN CAROTID ARTERY AND THORACIC AORTA USING THREE-PARAMETER ISOTROPIC HYPERELASTIC MODELS." Journal of Mechanics in Medicine and Biology 20, no. 03 (April 2020): 2050014. http://dx.doi.org/10.1142/s0219519420500141.

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Uniaxial stretching tests are used for mechanical identification of small fibrous regions of atheromatous arteries. Material constants in isotropic hyperelastic models are determined to minimize the fitting error for the stress–strain curve. We developed a novel method to better characterize the material constants in typical forms of Yeoh, Ogden, Chuong–Fung (CF) and Gasser–Ogden–Holzapfel (GOH) isotropic hyperelastic models for fibrous caps and normal intimal layers from human carotid artery and thoracic aorta by incorporating Young’s modulus, i.e., the initial tangent modulus of uniaxial stress–strain relationships, as one of three material constants. We derived a unified, isotropic form for the anisotropic exponential-type strain energy density functions of CF and GOH models. The uniaxial stress–strain relationship equations were expanded to Maclaurin series to identify Young’s modulus as a coefficient of the linear term of the strain and to examine the roles of the material constants in the nonlinear function. The remaining two material constants were determined by curvefitting. The incorporation of Young’s modulus into the CF and GOH models gave reasonable curvefitting, with errors [Formula: see text], whereas large errors ([Formula: see text]) were observed in one case for the Yeoh model and in two cases for the Ogden model.

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Ferreira, João, Marco Parente, and Renato Jorge. "Modeling of soft tissues with damage." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 231, no. 1-2 (August 19, 2016): 131–39. http://dx.doi.org/10.1177/1464420716662295.

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The characteristic highly non-linear biomechanics of soft tissues within their physiological range often involve degradation of the material properties. Some evidence shows that the stretch patterns induced in this (bio)structures lead to pathological conditions associated with the continuous degradation of the collagen fibres and ground substance of the material. In this work, a computational framework for modeling local anisotropic damage within non-linear geometrical considerations is proposed. Due to tissue and subject variability observed in the mechanical characterization of these types of materials, we adopt a strongly objective approach able to compute the material response for any functional form of the hyperelastic constitutive equations. The numerical examples of three-dimensional displacement and force-driven boundary value problems describe the capability to use multiple material models within the same computational framework. Particularities in the behaviour of the considered material models and the implications of considering damage effects to represent the Mullins effect are discussed.

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Baer, Anthony E., Tod A. Laursen, Farshid Guilak, and Lori A. Setton. "The Micromechanical Environment of Intervertebral Disc Cells Determined by a Finite Deformation, Anisotropic, and Biphasic Finite Element Model." Journal of Biomechanical Engineering 125, no. 1 (February 1, 2003): 1–11. http://dx.doi.org/10.1115/1.1532790.

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Cellular response to mechanical loading varies between the anatomic zones of the intervertebral disc. This difference may be related to differences in the structure and mechanics of both cells and extracellular matrix, which are expected to cause differences in the physical stimuli (such as pressure, stress, and strain) in the cellular micromechanical environment. In this study, a finite element model was developed that was capable of describing the cell micromechanical environment in the intervertebral disc. The model was capable of describing a number of important mechanical phenomena: flow-dependent viscoelasticity using the biphasic theory for soft tissues; finite deformation effects using a hyperelastic constitutive law for the solid phase; and material anisotropy by including a fiber-reinforced continuum law in the hyperelastic strain energy function. To construct accurate finite element meshes, the in situ geometry of IVD cells were measured experimentally using laser scanning confocal microscopy and three-dimensional reconstruction techniques. The model predicted that the cellular micromechanical environment varies dramatically between the anatomic zones, with larger cellular strains predicted in the anisotropic anulus fibrosus and transition zone compared to the isotropic nucleus pulposus. These results suggest that deformation related stimuli may dominate for anulus fibrosus and transition zone cells, while hydrostatic pressurization may dominate in the nucleus pulposus. Furthermore, the model predicted that micromechanical environment is strongly influenced by cell geometry, suggesting that the geometry of IVD cells in situ may be an adaptation to reduce cellular strains during tissue loading.

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Balzani, Daniel, Simone Deparis, Simon Fausten, Davide Forti, Alexander Heinlein, Axel Klawonn, Alfio Quarteroni, Oliver Rheinbach, and Joerg Schröder. "Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains." International Journal for Numerical Methods in Biomedical Engineering 32, no. 10 (December 7, 2015): e02756. http://dx.doi.org/10.1002/cnm.2756.

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Gurvich, Mark R. "On Multi-Scale Modeling of Elastomeric Laminated Composites for Structural Analysis." Rubber Chemistry and Technology 79, no. 2 (May 1, 2006): 217–32. http://dx.doi.org/10.5254/1.3547934.

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Abstract Analysis of complex structures is often based on multi-scale modeling, where effective properties of certain substructures are used instead of actual properties of smaller components. Laminated composites are usually considered as such sub-structures in components with laminated design. In case of elastomeric composites, well-known classical laminate theories could hardly be used due to significant non-linearity and incompressibility of material deformation. A convenient engineering variant of laminated model is proposed in this study for composites where neither physical nor geometrical non-linearity may be ignored. Possible material incompressibility is also taken into account. The model is primarily based on a previously developed constitutive approach to describe effective properties of anisotropic hyperelastic materials. Analytical and computational implementation of the model is considered in detail. Numerical examples illustrate accuracy and convenience of the model for representative cord/rubber composites.

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Guccione, J. M., A. D. McCulloch, and L. K. Waldman. "Passive Material Properties of Intact Ventricular Myocardium Determined From a Cylindrical Model." Journal of Biomechanical Engineering 113, no. 1 (February 1, 1991): 42–55. http://dx.doi.org/10.1115/1.2894084.

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The equatorial region of the canine left ventricle was modeled as a thick-walled cylinder consisting of an incompressible hyperelastic material with homogeneous exponential properties. The anisotropic properties of the passive myocardium were assumed to be locally transversely isotropic with respect to a fiber axis whose orientation varied linearly across the wall. Simultaneous inflation, extension, and torsion were applied to the cylinder to produce epicardial strains that were measured previously in the potassium-arrested dog heart. Residual stress in the unloaded state was included by considering the stress-free configuration to be a warped cylindrical arc. In the special case of isotropic material properties, torsion and residual stress both significantly reduced the high circumferential stress peaks predicted at the endocardium by previous models. However, a resultant axial force and moment were necessary to cause the observed epicardial deformations. Therefore, the anisotropic material parameters were found that minimized these resultants and allowed the prescribed displacements to occur subject to the known ventricular pressure loads. The global minimum solution of this parameter optimization problem indicated that the stiffness of passive myocardium (defined for a 20 percent equibiaxial extension) would be 2.4 to 6.6 times greater in the fiber direction than in the transverse plane for a broad range of assumed fiber angle distributions and residual stresses. This agrees with the results of biaxial tissue testing. The predicted transmural distributions of fiber stress were relatively flat with slight peaks in the subepicardium, and the fiber strain profiles agreed closely with experimentally observed sarcomere length distributions. The results indicate that torsion, residual stress and material anisotropy associated with the fiber architecture all can act to reduce endocardial stress gradients in the passive left ventricle.

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Casaroli, Gloria, Fabio Galbusera, René Jonas, Benedikt Schlager, Hans-Joachim Wilke, and Tomaso Villa. "A novel finite element model of the ovine lumbar intervertebral disc with anisotropic hyperelastic material properties." PLOS ONE 12, no. 5 (May 4, 2017): e0177088. http://dx.doi.org/10.1371/journal.pone.0177088.

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Ferreira, J. P. S., M. P. L. Parente, M. Jabareen, and R. M. Natal Jorge. "A general framework for the numerical implementation of anisotropic hyperelastic material models including non-local damage." Biomechanics and Modeling in Mechanobiology 16, no. 4 (January 25, 2017): 1119–40. http://dx.doi.org/10.1007/s10237-017-0875-9.

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Nolan, D. R., C. Lally, and J. P. McGarry. "Understanding the deformation gradient in Abaqus and key guidelines for anisotropic hyperelastic user material subroutines (UMATs)." Journal of the Mechanical Behavior of Biomedical Materials 126 (February 2022): 104940. http://dx.doi.org/10.1016/j.jmbbm.2021.104940.

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TOUNGARA, MAMADOU, GREGORY CHAGNON, and CHRISTIAN GEINDREAU. "NUMERICAL ANALYSIS OF THE WALL STRESS IN ABDOMINAL AORTIC ANEURYSM: INFLUENCE OF THE MATERIAL MODEL NEAR-INCOMPRESSIBILITY." Journal of Mechanics in Medicine and Biology 12, no. 01 (March 2012): 1250005. http://dx.doi.org/10.1142/s0219519412004442.

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Recently, hyperelastic mechanical models were proposed to well capture the aneurismal arterial wall anisotropic and nonlinear features experimentally observed. These models were formulated assuming the material incompressibility. However in numerical analysis, a nearly incompressible approach, i.e., a mixed formulation pressure-displacement, is usually adopted to perform finite element stress analysis of abdominal aortic aneurysm (AAA). Therefore, volume variations of the material are controlled through the volumetric energy which depends on the initial bulk modulus κ. In this paper, an analytical analysis of the influence of κ on the mechanical response of two invariant-based anisotropic models is first performed in the case of an equibiaxial tensile test. This analysis shows that for the strongly nonlinear anisotropic model, even in a restricted range of deformations, large values of κ are necessary to ensure the incompressibility condition, in order to estimate the wall stress with a reasonable precision. Finite element simulations on idealized AAA geometries are then performed. Results from these simulations show that the maximum stress in the AAA wall is underestimated in previous works, committed errors vary from 26% to 58% depending on the geometrical model complexity. In addition to affect the magnitude of the maximum stress in the aneurysm, we found that too small value of κ may also affect the location of this stress.

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Pagac, Marek, David Schwarz, Jana Petru, and Stanislav Polzer. "3D printed polyurethane exhibits isotropic elastic behavior despite its anisotropic surface." Rapid Prototyping Journal 26, no. 8 (June 26, 2020): 1371–78. http://dx.doi.org/10.1108/rpj-02-2019-0027.

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Purpose Mechanical properties testing of the hyperelastic thermoplastic polyurethane (TPU) produced by the continuous digital light processing (CDLP) method of additive manufacturing. Primarily, this paper aims to verify that 3D printed TPU still satisfies commonly assumed volumetric incompressibility and material isotropy in elastic range. The secondary aim is to investigate the accuracy and reproducibility of the CDLP method. Design/methodology/approach Cylindrical samples were printed and subjected to a volumetric compression test to reveal their bulk modulus K and maximal theoretical porosity (MTP). Dog bone specimens were oriented along different axes and printed. Their dimensions were measured, and they were subjected to cyclic uniaxial tests up to 100% strain to reveal the level of stress softening and possible anisotropy. The hyperelastic Yeoh model was fitted to the mean response. Findings The authors measured the bulk modulus of K = 1851 ± 184 MPa. The mean MTP was 0.9 ± 0.5%. The mean response was identical in both directions and the data could be fitted by the isotropic third order Yeoh function with R^2 = 0.996. The dimensions measurement revealed the largest error (above 5%) in the direction perpendicular to the direction of the digital light projection while the dimensions in other two dimensions were much more accurate (0.75 and 1%, respectively). Practical implications The TPU printed by CDLP can be considered and modelled as isotropic and practically volumetrically incompressible. The parts in the printing chamber should be positioned in a way that the important dimensions are not parallel to the direction of the digital light projection. Originality/value The authors experimentally confirmed the volumetric incompressibility and mechanical isotropy of the TPU printed using the CDLP method.

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Liu, Mingrui, Lidong Wang, and Xiongqi Peng. "Testing, characterizing, and forming of glass twill fabric/polypropylene prepregs." Journal of Composite Materials 53, no. 28-30 (May 24, 2019): 3939–50. http://dx.doi.org/10.1177/0021998319851215.

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This paper investigates the mechanical behaviors of thermoplastic woven prepregs via testing and forming experiments. Glass twill fabric/polypropylene prepregs are produced by chemical treatment on fabric surface and a hot pressure molding approach. Then, mechanical tests including uniaxial tensile and bias extension of the glass twill fabric and its prepregs are carried out to provide basic data set for material modelling. An anisotropic hyperelastic model based on strain energy decomposition is proposed. And its material parameters are obtained by fitting these experimental data. Hemispherical thermo-stamping experiments are implemented for model verification. Very good agreements between forming simulation results and experimental data including boundary profiles, local shear angles, and forming force magnitude are obtained. The present work provides a complete data set for the model development and verification of thermoplastic woven fabric prepregs.

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Vu, Ngoc-Hung, Xuan-Tan Pham, Vincent François, and Jean-Christophe Cuillière. "Inverse procedure for mechanical characterization of multi-layered non-rigid composite parts with applications to the assembly process." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 17 (July 7, 2019): 6167–76. http://dx.doi.org/10.1177/0954406219861126.

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In assembly process, non-rigid parts in free-state may have different forms compared to the designed model caused by gravity load and residual stresses. For non-rigid parts made by multi-layered fiber-reinforced thermoplastic composites, this process becomes much more complex due to the nonlinear behavior of the material. This paper presented an inverse procedure for characterizing large anisotropic deformation behavior of four-layered, carbon fiber-reinforced polyphenylene sulphide, non-rigid composite parts. Mechanical responses were measured from the standard three points bending test and the surface displacements of composite plates under flexural loading test. An orthotropic hyperelastic material model was implemented as a UMAT user routine in the Abaqus/Standard to analyze the behavior of flexible fiber-reinforced thermoplastic composites. Error functions were defined by subtracting the experimental data from the numerical mechanical responses. Minimizing the error functions helps to identify the material parameters. These optimal parameters were validated for the case of an eight-layered composite material.

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Beter, Julia, Bernd Schrittesser, Gerald Meier, Bernhard Lechner, Mohammad Mansouri, Peter Filipp Fuchs, and Gerald Pinter. "The Tension-Twist Coupling Mechanism in Flexible Composites: A Systematic Study Based on Tailored Laminate Structures Using a Novel Test Device." Polymers 12, no. 12 (November 24, 2020): 2780. http://dx.doi.org/10.3390/polym12122780.

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The focus of this research is to quantify the effect of load-coupling mechanisms in anisotropic composites with distinct flexibility. In this context, the study aims to realize a novel testing device to investigate tension-twist coupling effects. This test setup includes a modified gripping system to handle composites with stiff fibers but hyperelastic elastomeric matrices. The verification was done with a special test plan considering a glass textile as reinforcing with different lay-ups to analyze the number of layers and the influence of various fiber orientations onto the load-coupled properties. The results demonstrated that the tension-twist coupling effect strongly depends on both the fiber orientation and the considered reinforcing structure. This enables twisting angles up to 25° with corresponding torque of about 82.3 Nmm, which is even achievable for small lay-ups with 30°/60° oriented composites with distinct asymmetric deformation. For lay-ups with ±45° oriented composites revealing a symmetric deformation lead, as expected, no tension-twist coupling effect was seen. Overall, these findings reveal that the described novel test device provides the basis for an adequate and reliable determination of the load-coupled material properties between stiff fibers and hyperelastic matrices.

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Iwamoto, Takeshi, Mohammed Cherkaoui, and Esteban P. Busso. "A Numerical Investigation of Interface Dynamics during Martensitic Transformation in a Shape Memory Alloy Using the Level-Set Method." Key Engineering Materials 340-341 (June 2007): 1199–204. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.1199.

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In this study, the simulation of the motion of an interface during the stress-induced martensitic transformation of a shape memory alloy is performed using the level-set method. The kinetics of the phase transformation is defined as an anisotropic kinetic relation between the rate at which the weak discontinuity moves, given by its normal velocity, and the thermodynamics driving force. The latter is derived from a dissipation function, which obeys the 1st and 2nd law of thermodynamics and accounts for large strains. Furthermore, a hyperelastic constitutive framework is used to describe the constitutive behavior of the material. The model is implemented into the finite element method and is then used to solve a 2D phase transformation problem in a shape memory alloy.

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Ferreira, Elisabete, Joaquim Pinho-da-Cruz, and António Andrade-Campos. "Development of an Optimized Loading Path for Material Parameters Identification." Key Engineering Materials 554-557 (June 2013): 2200–2211. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.2200.

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Nowadays, the characterization of material is becoming increasingly important due to ma\-nu\-fac\-tu\-ring of new materials and development of computational analysis software intending to reproduce the real behaviour which depends on the quality of the models implemented and their material parameters. However, a large number of technological mechanical tests are carried out to characterize the mechanical properties of materials and similar materials may also have properties and parameters similar. Therefore, many researchers are often confronted with the dilemma of what should be the best set of numerical solution for all different results. Currently, such choice is made based on the empirical experience of each researcher, not representing a severe and objective criterion. Hence, via optimization it is possible to find and classify the most unique and distinguishable solution for pa\-ra\-me\-ters identification. The aim of this work is to propose a methodology that numerically designs the loading path of multiaxial testing machine to characterize metallic thin sheet behavior. This loading path has to be the most informative, exhibiting normal and shear strains as distinctly as possible. Thus, applying Finite Element Analysis (FEA) and Singular Value Decomposition (SVD), the loading path can be evaluated in terms of distinguishability and uniqueness. Consequently, the loading path that leads to the most distinguish and unique set of material parameters can be found using a standard optimization method and the approach proposed. This methodology has been validated to characterize the elastic moduli for an anisotropic material and extrapolated for an hyperelastic material.

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Mohammadi, H., D. Boughner, L. E. Millon, and W. K. Wan. "Design and simulation of a poly(vinyl alcohol)—bacterial cellulose nanocomposite mechanical aortic heart valve prosthesis." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 223, no. 6 (July 9, 2009): 697–711. http://dx.doi.org/10.1243/09544119jeim493.

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In this study, a polymeric aortic heart valve made of poly(vinyl alcohol) (PVA)—bacterial cellulose (BC) nanocomposite is simulated and designed using a hyperelastic non-linear anisotropic material model. A novel nanocomposite biomaterial combination of 15 wt % PVA and 0.5 wt % BC is developed in this study. The mechanical properties of the synthesized PVA—BC are similar to those of the porcine heart valve in both the principal directions. To design the geometry of the leaflets an advance surfacing technique is employed. A Galerkin-based non-linear finite element method is applied to analyse the mechanical behaviour of the leaflet in the closing and opening phases under physiological conditions. The model used in this study can be implemented in mechanical models for any soft tissues such as articular cartilage, tendon, and ligament.

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YAMADA, Hiroshi. "F-0801 Development of finite element analysis program of incompressible transversely isotropic hyperelastic material for the vascular anisotropic deformation." Proceedings of the JSME annual meeting IV.01.1 (2001): 1–2. http://dx.doi.org/10.1299/jsmemecjo.iv.01.1.0_1.

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Sun, Shulei, and Wenguo Chen. "An Anisotropic Hyperelastic Constitutive Model with Bending Stiffness Interaction for Cord-Rubber Composites: Comparison of Simulation Results with Experimental Data." Mathematical Problems in Engineering 2020 (July 24, 2020): 1–7. http://dx.doi.org/10.1155/2020/6750369.

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Based on the invariant theory of continuum mechanics by Spencer, the strain energy depends on deformation, fiber direction, and the gradients of the fiber direction in the deformed configuration. The resulting extended theory is very complicated and brings a nonsymmetric stress and couple stress. By introducing the gradient of fiber vector in the current configuration, the strain energy function can be decomposed into volumetric, isochoric, anisotropic, and bending deformation energy. Due to the particularity of bending deformation, the reinforced material has tensile deformation and compression deformation. The bending stiffness should be taken into consideration, and it is further verified by the bending simulation.

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Turner, Josh A., Gary H. Menary, Peter J. Martin, and Shiyong Yan. "Modelling the Temperature Dependent Biaxial Response of Poly(ether-ether-ketone) Above and Below the Glass Transition for Thermoforming Applications." Polymers 11, no. 6 (June 12, 2019): 1042. http://dx.doi.org/10.3390/polym11061042.

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Desire to accurately predict the deformation behaviour throughout industrial forming processes, such as thermoforming and stretch blow moulding, has led to the development of mathematical models of material behaviour, with the ultimate aim of embedding into forming simulations enabling process and product optimization. Through the use of modern material characterisation techniques, biaxial data obtained at conditions comparable to the thermoforming process was used to calibrate the Buckley material model to the observed non-linear viscoelastic stress/strain behaviour. The material model was modified to account for the inherent anisotropy observed between the principal directions through the inclusion of a Holazapfel–Gasser–Ogden hyperelastic element. Variations in the post-yield drop in stress values associated with deformation rate and specimen temperature below the glass transition were observable, and facilitated in the modified model through time-temperature superposition creating a linear relationship capable of accurately modelling this change in yield stress behaviour. The modelling of the region of observed flow stress noted when above the glass transition temperature was also facilitated through adoption of the same principal. Comparison of the material model prediction was in excellent agreement with experiments at strain rates and temperatures of 1–16 s−1 and 130–155 °C respectively, for equal-biaxial mode of deformation. Temperature dependency of the material model was well replicated with across the broad temperature range in principal directions, at the reference strain rate of 1 s−1. When concerning larger rates of deformation, minimum and maximum average error levels of 6.20% and 10.77% were noted. The formulation, and appropriate characterization, of the modified Buckley material model allows for a stable basis in which future implementation into representative forming simulations of poly-aryl-ether-ketones, poly(ether-ether-ketone) (PEEK) and many other post-yield anisotropic polymers.

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Ta, Anh-Tuan, Nadia Labed, Frédéric Holweck, Alain Thionnet, and François Peyraut. "A new invariant-based method for building biomechanical behavior laws – Application to an anisotropic hyperelastic material with two fiber families." International Journal of Solids and Structures 50, no. 14-15 (July 2013): 2251–58. http://dx.doi.org/10.1016/j.ijsolstr.2013.03.033.

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Fiorito, Marco, Daniel Fovargue, Adela Capilnasiu, Myrianthi Hadjicharalambous, David Nordsletten, Ralph Sinkus, and Jack Lee. "Impact of axisymmetric deformation on MR elastography of a nonlinear tissue-mimicking material and implications in peri-tumour stiffness quantification." PLOS ONE 16, no. 7 (July 9, 2021): e0253804. http://dx.doi.org/10.1371/journal.pone.0253804.

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Solid tumour growth is often associated with the accumulation of mechanical stresses acting on the surrounding host tissue. Due to tissue nonlinearity, the shear modulus of the peri-tumoural region inherits a signature from the tumour expansion which depends on multiple factors, including the soft tissue constitutive behaviour and its stress/strain state. Shear waves used in MR-elastography (MRE) sense the apparent change in shear modulus along their propagation direction, thereby probing the anisotropic stiffness field around the tumour. We developed an analytical framework for a heterogeneous shear modulus distribution using a thick-shelled sphere approximation of the tumour and soft tissue ensemble. A hyperelastic material (plastisol) was identified to validate the proposed theory in a phantom setting. A balloon-catheter connected to a pressure sensor was used to replicate the stress generated from tumour pressure and growth while MRE data were acquired. The shear modulus anisotropy retrieved from the reconstructed elastography data confirmed the analytically predicted patterns at various levels of inflation. An alternative measure, combining the generated deformation and the local wave direction and independent of the reconstruction strategy, was also proposed to correlate the analytical findings with the stretch probed by the waves. Overall, this work demonstrates that MRE in combination with non-linear mechanics, is able to identify the apparent shear modulus variation arising from the strain generated by a growth within tissue, such as an idealised model of tumour. Investigation in real tissue represents the next step to further investigate the implications of endogenous forces in tissue characterisation through MRE.

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Jaramillo, Héctor E. "Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus." Mathematical Problems in Engineering 2018 (November 7, 2018): 1–10. http://dx.doi.org/10.1155/2018/1570142.

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Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the intervertebral disc is nonlinear, heterogeneous, and anisotropic and, due to the low permeability, is usually represented as a hyperelastic model. The intervertebral disc is composed of the nucleus pulposus, the endplates, and the annulus fibrosus. The annulus fibrosus is modeled as a hyperelastic matrix reinforced with several fiber families, and researchers have used different strain energy density functions to represent it. This paper presents a comparative study between the strain energy density functions most frequently used to represent the mechanical behavior of the annulus fibrosus: the Yeoh and Mooney-Rivlin functions. A finite element model of the annulus fibrosus of the L4-L5 segment under the action of three independent and orthogonal moments of 8 N-m was used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction of annulus fibrosus and tetrahedron elements for the endplates were used, and an exponential energy function was employed to represent the mechanical behavior of the fibers. A total of 16 families were used; the fiber orientation varied with the radial coordinate from 25° on the outer boundary to 46° on the inner boundary, measuring it with respect to the transverse plane. The mechanical constants were taken from the reported literature. The range of motion was obtained by finite element analysis using different values of the mechanical constants and these results were compared with the reported experimental data. It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear region.

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Ma, Baoshun, Jia Lu, Robert E. Harbaugh, and Madhavan L. Raghavan. "Nonlinear Anisotropic Stress Analysis of Anatomically Realistic Cerebral Aneurysms." Journal of Biomechanical Engineering 129, no. 1 (July 21, 2006): 88–96. http://dx.doi.org/10.1115/1.2401187.

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Background. Static deformation analysis and estimation of wall stress distribution of patient-specific cerebral aneurysms can provide useful insights into the disease process and rupture. Method of Approach. The three-dimensional geometry of saccular cerebral aneurysms from 27 patients (18 unruptured and nine ruptured) was reconstructed based on computer tomography angiography images. The aneurysm wall tissue was modeled using a nonlinear, anisotropic, hyperelastic material model (Fung-type) which was incorporated in a user subroutine in ABAQUS. Effective material fiber orientations were assumed to align with principal surface curvatures. Static deformation of the aneurysm models were simulated assuming uniform wall thickness and internal pressure load of 100mmHg. Results. The numerical analysis technique was validated by quantitative comparisons to results in the literature. For the patient-specific models, in-plane stresses in the aneurysm wall along both the stiff and weak fiber directions showed significant regional variations with the former being higher. The spatial maximum of stress ranged from as low as 0.30MPa in a small aneurysm to as high as 1.06MPa in a giant aneurysm. The patterns of distribution of stress, strain, and surface curvature were found to be similar. Sensitivity analyses showed that the computed stress is mesh independent and not very sensitive to reasonable perturbations in model parameters, and the curvature-based criteria for fiber orientations tend to minimize the total elastic strain energy in the aneurysms wall. Within this small study population, there were no statistically significant differences in the spatial means and maximums of stress and strain values between the ruptured and unruptured groups. However, the ratios between the stress components in the stiff and weak fiber directions were significantly higher in the ruptured group than those in the unruptured group. Conclusions. A methodology for nonlinear, anisotropic static deformation analysis of geometrically realistic aneurysms was developed, which can be used for a more accurate estimation of the stresses and strains than previous methods and to facilitate prospective studies on the role of stress in aneurysm rupture.

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Kuchumov, Alex G., Aleksandr Khairulin, Marina Shmurak, Artem Porodikov, and Andrey Merzlyakov. "The Effects of the Mechanical Properties of Vascular Grafts and an Anisotropic Hyperelastic Aortic Model on Local Hemodynamics during Modified Blalock–Taussig Shunt Operation, Assessed Using FSI Simulation." Materials 15, no. 8 (April 7, 2022): 2719. http://dx.doi.org/10.3390/ma15082719.

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Cardiovascular surgery requires the use of state-of-the-art artificial materials. For example, microporous polytetrafluoroethylene grafts manufactured by Gore-Tex® are used for the treatment of cyanotic heart defects (i.e., modified Blalock–Taussig shunt). Significant mortality during this palliative operation has led surgeons to adopt mathematical models to eliminate complications by performing fluid–solid interaction (FSI) simulations. To proceed with FSI modeling, it is necessary to know either the mechanical properties of the aorta and graft or the rheological properties of blood. The properties of the aorta and blood can be found in the literature, but there are no data about the mechanical properties of Gore-Tex® grafts. Experimental studies were carried out on the mechanical properties vascular grafts adopted for modified pediatric Blalock–Taussig shunts. Parameters of two models (the five-parameter Mooney–Rivlin model and the three-parameter Yeoh model) were determined by uniaxial experimental curve fitting. The obtained data were used for patient-specific FSI modeling of local blood flow in the “aorta-modified Blalock–Taussig shunt–pulmonary artery” system in three different shunt locations: central, right, and left. The anisotropic model of the aortic material showed higher stress values at the peak moment of systole, which may be a key factor determining the strength characteristics of the aorta and pulmonary artery. Additionally, this mechanical parameter is important when installing a central shunt, since it is in the area of the central anastomosis that an increase in stress on the aortic wall is observed. According to computations, the anisotropic model shows smaller values for the displacements of both the aorta and the shunt, which in turn may affect the success of preoperative predictions. Thus, it can be concluded that the anisotropic properties of the aorta play an important role in preoperative modeling.

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Comunale, Giulia, Luigi Di Micco, Daniela Paola Boso, Francesca Maria Susin, and Paolo Peruzzo. "Numerical Models Can Assist Choice of an Aortic Phantom for In Vitro Testing." Bioengineering 8, no. 8 (July 21, 2021): 101. http://dx.doi.org/10.3390/bioengineering8080101.

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(1) Background: The realization of appropriate aortic replicas for in vitro experiments requires a suitable choice of both the material and geometry. The matching between the grade of details of the geometry and the mechanical response of the materials is an open issue that deserves attention. (2) Methods: To explore this issue, we performed a series of Fluid–Structure Interaction simulations, which compared the dynamics of three aortic models. Specifically, we reproduced a patient-specific geometry with a wall of biological tissue or silicone, and a parametric geometry based on in vivo data made in silicone. The biological tissue and the silicone were modeled with a fiber-oriented anisotropic and isotropic hyperelastic model, respectively. (3) Results: Clearly, both the aorta’s geometry and its constitutive material contribute to the determination of the aortic arch deformation; specifically, the parametric aorta exhibits a strain field similar to the patient-specific model with biological tissue. On the contrary, the local geometry affects the flow velocity distribution quite a lot, although it plays a minor role in the helicity along the arch. (4) Conclusions: The use of a patient-specific prototype in silicone does not a priori ensure a satisfactory reproducibility of the real aorta dynamics. Furthermore, the present simulations suggest that the realization of a simplified replica with the same compliance of the real aorta is able to mimic the overall behavior of the vessel.

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Kroon, M. "An Efficient Method for Material Characterisation of Hyperelastic Anisotropic Inhomogeneous Membranes Based on Inverse Finite-Element Analysis and an Element Partition Strategy." Quarterly Journal of Mechanics and Applied Mathematics 63, no. 2 (April 18, 2010): 201–25. http://dx.doi.org/10.1093/qjmam/hbq004.

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Nilsson, K. F., and B. Stora˚kers. "On Interface Crack Growth in Composite Plates." Journal of Applied Mechanics 59, no. 3 (September 1, 1992): 530–38. http://dx.doi.org/10.1115/1.2893756.

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Analysis of fracture growth, and in particular at interfaces, is pertinent not only to load-carrying members in composite structures but also as regards, e.g., adhesive joints, thin films, and coatings. Ordinarily linear fracture mechanics then constitutes the common tool to solve two-dimensional problems occasionally based on beam theory. In the present more general effort, an analysis is first carried out for determination of the energy release rate at general loading of multilayered plates with local crack advance either at interfaces or parallel to such. The procedure is accomplished for arbitrary hyperelastic material properties within von Karman plate theory and the results are expressed by aid of an Eshelby energy momentum tensor. By a feasible superposition it is then shown that the original nonlinear plate problem may be reduced to that of an equivalent beam in case of linear material properties. As a consequence of the so-established principle, the magnitude of mode-dependent singular stress amplitude factors is then directly determinable from earlier two-dimensional linear beam solutions for isotropic and anisotropic bimaterials and relevant at determination of cohesive and adhesive fracture. The procedure is illustrated by an analysis of combined buckling and crack growth of a delaminated plate having a nontrivial crack contour.

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Journal articles on the topic 'Hyperelastic anisotropic material'

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