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Aortic Valve Mechanics
Published in Michel R. Labrosse, Cardiovascular Mechanics, 2018
J. Dallard, M. Boodhwani, M. R. Labrosse
Given applications with biological soft tissues, nonlinear elasticity and, most specifically, hyperelasticity are important concepts. A hyperelastic material is one for which a strain energy density function W exists; it represents a measure of the energy stored in the material as a result of deformation (Banks et al., 2011). The strain energy density function gives access to the Cauchy stress tensor σ as: σ=2JF.∂W∂C.FT−pI.
A comparative study of the consistency of Galerkin-type and least-squares finite element formulations for bifurcation problems
Published in Alphose Zingoni, Insights and Innovations in Structural Engineering, Mechanics and Computation, 2016
Hyperelastic material laws, as e.g. of Neo-Hookean type, generally result in a nonlinear stress-strain relation respectively a nonlinear (and steady) load-deflection curve. Beside that, physical phenomena as e.g. buckling can occur and have a cruical impact on the stability of the structure. Due to the loss of stability caused by this critical loads and the possible failure of the structure, the used finite elements should be able to provide a reliable and accurate analysis of this bifurcation points. In (Auricchio, Beirão da Veiga, Lovadina, & Reali 2005), (Auricchio, Beirão da Veiga, Lovadina, & Reali 2010) and (Auricchio, Beirão da Veiga, Lovadina, Reali, Taylor, & Wriggers 2013) the authors investigate the stability respectively the occurence of bifurcation points using several mixed and higher order Galerkin elements under consideration of a simple Neo-Hookean material. As an outcome of these publications, the inability of some elements to detect the stability points has been shown. Therefore the authors investigate several boundary value problems under consideration of a nearly incompressible material. In (Müller, Starke, Schwarz, & Schröder 2014) the authors successfully used their least-squares formulation for the computation of such bifurcation points.
Linear Elasticity
Published in Prasun Kumar Nayak, Mijanur Rahaman Seikh, Continuum Mechanics, 2022
Prasun Kumar Nayak, Mijanur Rahaman Seikh
It is worthwhile noting at this point that elastic behavior is sometimes defined on the basis of the existence of a strain energy function from which the stresses may be determined by the differentiation in Eq (5.12). A material defined in this way is called a hyperelastic material. The stress is still a unique function of strain so that this energy approach is compatible with our earlier definition of elastic behavior. Thus, in keeping with our basic restriction to infinitesimal deformations, we shall develop the linearized form of Eq (5.12).
Non-linear elasticity experiment and analysis of acrylic material used for human occupied vehicle
Published in Ships and Offshore Structures, 2023
Bingxiong Zhao, Fang Wang, Youjie Li, Yu Wu, Jinfei Zhang, Ruilong Luo, Oleg Gaidai, Weicheng Cui
The form of the polynomial energy potential can be expressed as the following formula (1) (Dassault 2016). where U is the strain energy per unit of reference volume; N is the material coefficient; Cij and Di are material coefficients; and are the first and second deviatoric strain invariants, respectively; Jel is the elastic volume ratio, for incompressible material, Jel = 1. The hyperelastic material is a special case of a Cauchy elastic material. The nominal stress presented as formula (2) derived from the principle of virtual work . where λ is the principal stretch: the ratios of current length to length in the original configuration in the principal directions.
Numerical and experimental analysis of free vibrations and static bending of a sandwich beam with a hyperelastic core
Published in Mechanics Based Design of Structures and Machines, 2022
Omid Azarniya, Gholam Husain Rahimi
Nowadays, in various medical and polymer industries, the application of materials and structures with nonlinear elastic behavior has increased. Rubber refers to one of the most widely used materials in the polymer industry. The actual physical property of rubbers is high deformation and nonlinear stress-strain curves, hence, having a nonlinear elastic behavior called hyperelastic material. Utilization of hyperelastic materials in industries such as automotive, aerospace, bridge, buildings, etc., often used as sandwich structures. These structures frequently consist of two parts, the skin and the core. Often playing a significant role in enhancing the strength of sandwich structures and usually made of high-strength materials like composite materials or metals such as aluminum, skins have higher strength than the core (Forooghi and Alibeigloo 2022; Forooghi et al. 2021; Gazor, Rahimi, and Farrokhabadi 2018; Huang, Ren, and Forooghi 2021). Most researchers have paid attention to understanding the hyperelastic materials’ behavior under various conditions of static loading, dynamics, and vibrations. Vibration analysis refers to one of the critical analyses of the failure of these structures, with their design based on free vibration analysis so that the structure’s natural frequency is not close to its excitation frequencies range to prevent the resonance phenomenon in the system. The two main problems in hyperelastic systems include the nonlinear nature of the governing equations and the lack of exact solutions to these equations. Accordingly, numerical methods, including FEM, are employed to analyze them (Bai et al. 2022; Safarpour et al. 2021).
Rational hyperelastic modelling of elastic poured compound for the failure analysis of embedded rail system
Published in International Journal of Rail Transportation, 2022
Li Wang, Shaoguang Li, Ping Wang, Rong Chen, Zili Li
A hyperelastic material is still an elastic material but its stress–strain relationship is nonlinear especially when the material undergoes large deformation. In hyperelastic constitutive, the stress–strain relationship is derived from the strain energy density function Φ based on the three strain invariants I1, I2, I3, or principal stretch ratios λ1, λ2, λ3 [16–36].