Search for: strain-energy-density-functions
Article Acta Mechanica ; Volume 213, Issue 3-4 , 2010 , Pages 235-254 ; 00015970 (ISSN) ; Naghdabadi, R ; Sharif University of Technology
Springer-Verlag Wien 2010
Hyperelastic materials have high deformability and nonlinearity in load-deformation behavior. Based on a phenomenological approach, these materials are treated as a continuum, and a strain energy density is considered to describe their hyperelastic behavior. In this paper, the mechanical behavior characterization of these materials is studied from the continuum viewpoint. For this purpose, the strain energy density is expressed as sum of independent functions of the mutual multiple of principal stretches. These functions are determined by applying the governing postulates on the form of the strain energy density. It is observed that a consistent strain energy density is expressible in terms...
Article Materials Science and Engineering C ; Volume 32, Issue 7 , 2012 , Pages 1993-2000 ; 09284931 (ISSN) ; Aramoon, A ; Sharif University of Technology
In this paper, a new multi-scale approach is presented based on the modified boundary Cauchy-Born (MBCB) technique to model the surface effects of nano-structures. The salient point of the MBCB model is the definition of radial quadrature used in the surface elements which is an indicator of material behavior. The characteristics of quadrature are derived by interpolating data from atoms laid in a circular support around the quadrature, in a least-square scene. The total-Lagrangian formulation is derived for the equivalent continua by employing the Cauchy-Born hypothesis for calculating the strain energy density function of the continua. The numerical results of the proposed method are...
An exact analysis for the hoop elasticity and pressure-induced twist of CNT-nanovessels and CNT-nanopipes, Article Mechanics of Materials ; Volume 82 , 2015 , Pages 47-62A ; 01676636 (ISSN) ; Shodja, H. M ; Sharif University of Technology
Carbon nanotubes (CNTs) with and without end caps may be used for fluid storage and transport, respectively, referred to as CNT-nanovessel and CNT-nanopipe. The determination of the stiffness in the hoop (circumferential) and radial directions, ideal hoop strength, and hoop stress-strain curve of such nanostructures is of particular interest. Due to the proposed viewpoint, a chiral free-standing single-walled CNT (SWCNT) has a natural angle of twist and natural extension along the axis of the tube. For example, for the SWCNT (9,3) with diameter of 0.85 nm and chirality angle of 13.9°, the natural angle of twist per unit length is 1.45×10-3 rad/nm. Previously, only Vercosa et al. (2010) who...
Article Polymer Engineering and Science ; Volume 50, Issue 5 , 2010 , Pages 1058-1066 ; 00323888 (ISSN) ; Naghdabadi, R ; Kargarnovin, M. H ; Sharif University of Technology
Rubberlike materials are characterized by high deformability and reversibility of deformation. From the continuum viewpoint, a strain energy density function is postulated for modeling the behavior of these materials. In this paper, a general form for the strain energy density of these materials is proposed from a phenomenological point of view. Based on the Valanis-Landel hypothesis, the strain energy density of incompressible materials is expressed as the sum of independent functions of the principal stretches meeting the essential requirements on the form of the strain energy density. It is cleared that the appropriate mathematical expressions for constitutive modeling of these materials...
Hyperelastic materials modelling using a strain measure consistent with the strain energy postulates, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 224, Issue 3 , 2010 , Pages 591-602 ; 09544062 (ISSN) ; Naghdabadi, R ; Kargarnovin, M. H ; Sharif University of Technology
In this article, a strain energy density function of the Saint Venant-Kirchhoff type is expressed in terms of a Lagrangian deformation measure. Applying the governing postulates to the form of the strain energy density, the mathematical expression of this measure is determined. It is observed that this measure, which is consistent with the strain energy postulates, is a strain type with the characteristic function more rational than that of the Seth-Hill strain measures for hyperelastic materials modelling. In addition, the material parameters are calculated using a novel procedure that is based on the correlation between the values of the strain energy density (rather than the stresses)...
Micromechanics of brain white matter tissue: a fiber-reinforced hyperelastic model using embedded element technique, Article Journal of the Mechanical Behavior of Biomedical Materials ; Volume 80 , April , 2018 , Pages 194-202 ; 17516161 (ISSN) ; Shamloo, A ; Farahmand, F ; Sharif University of Technology
Elsevier Ltd 2018
A transverse-plane hyperelastic micromechanical model of brain white matter tissue was developed using the embedded element technique (EET). The model consisted of a histology-informed probabilistic distribution of axonal fibers embedded within an extracellular matrix, both described using the generalized Ogden hyperelastic material model. A correcting method, based on the strain energy density function, was formulated to resolve the stiffness redundancy problem of the EET in large deformation regime. The model was then used to predict the homogenized tissue behavior and the associated localized responses of the axonal fibers under quasi-static, transverse, large deformations. Results...
A hierarchical thermo-mechanical multi-scale technique for modeling of edge dislocations in nano-crystalline structures, Article Computational Materials Science ; Volume 141 , 2018 , Pages 360-374 ; 09270256 (ISSN) ; Khoei, A. R ; Heidarzadeh, N ; Jafarian, N ; Sharif University of Technology
Elsevier B.V 2018
In this paper, a hierarchical multi-scale technique is developed to investigate the thermo-mechanical behavior of nano-crystalline structures in the presence of edge dislocations. The primary edge dislocations are generated by proper adjustment of atomic positions to resemble discrete dislocations. The interatomic potential used to perform atomistic simulation is based on the Finnis-Sinclair embedded-atom method as many-body potential and, the Nose-Hoover thermostat is employed to control the effect of temperature. The strain energy density function is obtained for various representative volume elements under biaxial and shear loadings by fitting a fourth order polynomial in the atomistic...
Nonlinear mechanics of soft composites: hyperelastic characterization of white matter tissue components, Article Biomechanics and Modeling in Mechanobiology ; Volume 19, Issue 3 , 2020 , Pages 1143-1153 ; Shamloo, A ; Farahmand, F ; Sharif University of Technology
This paper presents a bi-directional closed-form analytical solution, in the framework of nonlinear soft composites mechanics, for top-down hyperelastic characterization of brain white matter tissue components, based on the directional homogenized responses of the tissue in the axial and transverse directions. The white matter is considered as a transversely isotropic neo-Hookean composite made of unidirectional distribution of axonal fibers within the extracellular matrix. First, two homogenization formulations are derived for the homogenized axial and transverse shear moduli of the tissue, based on definition of the strain energy density function. Next, the rule of mixtures and...
Article Journal of the Mechanical Behavior of Biomedical Materials ; Volume 60 , 2016 , Pages 157-176 ; 17516161 (ISSN) ; Ahmadian, M. T ; Firozbakhsh, K ; Aghdam, M. M ; Sharif University of Technology
In this paper, a micromechanical model for connective soft tissues based on the available histological evidences is developed. The proposed model constituents i.e. collagen fibers and ground matrix are considered as hyperelastic materials. The matrix material is assumed to be isotropic Neo-Hookean while the collagen fibers are considered to be transversely isotropic hyperelastic. In order to take into account the effects of tissue structure in lower scales on the macroscopic behavior of tissue, a strain energy density function (SEDF) is developed for collagen fibers based on tissue hierarchical structure. Macroscopic response and properties of tissue are obtained using the numerical...
Article Biomechanics and Modeling in Mechanobiology ; Volume 16, Issue 3 , 2017 , Pages 1077-1093 ; 16177959 (ISSN) ; Karimi Taheri, K ; Narooei, K ; Karimi Taheri, A ; Sharif University of Technology
Springer Verlag 2017
In this research, the nonlinear elastic behavior of human extensor apparatus was investigated. To this goal, firstly the best material parameters of hyperelastic strain energy density functions consisting of the Mooney–Rivlin, Ogden, invariants, and general exponential models were derived for the simple tension experimental data. Due to the significance of stress response in other deformation modes of nonlinear models, the calculated parameters were used to study the pure shear and balance biaxial tension behavior of the extensor apparatus. The results indicated that the Mooney–Rivlin model predicts an unstable behavior in the balance biaxial deformation of the extensor apparatus, while the...