Sharif Digital Repository

Hyperelastic behavior of isotropic incompressible rubbers is studied to develop a strain energy function which satisfies all the necessary characteristic properties of an efficient hyperelastic model. The proposed strain energy function includes only three material parameters which are somehow related to the physical quantities of the material molecular network. Moreover, the model benefits from mathematical simplicity, well suitting in all ranges of stretch and possessing the property of deformation-mode-independency. This reduces the required number of experimental tests for parameter calibration of the model. Results of the proposed model are compared with results of some available models... 

Hyperelastic behavior of isotropic incompressible rubbers are studied to develop a strain energy function. The proposed function includes only three material parameters which are related to physical properties of the material molecular network. Furthermore, the model benefits from well suitting in all ranges of stretch as well as possessing the property of deformation mode independency. This reduces the required number of experimental tests for parameter calibration. Results of the model are compared with results of Mooney-Rivlin, Arruda-Boyce, Gent and Gao models as well as the experimental data  

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... 

A three-dimensional visco-hyperelastic constitutive model is developed to describe the rate-dependent behavior of rubber-like materials at large deformations. The model encompasses a hyperelastic part which uses the "Exp-Ln" strain energy function to characterize the equilibrium response and a viscous part capturing the rate sensitivity using a hereditary integral form which links the overstress to the history of stored strain energy. A physically consistent rate-dependent relaxation time scheme is introduced which reduces the number of required material parameters and also facilitates the calibration process. The proposed model is verified using various uniaxial experimental data in... 

In this paper, the modal-based indices are used in damage identification of the wind turbine blade. In contrast of many of previous researches, the geometric nonlinearity due to the large structural deformation of the modern wind turbines blade is considered. In the first step, the finite element model (FEM) of the rotating blade is solved to obtain the modal features of the deformed structure under operational aerodynamic loading. Next, the accuracy and efficiency of the various modal-based damage indices including the frequency, mode shape, curvature of mode shape, modal assurance, modal strain energy (MSE) and the difference of indices (between the intact and damaged blades) are... 

The development of damage detection techniques for offshore jacket structures is vital to prevent catastrophic events. This paper applies a frequency response based method for the purpose of structural healthCgreater detection efficiency. In addition, the performance of the proposed method was evaluated in relation to multiple damages. The aforementioned points are illustrated using the numerical study of a two dimensional jacket platform, and the results proved to be satisfactory utilizing the proposed methodology  

In this paper, the concept of energy pairs in the micropolar continuum is introduced. A brief review of the micropolar continuum theory is presented for using in the subsequent derivations. A mathematical Lagrangian strain and a wryness tensor for the micropolar continuum are introduced. Using the first law of thermodynamics and for isothermal processes, the power of deformation is obtained and the energy pairs in the Eulerian and Lagrangian descriptions are defined. Also, the micropolar stress and couple stress tensors which are energy pairs to the micropolar Lagrangian strain and wryness measures are determined. © 2006 Elsevier Ltd. All rights reserved  

This paper proposes a new visco-hyperelastic constitutive law for modeling the finite-deformation strain rate-dependent behavior of foams as compressible elastomers. The proposed model is based on a phenomenological Zener model, which consists of a hyperelastic equilibrium spring and a Maxwell element parallel to it. The hyperelastic equilibrium spring describes the steady state response. The Maxwell element, which captures the rate-dependency behavior, consists of a nonlinear viscous damper connected in series to a hyperelastic intermediate spring. The nonlinear damper controls the rate-dependency of the Maxwell element. Some strain energy potential functions are proposed for the two... 

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... 

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)... 

Double cantilever beam (DCB) specimens of 2.5-mm-long SAC305 solder joints were prepared with thickness of copper adherends varying from 8 to 21 mm each. The specimens were tested under mode I loading conditions (ie, pure opening mode with no shear component of loading) with a strain rate of 0.03 second−1. The measured fracture load was used to calculate the critical strain energy release rate for crack initiation, Jci, in each case. Fracture behaviour showed a significant dependence on the adherend thickness; the Jci and plastic deformation of the solder at crack initiation decreased significantly with increase in adherend thickness. This behaviour was attributed to changes in stress... 

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... 

Double cantilever beam (DCB) specimens of 2.5-mm-long SAC305 solder joints were prepared with thickness of copper adherends varying from 8 to 21 mm each. The specimens were tested under mode I loading conditions (ie, pure opening mode with no shear component of loading) with a strain rate of 0.03 second−1. The measured fracture load was used to calculate the critical strain energy release rate for crack initiation, Jci, in each case. Fracture behaviour showed a significant dependence on the adherend thickness; the Jci and plastic deformation of the solder at crack initiation decreased significantly with increase in adherend thickness. This behaviour was attributed to changes in stress... 

The critical strain energy release rate for crack initiation, J ci , was measured under mode I loading for SAC305 solder joints between two copper substrates. Fracture tests were performed using double cantilever beam specimens at a strain rate of 0.03 s −1 . Different bond-line widths (i.e., joint size in the out-of-plane dimension) and thicknesses, were examined. The fracture force per unit width and J ci (the average value of four J-integral contours encircling the crack tip) were relatively insensitive to the width of the joint ranging from 8 mm to 21 mm. Variations in bond-line thickness (i.e., 150 μm, 250 μm and 450 μm) also had an insignificant influence on the fracture energy of... 

The critical strain energy release rate for crack initiation, J ci , was measured under mode I loading for SAC305 solder joints between two copper substrates. Fracture tests were performed using double cantilever beam specimens at a strain rate of 0.03 s −1 . Different bond-line widths (i.e., joint size in the out-of-plane dimension) and thicknesses, were examined. The fracture force per unit width and J ci (the average value of four J-integral contours encircling the crack tip) were relatively insensitive to the width of the joint ranging from 8 mm to 21 mm. Variations in bond-line thickness (i.e., 150 μm, 250 μm and 450 μm) also had an insignificant influence on the fracture energy of... 

In this paper, a continuum–atomistic multi-scale method is presented in modeling the nonlinear behavior of nano-materials under large deformation. In order to identify an appropriate strain energy function for crystalline nano-structures with different percentages of spherical voids, the hyperelastic method is employed for specimen whose behavior is determined based on the molecular dynamics analyses. In the atomistic level, the EAM many-body potential is employed to model the interactions between the atoms of Al RVEs. The atomistic strain energy density curves and surfaces are generated by applying the uniaxial, biaxial and simple shear deformations to the boundaries of RVEs. The material... 

In this paper, a new visco-hyperelastic constitutive law for describing the rate dependent behavior of foams is proposed. The proposed model was based on a phenomenological Zener model: a hyperelastic equilibrium spring, which describes the steady-state, long-term response, parallel to a Maxwell element, which captures the rate-dependency. A nonlinear viscous damper connected in series to a hyperelastic intermediate spring, controls the rate-dependency of the Maxwell element. Therefore, the stress is the sum of equilibrium stress on the equilibrium spring and overstress on the intermediate spring. In hyperelastic theory stress is not calculated directly as in the case of small-strain, linear...