Sharif Digital Repository

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 article, the one-dimensional phenomenological constitutive model originally proposed by Brinson for shape memory alloys is improved to predict asymmetric behavior in tension and compression. We propose an approach that decomposes stress-induced martensite volume fraction into two parts, one in tension and one in compression. Results of numerical examples show reasonable agreement with experimental data. Moreover, we implement the proposed model in a user-defined material subroutine in the nonlinear finite element software ABAQUS/Standard as a two-dimensional Euler-Bernoulli beam element. We simulate several beam problems and a shape memory alloy staple. Regarding the results, the... 

In many engineering applications, shape memory polymers (SMPs) usually undergo arbitrary thermomechanical loadings at finite deformation. Thus, development of 3D constitutive models for SMPs within the finite deformation regime has attracted a great deal of interest. In this paper, based on the classical framework of thermodynamics of irreversible processes, employing the logarithmic (or Hencky) strain as a more physical measure of strain, a 3D large-strain macromechanical model is presented. In the constitutive model development, we adopt a multiplicative decomposition of the deformation gradient into elastic and stored parts. In addition, employing the averaging scheme, the logarithmic... 

In this paper, using an analytical optimization method, optimum design of multi-layer compound cylinders with different materials in layers is investigated. For this purpose, considering Tresca criterion, maximum shear stress in each layer is minimized. At the optimum condition, the maximum shear stress at all layers occurs simultaneously. The general analytical relations for optimum dimension of layers, residual pressures and radial interferences are derived. The existence condition of the optimum solution is also investigated and the constraints for materials selection are derived too. It is shown that the allowable shear stress ratio of materials must be close to their geometric mean... 

In this paper, a Strain Energy Function (SEF) is proposed to characterize the hyperelastic behavior of transversely isotropic incompressible fiber-reinforced rubbers. The kinematics of the deformation is based on a strain measure consistent with the physics of the deformation. The SEF consists of an isotropic part and an anisotropic one where a simple form of SEF is used for both parts. In order to investigate the capabilities of the proposed model, two fiber-reinforced rubbers under homogeneous deformations are examined. The predictions of the model show a good agreement with the experimental data for both tensile and shear deformations. Also, torsion of a fiber-reinforced rubbery circular... 

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  

An energy-based ordinary differential equation is derived for a plastic wave propagating through a Taylor impact test specimen. Using the definition of true strain, an analytical equation is presented to calculate the strain rate across the plastic wave front. Having considered a Johnson-Cook plasticity model for the projectile material, the derived energy equation accompanied by a governing kinematics relation and the strain rate equation is numerically integrated to obtain the final deformed profile of the specimen. The results of the energy based model are then compared with those of the commonly used momentum-based approach as well as the existing experimental data in literature for... 

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is... 

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... 

In this paper, employing an analytical method, optimum design of multi-layer compound cylinders is investigated. To this end, considering Tresca criterion, maximum shear stress in each layer is minimized. Analytical relations for optimum values of a layer dimension, residual pressures and radial interferences are derived. A technique for shrink-fitting of layers is also proposed and relationships for radial interferences, residual pressures and required temperature differences during the shrink-fitting process are derived. Three different examples are presented to show the effectiveness of the proposed method. It is shown that increasing the number of layers makes shear stress distribution... 

In this paper, employing the logarithmic (or Hencky) strain as a more physical measure of strain, the time-dependent response of compressible viscoelastic materials is investigated. In this regard, we present a phenomenological finite strain viscoelastic constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The formulation is based on the multiplicative decomposition of the deformation gradient into elastic and viscoelastic parts, together with the use of the isotropic property of the Helmholtz strain energy function. Making use of a logarithmic mapping, we present an appropriate form of the proposed constitutive equations in the... 

The ever increasing applications of shape memory polymers have motivated the development of appropriate constitutive models for these materials. In this work, we present a 3 D constitutive model for shape memory polymers under time-dependent multiaxial thermomechanical loadings in the small strain regime. The derivation is based on an additive decomposition of the strain into six parts and satisfying the second law of thermodynamics in Clausius-Duhem inequality form. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. The viscous effects are also fully accounted for in the proposed model. Further, we... 

In this paper, the responses of shape memory polymer (SMP) helical springs under axial force are studied both analytically and numerically. In the analytical solution, we first derive the response of a cylindrical tube under torsional loadings. This solution can be used for helical springs in which both the curvature and pitch effects are negligible. This is the case for helical springs with large ratios of the mean coil radius to the cross sectional radius (spring index) and also small pitch angles. Making use of this solution simplifies the analysis of the helical springs to that of the torsion of a straight bar with circular cross section. The 3D phenomenological constitutive model... 

Employing a proper pulse shaper in the conventional split Hopkinson pressure bar (SHPB) test helps to achieve dynamic equilibrium condition and to fulfill a constant strain rate condition in the test specimen. To this end, the parameters affecting the incident pulse shape, i.e., pulse shaper thickness, pulse shaper diameter, striker bar length and striker bar velocity are experimentally studied. Moreover, simulation results, validated by experimental data together with wave propagation analysis, are exploited to provide general guidelines to properly design a pulse shaper. It is recommended to use a relatively large diameter pulse shaper for testing work-hardening materials. Also, for... 

In this article, satisfying the second law of thermodynamics, we present a 3D constitutive model for shape memory polymers. The model is based on an additive decomposition of the strain into four parts. Also, evolution laws for internal variables during both cooling and heating processes are proposed. Since temperature has considerable effect on the shape memory polymer behavior, for simulation of a shape memory polymer-based structure, it is required to perform a heat-transfer analysis. Commonly, an experimentally observed temperature rate-dependent behavior of shape memory polymers is justified by a rate-dependent glassy temperature, but using the heat-transfer analysis, it is shown that... 

In this article, an analytical elastic-plastic solution for thick-walled cylinders made of Functionally Graded Materials (FGMs) subjected to internal pressure and thermal loading is presented. Based on the experimental results, a mathematical model to predict the yielding through the thickness of FG AlA359/SiCp cylinder is developed. It is shown that under the temperature gradient loading, there is a point in the cylinder where the circumferential stress changes from compressive to tensile. The position of this point depends on the geometry and material properties of the FG cylinder and is independent of the temperature gradient  

In this study, a three-dimensional (3D) beam element based on Timoshenko beam theory is introduced for shape memory alloys (SMAs). Employing the microplane approach, we use a 3D SMA constitutive model extended from a 1D model proposed by Brinson. The SMA model is implemented into a user-defined subroutine (UMAT) in the nonlinear finite element software ABAQUS/Standard. Results of numerical examples show reasonable agreement with experimental data in proportional and non-proportional loadings. Furthermore, several applications (staple, spring, structure) are simulated and the results are compared with those of continuum elements. According to the results, the 3D SMA beam element can be used... 

In this study, an analytical solution is presented for pure bending of shape memory alloy (SMA) beams with symmetric cross section as well as symmetric behavior in tension and compression. To this end, a three-dimensional constitutive equation is reduced to one-dimensional form and employed to study the bending response of SMA beams at high (pseudo-elasticity) and low (shape memory effect) temperatures. An analytical expression for bending stress as well as polynomial approximation for shear stress and deflection are obtained. Derived equations for bending are employed to analyze an SMA beam with rectangular cross section and results are compared with those of the finite element method. The... 

Porous shape memory alloys (SMAs) exhibit the interesting characteristics of porous metals together with shape memory effect and pseudo-elasticity of SMAs that make them appropriate for biomedical applications. In this paper, a 3-D phenomenological constitutive model for the pseudo-elastic behavior and shape memory effect of porous SMAs is developed within the framework of irreversible thermodynamics. Comparing to micromechanical and computational models, the proposed model is computationally cost effective and predicts the behavior of porous SMAs under proportional and non-proportional multiaxial loadings. Considering the pressure dependency of phase transformation in porous SMAs, proper... 

Strain and stress concentrations are studied for elastomers at finite deformations. Effects of strain-induced crystallization, filler reinforcement and deformation rate are also investigated, and micromechanical descriptions are provided for the observed results. A simple problem is subjected to finite element simulations to show the results evidently. Material parameters are obtained from experimental tests conducted on standard tensile samples of filled and unfilled natural rubber (NR) as well as styrene–butadiene rubber (SBR) as crystallizing and non-crystallizing rubbers, respectively. In all simulations, the strain concentration factor KE is shown to decrease monotonically where the...