Sharif Digital Repository

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, 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 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... 

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... 

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, 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... 

In the present study, considering two-dimensional porosity distribution through a functionally graded porous (FGP) beam, its optimal distributions are obtained. A multi-objective optimization problem is defined to maximize critical buckling load and minimize mass of the beam, simultaneously. To this end, Timoshenko beam theory is employed and equilibrium equations for two-dimensional functionally graded porous (2D-FGP) beam are derived. For the solution, we present generalized differential quadrature method (GDQM) and consider two symmetric boundary conditions (Clamped-Clamped and Hinged-Hinged). Solving generalized eigenvalue problem, critical buckling load for 2D-FGP beam is then obtained.... 

In this work, energy absorption of ceramic tiles wrapped by aluminum foil on its impact face is experimentally and numerically studied. Penetration tests as well as numerical simulations are employed to obtain Ballistic Limit Velocity (BLV) of the tiles. Experimental and numerical results yield BLV of bare tiles as 145 ± 2 and 141.5 m/s, respectively. For the wrapped tiles, these values are increased to 168 ± 2 and 162 m/s, respectively. Therefore, 13% increase in BLV of the ceramic tiles is obtained by just 2.4% increase in its weight. Moreover, it is shown that energy absorption of the wrapped tiles is at least 11% greater than that of the bare ones. Based on the results, the increase in... 

This paper presents a three-dimensional phenomenological constitutive model for magnetic shape memory alloys (MSMAs), developed within the framework of irreversible continuum thermodynamics. To this end, a proper set of internal variables is introduced to reflect the microstructural consequences on the material macroscopic behavior. Moreover, a stress-dependent thermodynamic force threshold for variant reorientation is introduced which improves the model accuracy. Preassumed kinetic equations for magnetic domain volume fractions, decoupled equations for magnetization unit vectors and appropriate presentation of the limit function for martensite variant reorientation lead to a simple... 

In this study, an analytical solution is presented for elastic-plastic pure bending of a linear kinematic hardening curved beam with rectangular cross section both in monotonic loading and unloading. Compared to exact plane plasticity solution (already reported in the literature in loading) which needs solution of a system of equations, the proposed method is based on the hyperbolic strain distribution on the cross section which yields a simple approximate solution. To this end, we employ Winkler's theory, and assume plane cross sections remain plane after loading proved by the exact elasticity and plasticity solutions for pure bending of curved beams with rectangular cross section. At the... 

In this paper, assuming porosity varies only along thickness direction, its optimal distributions in functionally graded porous (FGP) beams are tailored. Two multi-objective optimization problems are defined. In the first one, critical buckling load and mass are optimized simultaneously while in the second one, we concentrate on simultaneous optimization of mass and fundamental frequency. Employing Timoshenko beam theory, we present governing equations for a FGP beam. For the solution, we use Ritz method and propose appropriate trial functions according to the boundary conditions (Hinged-Hinged, Clamped-Clamped, Clamped-Hinged and Clamped-Free). Since the porosity distribution along... 

In the present study, an attempt is made to present the governing equations on the post-buckling of two-dimensional (2D) FGP beams and propose appropriate optimization procedure to achieve optimal post-buckling behavior and mass. To this end, Timoshenko beam theory, Von-Karman nonlinear relations, virtual work principle, and generalized differential quadrature method are considered to derive and solve governing equations and associated boundary condition (Hinged–Hinged) for an unknown 2D porosity distribution. Proposed method is validated using the papers in the literature. The optimization procedure including defining porosity distributions (interpolations), post-buckling function and... 

The main process in lithium-ion batteries is insertion/extraction of lithium into/from active electrode particles. Some active material of lithium-ion battery electrodes experiences a large volume change due to changes in lithium concentration. Since the failure of the electrode might be caused by large stresses, the mechanical phenomena in the electrode which are associated with the insertion and extraction of lithium, are of particular importance. This paper establishes an integrated framework of balance laws and thermodynamically consistent equations which couples lithium diffusion with a small elastic deformation. We investigate the effect of hydrostatic stress on lithium diffusion and... 

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 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...