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Shape memory alloys are referred to as a group of alloys that can retrieve the permanent deformation and strain applied to them and eventually return to their original form. So far, various studies have been done to determine the behavior of these alloys under cyclic loading. Most of the studies have mainly been conducted by using the foundations of Continuum Mechanics in order to examine the properties of memory alloys. In this study, instead of using the Continuum Mechanics, a Molecular Dynamics simulation method using Lennard-Jones potential is utilized. The changes in the behavior and properties of memory alloy under cyclic loading are being examined. First, the functional form... 

Shape memory alloys are referred to as a group of alloys that can retrieve the permanent deformation and strain applied to them and eventually return to their original form. So far, various studies have been done to determine the behavior of these alloys under cyclic loading. Most of the studies have mainly been conducted by using the foundations of Continuum Mechanics in order to examine the properties of memory alloys. In this study, instead of using the Continuum Mechanics, a Molecular Dynamics simulation method using Lennard-Jones potential is utilized. The changes in the behavior and properties of memory alloy under cyclic loading are being examined. First, the functional form... 

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... 

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... 

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, 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, 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.... 

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 new inelastic mechanism, detwinning-induced plasticity (DIP), is proposed to model the response of NiTi SMAs to cyclic loading, based on thermodynamic considerations. DIP is incorporated into a constitutive framework for NiTi SMA. The constitutive framework also includes well-established inelastic mechanisms of phase transformation, transformation-induced plasticity, residual martensite, and detwinning. The model is constructed at the single crystal scale using the framework of thermodynamics and a crystal plasticity formulation. An explicit scale-transition rule is adopted for the simulation of polycrystalline materials, allowing direct comparison of the model predictions with published... 

In this paper, based on three-dimensional phenomenological model and using a user-defined material subroutine mechanical behavior of shape memory alloy (SMA) wire ropes (or cables) and their components have been studied through implicit solution method in Abaqus software. Material parameters have been extracted using available experimental data and numerical simulations. Due to the convoluted geometry and interwire contact status within a cable, a finite element analysis is firstly performed for a 1 × 37 steel wire rope to validate modeling and mechanical interactions of a wire rope. Afterwards, superelastic and shape memory effect cables with different constructions (7 × 7 and 1 × 27) are... 

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 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... 

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 paper, a general class of Eshelby-like or weighted stress tensors based on the right stretch tensor is defined as the product of a general type of Lagrangian stress tensor and a class of stretch measure. In addition, basis free relations for conjugate strains of Eshelby-like stress tensors are investigated, which are based on Hill's definition of energy conjugacy. The equations for strain tensors conjugate to Eshelby-like stress tensors are generally determined, but the case in which the conjugate strains are coaxial with the right stretch tensor is mostly investigated. © 2006 Elsevier Ltd. All rights reserved  

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, 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... 

Porous shape memory alloys are a class of very interesting materials exhibiting features typical of porous metals and of shape memory alloys. In contrast to dense shape memory alloys, considerable plastic strain accumulates in porous shape memory alloys even during phase transformation. Moreover, due to the microstructure of porous materials, phase transformation and plasticity phenomena are significantly pressure-dependent. In this article, we propose a three-dimensional phenomenological constitutive model for the thermomechanical behavior of porous shape memory alloys able to predict shape memory effect, pseudo-elastic behavior and plastic behavior under proportional as well as... 

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... 

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... 

Amorphous lithium metal alloys (LixM, with M=Si, Ge, Sn, …) are attractive anode materials for lithium-ion batteries owing to their high energy-storage capacity and safety characteristics. However, repeated insertion of lithium often leads to chemo-mechanical degradation of the alloy, which can severely reduce the battery capacity and cycle life. Better understanding of the chemo-mechanical response of lithium alloys is needed to guide the design of damage-resistant anode microstructures. In this work, we propose a constitutive theory that couples large, viscoplastic deformations to the insertion and extraction of lithium in amorphous electrode materials. The theory relies on the concept of...