A constitutive model for finite deformation response of layered polyurethane-montmorillonite nanocomposites

A constitutive model is developed to predict the finite deformation response of multilayered polyurethane (PU)-montmorillonite (MTM) nanocomposites. In PU-MTM nanocomposites, the PU matrix in the vicinity of the MTM nanoparticles is modified leading to an interphase region, and its effect on the finite deformation response of these nanocomposites is largely neglected in many existing models. In this work, the entire spatial volume is considered to be occupied by multi-layers of bulk PU and effective particles which consist of MTM nanoparticles and the modified PU interphase region. A Langevin chain based eight chain model is used to capture the large stretch hyperelastic behavior of bulk PU. The effective particle component of the model consists of a linear elastic spring to capture the initial elastic response, a non-linear viscoplastic dash-pot for the strain-rate dependent yield strength of nanocomposites, and a non-linear spring element in parallel to the dash-pot for the strain-hardening response. The model adopts the concept of amplified strain of the confined PU chains to accommodate the applied strain owing to the limited strain in the MTM nanoparticles. The constitutive model predicts all the major features of the stress-strain constitutive response of a family of PU-MTM nanocomposites including the initial linear elastic response, yield strength and post yield strain hardening for all volume fractions of MTM nanoparticles, thus confirming the efficacy of the proposed constitutive model.     

A thermodynamic framework for the modeling of crystallizable shape memory polymers

Shape memory polymers are a relatively new class of materials that have the ability to retain a temporary shape, which can be reset to the original shape with the use of a suitable trigger, typically an increase in temperature. The temporary shapes can be very complex and the deformations involved large. These materials are finding use in a large variety of important applications; hence the need to model their behavior. In this paper, we develop constitutive equations to model the thermo-mechanical behavior of crystallizable shape memory polymers. Crystallizable shape memory polymers are called crystallizable because the temporary shape is fixed by a crystalline phase, while return to the original shape is due to the transition of this crystalline phase. The modeling is carried out using a framework that was developed recently for studying crystallization in polymers and is based on the theory of multiple natural configurations. In this paper we formulate constitutive equations for the original amorphous phase and the semi-crystalline phase that is formed after the onset of crystallization. In addition we model the transition of the crystalline phase to capture the return of the polymer to its original shape. These models for shape memory effects in polymers have been developed within a full thermodynamic framework, extending our previous work in which the models were developed within a mechanical setting [G. Barot, I.J. Rao, Constitutive modeling of the mechanics associated with crystallizable shape memory polymers, ZAMP 57 (4) (2006) 652-681]. The model is applied to the problem of inflation and extension of a hollow cylinder. The results are consistent with what has been observed in experiments.     

Non-isothermal finite element modeling of a shape memory alloy actuator using ANSYS

Many applications involve actuated devices made of shape memory alloys, but the lack of efficient numerical tools hinders the development of such technologies. Software using a finite element method like ANSYS allows the user to predict complex responses of a system without extensive programming. In this paper, a homemade phenomenological 1D bilinear model is programmed through the USERMAT procedure in ANSYS. The model allows the representation of both mechanical and thermal hystereses. The martensitic transformation is controlled by transformation criteria similar to those used in conventional plasticity, and subcycles are modeled by a simple elastic return through the hysteresis. The model is validated through isothermal tensile testing, assisted two-way shape memory testing and stress generation testing, and a good agreement with experimental results is shown. Finally, thermomechanical response of a single-degree-of-freedom actuator is simulated as a typical application and a case study involving the shape change of a radio controlled aircraft wing shows the potential of the numerical simulations.     

A constitutive model for cyclic actuation of high-temperature shape memory alloys

In this work, a three dimensional constitutive model for High Temperature Shape Memory Alloys (HTSMAs) is presented. To describe the evolution of the cyclic actuation behavior of such alloys, viscoplastic mechanisms and transformation induced plasticity are introduced in addition to the classical transformation behavior of shape memory alloys. Based on continuum thermodynamics, the evolution of phase transformation, plasticity induced transformation, retained martensite and viscoplasticity are described. Deformation mechanisms that occur over the operational range of such HTSMAs have been identified from the thermomechanical behavior of a NiTiPd alloy. The proposed model has therefore been calibrated and validated based on the thermomechanical response of the studied NiTiPd HTSMA alloy during thermal cycles under compression. Careful attention is devoted to the calibration procedure to identify the contribution of the different mechanisms independently. Finite Element Analysis (FEA) is performed to demonstrate the capabilities of the model to describe the cyclic behavior of HTSMA devices.     

Influence of thermoviscoelastic properties and loading conditions on the recovery performance of shape memory polymers

This work investigated the influence of material properties and loading conditions on the recovery performance of amorphous shape memory polymers using a recently developed thermoviscoelastic model. The model incorporated the time-dependent mechanisms of stress and structural relaxation and viscoplastic flow to describe the glass transition of the material from a soft viscoelastic rubber to a hard viscoplastic glass. The model captured many important features of the unconstrained strain recovery response and of the stress hysteresis observed in the constrained recovery response. A parameter study was developed that varied the model and loading parameters one-by-one to compare their effects on the start and end temperatures and recovery rate of the unconstrained recovery response and on the stress hysteresis of the constrained recovery response. The loading parameters included the cooling rate, the annealing time, and the high and low temperatures of the programming stage and the heating rate of the recovery stage. The results confirmed experimental observations that viscoelasticity is the underlying mechanism of the unconstrained recovery response. In contrast, the constrained recovery response was influenced by the interaction of many different mechanisms, including thermal expansion and structural and stress relaxation. For the loading parameters, the cooling rate of the programming stage and the heating rate of the recovery stage had the largest influence on both the constrained and unconstrained recovery response.     

A physical mechanism based constitutive model for temperature-dependent transformation ratchetting of NiTi shape memory alloy: One-dimensional model

In this paper, the effect of test temperature on the transformation ratchetting of super-elastic NiTi shape memory alloy was first investigated in the cyclic tension-unloading tests. It is shown that all the residual strain, dissipation energy, the start stress of martensite transformation and their evolutions during the cyclic loading depend greatly upon the test temperature. Based on the experimental observations, a new one-dimensional constitutive model is constructed by considering two different inelastic deformation mechanisms (i.e., martensite transformation and transformation-induced plasticity). The proposed model employs a new evolution rule of transformation-induced plasticity which considers the physical mechanism of the plastic deformation, i.e., the dislocation slipping in the austenite phase near the austenite–martensite interfaces. Furthermore, the interaction between dislocation and martensite transformation is also taken into account in the proposed model. The capability of the proposed model to predict the uniaxial temperature-dependent transformation ratchetting of NiTi shape memory alloy is verified by comparing the predictions with the experimental data.     

A Two-network thermomechanical model of a shape memory polymer

The aim of this work is to demonstrate a Helmholtz potential based approach for the development of the constitutive equations for a shape memory polymer undergoing a thermomechanical cycle. The model is able to simulate the response of the material during heating and cooling cycles and the sensitive dependence of the response on thermal expansion. We notice that the yield-stress of the material controls the gross features of the response of the model, and suggests that the material yields differently depending on not just the current value of the temperature but also on whether the temperature of the material dropped or increased from the previous time-step somewhat similar to the Bauschinger effect in plasticity, except that here the controlling parameter is the rate of temperature change rather than rate of plastic strain. The results of the simulation are in qualitative and quantitative agreement with experiments performed on two different shape memory polymer samples: polyurethane and epoxy resin. We find that modeling the hysteresis of the yield stress of the material during temperature changes is the key to the results.     

4D printing shape memory polymers for dynamic jewellery and fashionwear

4D printing is a novel approach that enables dynamic functionality in ordinary static object. We used a methacrylated semicrystalline polymer to print objects exhibiting thermally triggered shape memory behaviour. By exploring various molecular weights, it was found that a methacrylated polycaprolactone polymer with a number average molecular weight of 10,000?g?mol^?1 exhibited the best thermal and mechanical behaviour. The effect of dyes’ addition to the ink formulation on the photopolymerisation and on the printing processes was evaluated. The ink was utilised for demonstrating fabrication of dynamic jewellery and a shoe accessory by Digital Light Processing printing.     

Curing characteristics of shape memory polymers in 3D projection and laser stereolithography

The radical shift in 3D printing to fabricate soft active materials such as shape memory polymers (SMPs) has brought along other techniques in realising 4D printing. Stereolithography (SL) process has recently been one of the popular systems for printing SMPs. In this paper, the curing characteristics and behaviour of the SMPs fabricated via projection-type and laser-scanning-type SL process were analysed. Factors such as the UV exposure of the projection type and variation in resin compositions have significant differences in terms of energy density and curing depths when compared to the laser scanning type. Hence, theoretical calculations were made to determine the critical energy density and threshold penetration depth attainable, which enables newly developed SMP materials to be successfully printable using different types of UV-based 3D printing systems.     

Characterisation of phases and deformation temperature for additively manufactured shape memory polymer components fabricated from rubberised acrylonitrile butadiene styrene

ABSTRACT

Integrating shape memory polymers into additive manufacturing processes enables a form of 4D printing where a printed part can be manipulated into varying geometries upon the application of external stimuli. The work here explores the raster pattern sensitivity of the shape memory properties of two iterations of a polymer blend system composed of thermoplastic rubber and acrylonitrile butadiene styrene. Tensile test specimens were fabricated in three different raster patterns through the use of material extrusion additive manufacturing and deformed at room (25°C), low (?40°C) and high temperatures (105 and 110°C). Shape memory parameters were assessed and the shape fixation ratio was found to exhibit a sensitivity to raster pattern when deformation occurred at room and low temperatures, while the shape recovery ratio was found to be sensitive to raster pattern when deformation occurred at elevated temperatures. The influence of phase content was also explored and a decrease in rubber content led to an improvement in shape memory properties. The alignment of polymer phases with print raster direction was also found to influence raster pattern sensitivity.     

A constitutive model for unsaturated soils: thermomechanical and computational aspects

This paper first presents a complete formulation of a constitutive model that deals with the irreversible behaviour of unsaturated soils under various loading and drying/wetting conditions. A standard form of incremental stress-strain relations is derived. The constitutive model is then cast into the thermodynamical theories and verified using the thermomechanical principles. It is shown that hydraulic hysteresis does not contribute to the plastic dissipation, though it contributes to the plastic work. All plastic work associated with a plastic increment of the degree of saturation is stored and can be recovered in a reversed plastic increment of saturation. The incremental constitutive equations are also reformulated for implementation in finite element codes where displacements and pore pressures are primary unknowns. Qualitative predictions of the constitutive model show that incorporating two suction related yield surfaces and non-associated flow rules into the Barcelona Basic Model opens a full range of possibilities in modelling unsaturated soil behaviour.     

形状记忆合金超弹性本构关系的神经网络模型

通过试验，研究了受过循环变形、具有稳定超弹性变形性能的形状记忆合金丝在拉伸到不同应变幅值条件下卸载的超弹性变形行为。根据试验测得的结果，提出了基于神经网络的形状记忆合金超弹性本构关系模型，并把模型计算的结果和实验数据进行了比较分析，结果表明，该模型具有很高的精度。该模型避免了已有模型在参数确定上的困难，具有一定的工程应用价值，为建立形状记忆合金本构模型提供了一个新的思路。     

A thermo-micro-mechanical modeling for smart shape memory alloy woven composite under in-plane biaxial deformation

This paper presents a theoretical study of the in-plane behavior of Smart Shape Memory Alloy Woven Composites (SSMAWC) under biaxial loading by developing an integrated micromechanical constitutive model. The model studied in this research is established on the geometric parameters of fibers, metal layers, unit cell, the material constants of composite constituents, and the orientation of fibers, in which the fibers in one direction are SMA ones. The Helmholtz free energy of a Shape Memory Alloy, in 3-Dimensional and 1-Dimensional applications is derived. Using mechanical energy of matrix and elastic yarns, the constitutive relations are developed with the use of strain energy approach and energy variation theorem. The kinetic relations of SMA depicted by Brinson is coupled with the final governing equation of the composite to predict the stress history in smart shape memory alloy woven composites. The deflection of the structure, subjected to uniform biaxial loading is studied numerically. It is found that the effect of Shape Memory Effect (SME) of the SMA wires on the behavior of plain woven flexible fabric composite is significant.     

A revisit to atomistic rationale for slip in shape memory alloys

Performance degradation in shape memory alloys (SMA) arises due to a gradual loss of strain recoverability attributable to slip mediated plasticity. The slip-induced changes in SMAs can be profound creating accumulation of permanent strains, altering the critical stress and hysteresis in an adverse manner. Slip nucleation in ordered SMA lattices can often be triggered due to energetically favorable dissociation reactions. Partial slip can dominate over full slip, generating planar defects (e.g. anti-phase boundary, superlattice or complex stacking faults) as evidenced through electron microscopy. Considerable advances are made lately on physically rationalizing the observed plastic micromechanism(s) benefitting from quantum mechanical models. In-depth analyses of crystal variables (e.g. lattice ordering, atomic stacking and stable/metastable fault structures) subjected to intrinsic solid-state effects have unequivocally established the genesis of empirical slipping propensity in terms of atomic fault energetics. This article systematically revisits the empirical physical evidence of slip in important SMAs from the literature, presents the pertinent experimental findings, and then embarks on reviewing the investigations of atomistic studies as exemplified by the authors’ group. In closing, we discourse on the potential use of lattice scale theories in devising other important structure-property relationships such as role of precipitates, cracking resistance, constitutive modeling.     

A Lagrangian model for hardening behaviour of materials at finite deformation based on the right plastic stretch tensor

In this paper a modified multiplicative decomposition of the right stretch tensor is proposed and used for finite deformation elastoplastic analysis of hardening materials. The total symmetric right stretch tensor is decomposed into a symmetric elastic stretch tensor and a non-symmetric plastic deformation tensor. The plastic deformation tensor is further decomposed into an orthogonal transformation and a symmetric plastic stretch tensor. This plastic stretch tensor and its corresponding Hencky’s plastic strain measure are then used for the evolution of the plastic internal variables. Furthermore, a new evolution equation for the back stress tensor is introduced based on the Hencky plastic strain. The proposed constitutive model is integrated on the Lagrangian axis of the plastic stretch tensor and does not make reference to any objective rate of stress. The classic problem of simple shear is solved using the proposed model. Results obtained for the problem of simple shear are identical to those of the self-consistent Eulerian rate model based on the logarithmic rate of stress. Furthermore, extension of the proposed model to the mixed nonlinear isotropic/kinematic hardening behaviour is presented. The model is used to predict the nonlinear hardening behaviour of SUS 304 stainless steel under fixed end finite torsional loading. Results obtained are in good agreement with the available experimental results reported for this material under fixed end finite torsional loading.     

A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation

 This paper presents a rate-independent elastoplastic constitutive model for (nearly) incompressible biological fiber-reinforced composite materials. The constitutive framework, based on multisurface plasticity, is suitable for describing the mechanical behavior of biological fiber-reinforced composites in finite elastic and plastic strain domains. A key point of the constitutive model is the use of slip systems, which determine the strongly anisotropic elastic and plastic behavior of biological fiber-reinforced composites. The multiplicative decomposition of the deformation gradient into elastic and plastic parts allows the introduction of an anisotropic Helmholtz free-energy function for determining the anisotropic response. We use the unconditionally stable backward-Euler method to integrate the flow rule and employ the commonly used elastic predictor/plastic corrector concept to update the plastic variables. This choice is expressed as an Eulerian vector update the Newton's type, which leads to a numerically stable and efficient material model. By means of a representative numerical simulations the performance of the proposed constitutive framework is investigated in detail. Received: 12 December 2001 / Accepted: 14 June 2002 Financial support for this research was provided by the Austrian Science Foundation under START-Award Y74-TEC. This support is gratefully acknowledged.     

A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators

This paper presents the development of a semi-analytical axisymmetric shell finite element model with piezoelectric layers using the 3D linear elasticity theory. The piezoelectric effect of the material could be used as sensors and/or actuators in way to control shell deformation. In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction. Thus, the 3D elasticity equations of motion are reduced to 2D equations involving circumferential harmonics. In the finite element formulation the dependent variables, electric potential and loading are expanded in truncated Fourier series. Special emphasis is given to the coupling between symmetric and anti-symmetric terms for laminated materials with piezoelectric rings. Numerical results obtained with the present model are found to be in good agreement with other finite element solutions.     

A semi-analytical finite element model for the analysis of laminated 3D axisymmetric shells: Bending, free vibration and buckling

A general semi-analytical finite element model is developed for bending, free vibration and buckling analysis of shells of revolution made of laminated orthotropic elastic material. The 3D elasticity theory is used and the equations of motion are obtained by expanding the displacement field and load in the Fourier series in terms of the circumferential coordinate, θ. The coefficients of the expansion are functions of (r, z), and they are approximated using the finite element method. This leads to a semi-analytical finite element in the (r, z) plane. The element is validated by comparing the present results with the analytical and numerical solutions available in the literature.