Thermomechanical Constitutive Model Research Articles

Phase transformation and energy dissipation of porous shape memory alloy structure under blast loading

Porous shape memory alloy (SMA) materials being porous structures combined with the behaviors of SMA material can offer tremendous potential for future energy absorbing structural components. Although several studies have been performed in recent past to examine the influence of pores towards phase transformation, they are limited to quasi-static loading conditions. Investigation of phase transformation and associated energy dissipation for porous structural component made of SMA materials is highly necessary for impact/blast loading. Therefore, using explicit finite element method, a predictive modeling framework is developed to solve the governing equations. A forward Euler algorithm is utilized to implement the thermo-mechanical constitutive model of SMA. Several porous SMA structures are idealized with array of macroscopic pores embedded in SMA plates. Parametric studies are performed to investigate the influence of pore sizes and arrangement on phase transformation behaviors and energy dissipation characteristics. The results provide key insights on the role of pores and their interaction in energy dissipation for SMA structures.

A Temperature-Dependent, Nonlinear Kinematic/Isotropic Hardening Material Constitutive Model of the Surface Layer of 37Cr4 Steel Subjected to Slide Burnishing

Slide burnishing (SB) is a simple and efficient method for finishing symmetric rotary metal parts. The thermo-mechanical nature of SB has not been studied in the literature and is, therefore, an object of investigation in this article. A combination of finite element method (FEM) analyses and experiments is used, and a very important part of building the FEM model is the constitutive model of the surface layer of the workpiece being slide burnished. A temperature-dependent, nonlinear kinematic/isotropic hardening material constitutive model of the surface layer of 37Cr4 steel has been modelled on the basis of temperature-dependent indentation tests and inverse FEM analyses. In order to illustrate the benefits of this thermo-mechanical constitutive model, 3D FEM simulations of the SB of holes have been conducted; doing so establishes the effect of the generated temperature on the residual hoop stress distribution around the processed hole. Fully coupled thermal stress, sequentially coupled, and temperature-independent FEM simulations have been conducted to determine the residual hoop stresses. Alternatively, these stresses are experimentally obtained through the modified “split ring” method. It has been proven that a sequentially coupled thermal stress FEM simulation with nonlinear kinematic/isotropic hardening predicts the residual hoop stresses in such a manner as to be in satisfactory agreement with the experimental outcomes. It has been established that the generated temperature reduces the beneficial effect from the introduced residual stresses, thus reducing the fatigue life of the corresponding structural component.

Thermomechanical constitutive modeling of fiber reinforced shape memory polymer composites based on thermodynamics with internal state variables

Shape memory polymer composites (SMPCs) can be used to improve the mechanical properties of the shape memory polymers (SMPs). They also have the potential to enhance or enable new stimulus approaches and novel shape memory effects (SMEs). In this paper, a thermoviscoelastic finite deformation constitutive model is developed for thermally activated unidirectional continuous elastic fiber reinforced SMPCs. Since the structural relaxation and viscous flow mainly exist in the SMP matrix, an internal state variable modeling approach is used to describe the thermomechanical behavior of the SMPCs. Recent works mainly focus on the thermomechanical behavior of carbon fiber reinforced SMPCs in the small strain range, for the tensile tolerant strain of carbon fiber is small. The model that is developed here shows that the unidirectional continuous carbon fiber reinforced SMPCs with proper fiber inclination angle and volume fraction can also be used in finite deformation range for the first time. The finite deformation thermomechanical response of unidirectional continuous carbon fiber reinforced SMPCs with different inclination angles and volume fractions is addressed here. Therefore, this study provides useful guidance for reasonable design of unidirectional continuous elastic fiber reinforced SMPCs.

Numerical/experimental assessment of 3D‐printed shape‐memory polymeric beams

ABSTRACTThe main objective of this article is to present different computational tools to replicate thermomechanical shape‐memory responses of beam‐like structures fabricated by three‐dimensional (3D) printing technology. To simulate thermomechanical behaviors of shape‐memory polymer (SMP) beams, one‐dimensional (1D) finite element model (FEM) building with MATLAB and 3D FEM by means of COMSOL Multiphysics are established. All governing equations are developed based on a 3D thermomechanical SMP constitutive model. 1D FEM is derived on the basis of the Euler–Bernoulli beam theory and linear geometrical assumption. The 3D SMP constitutive model is implemented into geometrically nonlinear COMSOL Multiphysics software through a user‐defined material subroutine to provide a powerful 3D simulation tool. Comparative studies on FEMs of MATLAB and COMSOL Multiphysics reveal that geometrically linear assumption is appropriate for models in large/small deformation under tension/bending. 1D analytical solution for deflection of an SMP beam employing Euler–Bernoulli beam theory is also developed. An experiment is conducted to demonstrate a full shape‐memory cycle of SMPs. It is experimentally shown that a 3D‐printed beam recovers the deformation incurred by external loads upon heating over the transition temperature. The accuracy of the 3D FEM in COMSOL Multiphysics is checked with analytical solutions and experimental data. It is found that simulation results of the program are in good agreement with characteristics observed in the experiment and analytical solutions. The developed computational tools are expected to be instrumental in the design of simple/complicated SMP structures. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019, 136, 47422.

Shape memory alloy–actuated prestressed composites with application to morphing automotive fender skirts

This work presents smart laminated composites that enable morphing vehicle structures. Morphing panels can be effective for drag reduction, for example, adaptive fender skirts. Mechanical prestress provides tailored curvature in composites without the drawbacks of thermally induced residual stress. When driven by smart materials such as shape memory alloys, mechanically-prestressed composites can serve as building blocks for morphing structures. An analytical energy-based model is presented to calculate the curved shape of a composite as a function of force applied by an embedded actuator. Shape transition is modeled by providing the actuation force as an input to a one-dimensional thermomechanical constitutive model of a shape memory alloy wire. A design procedure, based on the analytical model, is presented for morphing fender skirts comprising radially configured smart composite elements. A half-scale fender skirt for a compact passenger car is designed, fabricated, and tested. The demonstrator has a domed unactuated shape and morphs to a flat shape when actuated using shape memory alloys. Rapid actuation is demonstrated by coupling shape memory alloys with integrated quick-release latches; the latches reduce actuation time by 95%. The demonstrator is 62% lighter than an equivalent dome-shaped steel fender skirt.

Moisture-dependent thermo-mechanical constitutive modeling of wood

PurposeThe purpose of this study is the numerical investigation of densification and molding processes of wood. Providing theoretical and numerical approaches with respect to a consistent multi-physical finite element method framework are further goals of this research.Design/methodology/approachConstitutive phenomenological descriptions of the thermo-mechanical and moisture-dependent material characteristics of wood are introduced. Special focus is given to a consistent hygro-thermo-mechanical modeling at finite deformations to capture the realistic material behavior of wood, especially when it is subjected to densification and molding processes.FindingsRealistic theoretical formulations of different hygro-thermo-mechanical processes are provided. A successful numerical modeling is demonstrated for beech wood by validation at experimental findings.Originality/valueThe constitutive laws and numerical findings are new, as they govern a multi-physical large deformation framework and are applied to the advanced technology of densification and molding of wood.

A Multiscale Analysis on the Superelasticity Behavior of Architected Shape Memory Alloy Materials.

In this paper, the superelasticity effects of architected shape memory alloys (SMAs) are focused on by using a multiscale approach. Firstly, a parametric analysis at the cellular level with a series of representative volume elements (RVEs) is carried out to predict the relations between the void fraction, the total stiffness, the hysteresis effect and the mass of the SMAs. The superelasticity effects of the architected SMAs are modeled by the thermomechanical constitutive model proposed by Chemisky et al. 2011. Secondly, the structural responses of the architected SMAs are studied by the multilevel finite element method (FE), which uses the effective constitutive behavior of the RVE to represent the behavior of the macroscopic structure. This approach can truly couple the responses of both the RVE level and structural level by the real-time information interactions between two levels. Through a three point bending test, it is observed that the structure inherits the strong nonlinear responses—both the hysteresis effect and the superelasticity—of the architected SMAs at the cellular level. Furthermore, the influence of the void fraction at the RVE level to the materials’ structural responses can be more specifically and directly described, instead of using an RVE to predict at the microscopic level. Thus, this work could be referred to for optimizing the stiffness, the hysteresis effect and the mass of architected SMA structures and extended for possible advanced applications.

A semi-analytical modelling of cutting using crystal plasticity theory and flow line approach

A semi-analytical model for orthogonal cutting taking into account microstructure evolution and its influence on the chip formation process is developed for polycrystalline materials. To describe the 2D material flow in the chip, a thermomechanical crystal plasticity constitutive model was combined with the flow line approach. The microstructure evolution, as well as material flow stress and temperature rise, are obtained through a Visco-Plastic Self-Consistent (VPSC) mean field crystal plasticity model combined with a Mechanical Threshold Stress (MTS) physical-based hardening law. The proposed approach allows capturing in a relative simple way the variations of thermomechanical fields such as stress, strain, strain rate and temperature in the primary shear zone. The model validation is conducted by successful comparisons with experimental results of Shi and Liu [63] in terms of cutting forces and chip thickness during orthogonal cutting of a HY 100 steel alloy. The predicted results indicate that equivalent strain and temperature increase from the chip free surface to the tool tip. In contrast, the equivalent stress exhibits a reverse trend.

Ballistic performance of tungsten particle / metallic glass matrix composite long rod

Abstract In the present manuscript numerical analysis on the ballistic performance of a tungsten particle/metallic glass matrix (WP/MG) composite rod is conducted by integrating with related experimental investigations. In the corresponding finite element method (FEM) simulations a modified coupled thermo-mechanical constitutive model is employed to describe the mechanical properties of metallic glass (MG) matrix, and geometrical models of the WP/MG composite rod are established based on its inner structure. The deformation and failure characteristics of the rod and target materials are analyzed in detail, and the influences of various factors on the ballistic performance of the WP/MG composite long rod are discussed. Related analysis demonstrates that the penetrating performance of the WP/MG rod is similar to that of the tungsten fiber/metallic glass matrix (WF/MG) composite long rod, i.e., a “self-sharpening” behavior also occurs during the penetration process, and correspondingly its penetrating capability is better than that of the tungsten heavy alloy (WHA) rod. However, the mass erosion manner of the WP/MG rod is different and the erosion is relatively severe, thus its penetrating capability is a little lower compared with that of the WF/MG one. Moreover, the impact velocity and the target strength have significant influences on the ballistic performance of the WP/MG composite rod, whereas the effect of initial nose shape is very little.

A Time-Dependent Finite Element Formulation for Thick Shape Memory Polymer Beams Considering Shear Effects

In this paper, employing a thermomechanical small strain constitutive model for shape memory polymers (SMP), a beam element made of SMPs is presented based on the kinematic assumptions of Timoshenko beam theory. Considering the low stiffness of SMPs, the necessity for developing a Timoshenko beam element becomes more prominent. This is due to the fact that relatively thicker beams are required in the design procedure of smart structures. Furthermore, in the design and optimization process of these structures which involves a large number of simulations, we cannot rely only on the time consuming 3D finite element analyses. In order to properly validate the developed formulations, the numeric results of the present work are compared with those of 3D finite element results of the authors, previously available in the literature. The parametric study on the material parameters, e.g., hard segment volume fracture, viscosity coefficient of different phases, and the external force applied on the structure (during the recovery stage) are conducted on the thermomechanical response of a short I-shape SMP beam. For instance, the maximum beam deflection error in one of the studied examples for the Euler–Bernoulli beam theory is 7.3%, while for the Timoshenko beam theory, is 1.5% with respect to the 3D FE solution. It is noted that for thicker or shorter beams, the error of the Euler–Bernoulli beam theory even more increases. The proposed beam element in this work could be a fast and reliable alternative tool for modeling 3D computationally expensive simulations.

A 3D thermomechanical constitutive model for polycarbonate and its application in ballistic simulation

This paper presents a 3D thermomechanical constitutive model for polycarbonate (PC) polymers, aiming to predict the material characteristics of PC under complex thermomechanical boundary and strong impact loading conditions. The model is applied to simulate the high‐velocity ballistic impact tests. Quasi‐static tension, Split‐Hopkinson Tension Bar (SHTB), and ballistic impact tests are carried out to experimentally investigate the thermomechanical behavior of PC. Fundamental characteristics of PC, such as the transient yield peak, the post‐yield softening and the subsequent hardening, are characterized by introducing two scalar and one tensorial internal variables. Constitutive equations, specifically, (i) the plastic flow rule; (ii) the evolution equations associated with the internal variables; (iii) the temperature evolution; (iv) the strain rate, temperature and pressure‐dependent yield limit are derived within a thermodynamically consistent framework. The model is then implemented into the finite element software ABAQUS/Explicit by means of a user‐defined material subroutine VUMAT. Finally, numerical simulations are carried out and validated against experimental data. Finite element simulations of the ballistic tests well demonstrate the capabilities of the proposed model to accurately predict thermomechanical behavior of PC undergoing high‐velocity impact loadings. POLYM. ENG. SCI., 58:2237–2248, 2018. © 2018 Society of Plastics Engineers

A 1D thermomechanical network transition constitutive model coupled with multiple structural relaxation for shape memory polymers

A new thermomechanical network transition constitutive model is proposed in the study to describe the viscoelastic behavior of shape memory polymers (SMPs). Based on the microstructure of semi-crystalline SMPs, a new simplified transformation equation is proposed to describe the transform of transient networks. And the generalized fractional Maxwell model is introduced in the paper to estimate the temperature-dependent storage modulus. In addition, a neo-KAHR theory with multiple discrete relaxation processes is put forward to study the structural relaxation of the nonlinear thermal strain in cooling/heating processes. The evolution equations of the time- and temperature-dependent stress and strain response are developed. In the model, the thermodynamical and mechanical characteristics of SMPs in the typical thermomechanical cycle are described clearly and the irreversible deformation is studied in detail. Finally, the typical thermomechanical cycles are simulated using the present constitutive model, and the simulation results agree well with the experimental results.

A non-local implicit gradient-enhanced model for thermomechanical behavior of shape memory alloys

A three-dimensional, implicit gradient-enhanced, fully coupled thermomechanical constitutive model is developed within the framework of thermodynamic principles for NiTi shape memory alloys. This work focuses on unstable behaviors of NiTi samples under different thermomechanical loading conditions. Temperature variation and its coupling effect on non-local behavior of a shape memory alloy during a loading–unloading cycle at different strain rates are considered. The proposed constitutive equations are implemented into the finite element software ABAQUS, and the numerical investigations indicate that the used procedure is an effective computational tool for simulation of several behaviors of NiTi samples including phase front nucleation and propagation, stress–strain–temperature responses, and transformation-induced stress relaxation. The obtained results are shown to be in a good agreement with available experimental and numerical findings in the literature. The effectiveness of the model in removing mesh sensitivity is evaluated by investigating the mesh-dependence issue for the low strain rate problems through numerical examples.

A mesoscopic numerical analysis for combustion reaction of multi-component PBX explosives

A mesoscopic combustion reaction model of multi-component PBX explosives by using a coupled thermo-mechanical constitutive model is studied. Thereinto, based on the heat balance equation, the present temperature can be calculated; the changing physical state of different materials is described by establishing different equations of state, and based on specially appointed constitutive equations, the microcracks in PBXs are described. Furthermore, the concept of combustion reaction degree is established, which takes temperature as a criterion for changing physical state. The model is implemented within the framework of the material point method so that the different gradient in the governing differential equations could be discretized in a single computational domain and that continuous remeshing is not required with increasing reaction time. The proposed model-based simulation procedure is verified with the burn rate, the peak pressure, and temperature of PBX explosives under macroscopic scale.

On the mechanical properties of particle reinforced metallic glass matrix composites

In the present manuscript a modified coupled thermo-mechanical constitutive model is employed to describe the mechanical property of metallic glass (MG) matrix, and the geometrical models of particle reinforced MG matrix composites are established based on the inner structures. Then finite element method (FEM) numerical simulations on the mechanical properties of composites are conducted systemically by integrating with related experimental investigations, and the effects of different factors, including the volume fraction of particle (which determines the amount of particle and the interspace between particles), the mechanical property of particle material and the strain rate, on the deformation and failure characteristics of composites are analyzed. Related analysis demonstrates that the composite mainly displays as a shear manner, however, the reinforced particles can lead to an improvement for its plasticity. Furthermore, several internal and external factors have significant influences on the deformation and failure characteristics of composites. The corresponding mechanical properties depend firmly on the initiation and propagation of shear band and shear crack within the composite.

Thermomechanically Tunable Elastic Metamaterials With Compliant Porous Structures

Adding programmable function to elastic metamaterials makes them versatile and intelligent. The objective of this study is to design and demonstrate thermomechanically tunable metamaterials with a compliant porous structure (CPS) and to analyze their thermomechanical behaviors. CPS, the unit cell of the metamaterial, is composed of rectangular holes, slits, and bimaterial hinges. By decomposing kinematic rotation of a linked arm and elastic deformation of a bimaterial hinge, a thermomechanical constitutive model of CPS is constructed, and the constitutive model is extended to a three-dimensional (3D) polyhedron structure for securing isotropic thermal properties. Temperature-dependent properties of base materials are implemented to the analytical model. The analytical model is verified with finite element (FE) based numerical simulations. A controllable range of temperature and strain is identified that is associated with a thermal deformation of the bimaterial hinge and contact on the slit surfaces of CPS. We also investigate the effect of geometry of CPS on the thermal expansion and effective stiffness of the metamaterial. The metamaterial with CPS has multiple transformation modes in response to temperature while keeping the same mechanical properties at room temperature, such as effective moduli and Poisson’s ratios. This work will pave the road toward the design of programmable metamaterials with both mechanically and thermally tunable capability, providing unique thermomechanical properties with a programmable function.

Nonlinear thermomechanical response and constitutive modeling of viscoelastic polyethylene membranes

Thin films of linear low-density polyethylene show a significant time-dependent behavior, strongly reliant on temperature and strain rate effects. A constitutive nonlinear thermo-viscoelastic relation is developed to characterize the response of thin membranes up to yielding, in a wide range of temperatures, strain rates, and mechanical loading conditions. The presented plane stress orthotropic formulation involves the free volume theory of viscoelasticity and the time-temperature superposition principle, necessary to describe non-linearities and non-isothermal conditions. Uniaxial tension tests at constant strain rate and long-duration biaxial inflation experiments have been employed in the calibration of the material parameters. The model has been implemented in the Abaqus finite element code by means of a user-defined subroutine based on a recursive integration algorithm. The accuracy of the constitutive relation has been validated against experimental data of full field diaphragm inflation tests and uniaxial tension, relaxation and cyclic experiments, covering sub-ambient temperatures and strain rate ranges observed during the operation of stratospheric balloons.

Nonlinear Analysis of Shape Memory Devices With Duffing and Quadratic Oscillators

In this paper, we investigate the linear and nonlinear response of shape memory alloy (SMA)-based Duffing and quadratic oscillator under large deflection conditions. In this study, we first present thermomechanical constitutive modeling of SMA with a single degree-of-freedom system. Subsequently, we solve equation to obtain linear frequency and nonlinear frequency response using the method of harmonic balance and validate it with numerical solution as well as averaging method under the isothermal condition. However, for nonisothermal condition, we analyze the influence of cubic and quadratic nonlinearity on nonlinear response based on method of harmonic balance. Analysis of results leads to various ways of controlling the nature and extent of nonlinear response of SMA-based oscillators. Such findings can be effectively used to control external vibration of different systems.

Thermo-mechanical coupling damage constitutive model of rock based on the Hoek–Brown strength criterion

Studying the thermal damage constitutive model of rock using statistical theory can better reflect the damage evolution process and the stress–strain relationship of rock under temperature and loading, which is one of the key problems especially in deep rock mechanics. The thermal-mechanical coupling damage constitutive model of rock is established using the Hoek–Brown strength criterion, based on the Weibull distribution and the continuous damage theory. The rationality of the model is also verified by experiments. The main conclusions are as follows. The stress–strain curves of rock can be divided into four stages according to the damage evolution characteristics, including the non-damage of loading, damage stability expansion, damage intensification expansion, and damage stability expansion to saturation, and the method of determining the demarcation points of each stage is given clearly. The initial damage point of the rock is about 25% of the peak stress, the damage value is about 0.3 when the rock reaches the peak stress and about 0.6 when reaches the residual stress. Both the damage value and the strain energy release rate of the rock corresponding to the peak stress show exponential growth with the increase in confining pressure. The maximum damage evolution rate of the rock shows exponential decay as the confining pressure rises, indicating that the confining pressure can delay the development of cumulative damage. The modified damage constitutive model considering compaction coefficient is in good agreement with the test curves in the stage of compaction, linear elasticity, yield, and pre-peak strength. It is hoped that through the research of this paper, it can provide references for studying the macroscopic mechanical response from the damage propagation characteristics of the rock in the future.

A constitutive model of shape memory polymers based on glass transition and the concept of frozen strain release rate

Shape memory polymers (SMPs) are a type of polymeric smart material. They can maintain a deformed shape and return to their original shape according to external stimuli, such as temperature, light, pH, magnetic field and so on. In the last decade, SMPs have gained increasing attention due to their unique properties and have thus led great progress in developing proper constitutive models. In this paper, we propose and establish a new phase-evolution-based thermomechanical constitutive model for amorphous SMPs by considering the materials as a mixture of the rubbery phase and glassy phase. The shape memory effect (SME) is captured under the assumption that the rubbery phase can transform into the glassy phase and that part of the strain will be frozen during the glass transition. To make the model be more feasible, furthermore, we improve the model by introducing a time factor and considering the influence of frozen strain release rate. To validate the robustness and applicability of the proposed new model, we reproduce the shape memory behaviors (SMBs) of two different materials under different constraints and conditions. The results show a remarkable consistency between the new model simulation and experimental data.