Dynamics of Shape Memory Alloys Patches with Mechanically Induced Transformations

A mathematical model is constructed for the modelling of two di- mensional thermo-mechanical behavior of shape memory alloy patches. The model is constructed on the basis of a modified Landau-Ginzburg theory and includes the coupling effect between thermal and mechanical fields. The free energy functional for the model is exemplified for the square to rectangular transformations. The model, based on nonlinear coupled partial differential equations, is reduced to a system of differential-algebraic equations and the backward differentiation methodology is used for its numerical analysis. Computational experiments with representative distributed mechanical loadings are carried out for patches of different sizes to analyze thermo-mechanical waves, coupling effects, and 2D phase transformations

Finite Volume Analysis of Nonlinear Thermo-mechanical Dynamics of Shape Memory Alloys

In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modelling of shape memory alloys. Computational experiments are carried out to study the thermo-mechanical wave interactions in a shape memory alloy rod, and a patch. Both mechanically and thermally induced phase transformations, as well as hysteresis effects, in a one-dimensional structure are successfully simulated with the developed methodology. In the two-dimensional case, the main focus is given to square-to-rectangular transformations and examples of martensitic combinations under different mechanical loadings are provided.Comment: Keywords: shape memory alloys, phase transformations, nonlinear thermo-elasticity, finite volume metho

Numerical Model For Vibration Damping Resulting From the First Order Phase Transformations

A numerical model is constructed for modelling macroscale damping effects induced by the first order martensite phase transformations in a shape memory alloy rod. The model is constructed on the basis of the modified Landau-Ginzburg theory that couples nonlinear mechanical and thermal fields. The free energy function for the model is constructed as a double well function at low temperature, such that the external energy can be absorbed during the phase transformation and converted into thermal form. The Chebyshev spectral methods are employed together with backward differentiation for the numerical analysis of the problem. Computational experiments performed for different vibration energies demonstrate the importance of taking into account damping effects induced by phase transformations.Comment: Keywords: martensite transformation, thermo-mechanical coupling, vibration damping, Ginzburg-Landau theor

Multiscale localized differential quadature in 2D partial differential equation for mechanics of shape memory alloys

In this research, the applicability of the Multiscale Localized Differential Quadrature (MLDQ) method in two-dimensional shape memory alloy (SMA) model was explored. The MLDQ method was governed in solving several partial differential equations. Besides, the finite difference (FD) method was used to solve some examples of partial differential equations and the solutions obtained were compared with those obtained by MLDQ method in order to show the accuracy of the numerical method. The MLDQ method was developed by increasing the number of grid points in critical region, and approximating the derivatives at the certain selected grid points. This present method together with the fourth-order Runge-Kutta (RK) method has been applied in differential equations such as wave equation and high gradient problems,. The MLDQ method can achieves accurate numerical solutions compared with FD method which is a low order numerical method by using a few number of grid points. The multiscale method was employed at the critical region which can break down the region of interest from coarser into finer grid points. Furthermore, FORTRAN programs were developed based on MLDQ method in solving some problems as above. The shared memory architecture of parallel computing was done by using OpenMP in order to reduce the time taken in simulating the numerical results. Consequently, the results show that the MLDQ method was a good numerical technique in two-dimensional SMA

Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys

In this research, the applicability of the Multiscale Localized Differential Quadrature (MLDQ) method in two-dimensional shape memory alloy (SMA) model was explored. The MLDQ method was governed in solving several partial differential equations. Besides, the finite difference (FD) method was used to solve some examples of partial differential equations and the solutions obtained were compared with those obtained by MLDQ method in order to show the accuracy of the numerical method. The MLDQ method was developed by increasing the number of grid points in critical region, and approximating the derivatives at the certain selected grid points. This present method together with the fourth-order Runge-Kutta (RK) method has been applied in differential equations such as wave equation and high gradient problems,. The MLDQ method can achieves accurate numerical solutions compared with FD method which is a low order numerical method by using a few number of grid points. The multiscale method was employed at the critical region which can break down the region of interest from coarser into finer grid points. Furthermore, FORTRAN programs were developed based on MLDQ method in solving some problems as above. The shared memory architecture of parallel computing was done by using OpenMP in order to reduce the time taken in simulating the numerical results. Consequently, the results show that the MLDQ method was a good numerical technique in two-dimensional SMA

Constitutive modeling of glassy memory polymers

The aim of this research is to develop constitutive models for non-linear materials. Here, issues related for developing constitutive model for glassy shape memory polymers are addressed in detail. Shape memory polymers are novel material that can be easily formed into complex shapes, retaining memory of their original shape even after undergoing large deformations. The temporary shape is stable and return to the original shape is triggered by a suitable mechanism such heating the polymer above a transition temperature. Glassy shape memory polymers are called glassy because the temporary shape is fixed by the formation of a glassy solid, while return to the original shape is due to the melting of this glassy phase. The constitutive model has been developed to capture the thermo-mechanical behavior of glassy shape memory polymers using elements of nonlinear mechanics and polymer physics. The key feature of this framework is that a body can exist stress free in numerous natural configurations, the underlying natural configuration of the body changing during the process, with the response of the body being elastic from these evolving natural configurations. The aim of this research is to formulate a constitutive model for glassy shape memory polymers (GSMP) which takes in to account the fact that the stress-strain response depends on thermal expansion of polymers. The model developed is for the original amorphous phase, the temporary glassy phase and transition between these phases. The glass transition process has been modeled using a framework that was developed recently for studying crystallization in polymers and is based on the theory of multiple natural configurations. Using the same frame work, the melting of the glassy phase to capture the return of the polymer to its original shape is also modeled. The effect of nanoreinforcement on the response of shape memory polymers (GSMP) is studied and a model is developed. In addition to modeling and solving boundary value problems for GSMP\u27s, problems of importance for CSMP, specifically a shape memory cycle (Torsion of a Cylinder) is solved using the developed crystallizable shape memory polymer model. To solve complex boundary value problems in realistic geometries a user material subroutine (UMAT) for GSMP model has been developed for use in conjunction with the commercial finite element software ABAQUS. The accuracy of the UMAT has been verified by testing it against problems for which the results are known

Design of a composite morphing wing

Morphing aircraft components can increase the possibility of optimising the performance of an aircraft at various flight conditions. A morphing aircraft wing can change the wing shape to modify the lift and drag distribution on the wing surface, allowing the lift-to-drag ratio to be tailored to the desired performance. A camber morphing and a trailing edge morphing wing changes the aerodynamic lift by altering the camber and by deflecting the wing trailing edge, potentially reducing the aerodynamic drag by eliminating the gaps; which exist between the main wing and the control surfaces of a conventional wing. Among the technology used to achieve camber morphing and trailing edge morphing, were mechanical and smart actuations, such as piezoelectrics and shape memory alloys (SMAs). Compliant structures, cellular structures, shape memory polymers, and multi-stable structures were exploited to improve the flexibility of the aerofoil sections or wings. SMA wires were one of the smart actuators which had been extensively utilised to morph various aerofoils/wings, mainly due to the high actuation force and compatibility, which reduce the volume and weight of the actuators and the complexity of moving mechanical components. In this research, a user defined material model (UMAT) was developed within the explicit LS-DYNA FE code, for NiTi shape memory alloy (SMA) wires, and used for actuation of the composite morphing wing. The Tanaka SMA constitutive model was implemented in MATLAB and FORTRAN codes for the SMA-actuation of various structures. The UMAT was used to simulate actuations of various complex morphing structures, including several aluminium and composite aerofoils with corrugated sections, and a pre-curved corrugated plate. Actuations of the two aluminium aerofoils, with corrugated sections in the lower surface and the middle cantilever section, by a 0.5mm-diameter SMA wire with a maximum recoverable strain or a pre-strain of 1.6%, resulted in trailing edge (TE) deflections of 7.8 mm and 65.9 mm, respectively. Actuation of the carbon fibre (CF) composite aerofoil, with the corrugated section as a middle cantilever section, and with 8 layers of CF in ±45° directions, produced a TE deflection of 52.0 mm. To demonstrate the SMA-actuated morphing concept, a composite 3D-printing technology was explored to manufacture a carbon fibre (CF) composite structure, consisted of a flat vertical front plate, a corrugated section, and a rear trailing edge (TE) section. Due to the nature of 3D-printing, two layers of CF were 3D-printed along the circumference of the corrugation and the TE section, and the minimum thickness of the structure was 3 mm. Experimentally, actuation of the CF composite corrugated structure by a NiTi SMA wire with a diameter of 0.2 mm and a pre-strain of 4.77%, and with a diameter of 0.5 mm and a pre-strain of 1.68%, aligned in the chordwise direction, resulted in 1.1 mm and 6.0 mm TE deflections, respectively. Cyclic tests (10 and 30 cycles) of the actuation of the CF composite corrugated structure showed the TE deflection converged after few cycles. A 1.25m-span composite morphing wing was finally designed and manufactured, consisted of a CF composite D-nose spar which resisted the main aerodynamic loading, and rear sections which were made of rigid and flexible foams. CF composite spar flanges, spar web, front and rear ribs, were 3D-printed, and were assembled with a CF composite skin which was autoclave-manufactured, to form the CF composite D-nose spar. Sections of rigid and flexible foams were CNC-machined and were attached to the front CF composite D-nose spar, 3D-printed long rear ribs, trailing edge sections and the morphed corrugated structure, to form a complete composite morphing wing.Open Acces