Thermomechanical behavior of pseudoelastic NiTi shape memory alloys

The thermomechanical behavior of polycrystalline Ni-rich pseudoelastic NiTi shape memory alloys is analyzed. Special focus is on regions within the stress strain diagram which are regarded as linear elastic in common phenomenological material models, i.e. the region between zero stress and the beginning of the pseudoelastic plateau as well as the region within the hysteresis. In both cases, severe temperature changes can be observed. A possible explanation for this effect is twofold: On the one hand, it might be explained by the presence of an R-phase transformation. On the other hand, unstructured martensite of the B19' phase may form. However, the assumption of a purely thermo-elastic material behavior in those regions does not seem to hold true in general. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of asymmetric effects for shape memory alloys

Experimental results of shape memory alloys show a pronounced asymmetric behaviour between tension, compression and shear. For simulation of these effects in the constitutive equations different transformation strain tensors are introduced. These are related to the different variants for the multi-variant- and detwinned-martensite as a consequence of different stress states. In the framework of plasticity the concept of stress mode dependent weighting functions is applied in order to characterize the different stress states. Verification of the proposed methodology is succeeded for simulation of the pseudoelastic behaviour of shape memory alloys with different hardening characteristics in tension, compression and shear. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Asymmetric Effects in Plasticity

In the framework of plasticity the simulation of materials is addressed, which experimentally exhibit different behavior in different loading scenarios, such as tension, compression and shear. To this end an additive decomposition of the yield function and the plastic potential, is assumed into a sum of weighted stress mode related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the Lode angle, such that stress mode dependent scalar weighting functions can be constructed. Verification of the proposed methodology is succeeded for simulation of the pseudoelastic behavior of shape memory alloys with different hardening characteristics in tension and shear. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constitutive modeling of the mechanics associated with crystallizable shape memory polymers

Shape memory polymers are novel materials 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 as heating. In this paper, we develop constitutive equations to model the 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 melting of this crystalline phase. The modeling is done using a framework that was developed recently for studying crystallization in polymers ([28], [25], [27], [31]) 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 melting of the crystalline phase to capture the return of the polymer to its original shape. The model has been used to simulate a typical uni-axial cycle of deformation, the results of this simulation compare very well with experimental data. In addition to this we also simulate circular shear of a hollow cylinder and present results for different cases in this geometry.     

Constitutive modeling of the mechanics associated with crystallizable shape memory polymers

Shape memory polymers are novel materials 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 as heating. In this paper, we develop constitutive equations to model the 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 melting of this crystalline phase. The modeling is done using a framework that was developed recently for studying crystallization in polymers ([28], [25], [27], [31]) 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 melting of the crystalline phase to capture the return of the polymer to its original shape. The model has been used to simulate a typical uni-axial cycle of deformation, the results of this simulation compare very well with experimental data. In addition to this we also simulate circular shear of a hollow cylinder and present results for different cases in this geometry. Received: January 5, 2005     

Influence of magnetic field on the rheological properties of liquid GaInSn alloy

In this work we studied experimentally the effect of an applied magnetic field and shear rate on the viscosity of a liquid GaInSn alloy. The experimental investigations were performed at room temperature in a homebuilt shear stress controlled rheometer. To consider the magnetohydrodynamical effects occurring in the melt numerical simulation of the flow field in the melt have been made. The results show a remarkable increase of the viscosity with increasing magnetic field strength. With increasing shear rate applied to the liquid GaInSn alloy a reduction of the change of viscosity is found. As first assumption this rheological behavior of GaInSn can be accounted to the presence of solid oxide fractions in the melt. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of Single Crystal Magnetostriction Based on Numerical Energy Relaxation Techniques

In this work, an incremental energy minimization technique is proposed to simulate the magnetomechanically-coupled, nonlinear, anisotropic and hysteretic response of single crystalline magnetic shape memory alloys (MSMA). The model captures the three key physical mechanisms that cause this characteristic behavior, namely the field- or stress-induced martensite variant reorientation (twin boundary motion), magnetic domain wall motion, and local magnetization rotation, through an (incremental) energy minimizing evolution of internal state variables. Representative numerical response predictions are presented, compared to experimental observations, and discussed with respect to the associated microstructure evolution. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Imperfect interface effect for nano-composites accounting for fiber section shape under antiplane shear

This paper investigates the elastic responses of fibrous nano-composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is the shear lag (or the spring layer) model; the presented nano interfacial stress model is the Gurtin–Murdoch surface/interface model; and the three-phase confocal elliptical cylinder model is the geometry model accounting for the fiber section shape. By virtue of the complex variable method, a generalized self-consistent method is employed to derive the closed from solution of the effective antiplane shear modulus of the fibrous nano-composites with imperfect interface. Five existing solutions can be regarded as the limit form the present analytic expression. The influences of the interface elastic constant, the interfacial imperfection parameter, the size of the elliptic section fiber, the fiber section aspect ratio, the fiber volume fraction and the fiber elastic property on the effective antiplane shear modulus of the nano-composites are discussed. Particularly, numerical results demonstrate that the interfacial elastic imperfection will always cause a significant reduction in the effective antiplane shear modulus; and the fiber interface stress effect on the effective modulus of the fibrous nano-composites will weaken with the interfacial imperfection increases.     

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.     

Pseudoelasticity of Shape Memory Alloys - a 1D Material Model and Finite Element Implementation

This contribution is concerned with the formulation of a 1D-constitutive model accounting for the pseudoelastic behavior of shape memory alloys. The stress-strain-relationship is idealized by a hysteresis both in the compression as in the tension loading range. It is characterized by an upper loading path, which is to be ascribed to the transformation of the lattice to a martensitic structure. Unloading the material, a lower path is described, because of the reverse transformation into austenitic lattice. The constitutive model is based on a switching criterion which serves as a potential function for the evolution of the internal state variables. The model distinguishes between local and global variables to describe the hysteresis effects for the compression and tension range. A strain driven algorithm which captures the complete nonlinear material behavior is presented. The boundary value problem is solved for a truss element applying the finite element method. A consistent linearization of the nonlinear equations is derived. Simple examples will demonstrate the applicability of the proposed model. For future developments the usage of shape memory alloys within civil engineering structures is aimed. The advantage of the material is the very good damping behavior and the potential to overcome great strains. Both properties are distinguished to be of engineering interest. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The new airfoil model NACA0015, modal analysis and flutter properties

The experimental airfoil model NACA0015 was used to study aeroelastic phenomena during self-excited profile vibration. It provides data for control of aeroelastic calculation programs at subsonic speeds of the stream. The model movability is two-dimensional with two-degree of freedom dynamic system, one in pitch and the second in plunge, and is proposed to be a dynamic system having two near corresponding eigenfrequencies. To quantitatively evaluate flow field using interferometry, a special test section design and profile was constructed. It utilized a large visual field for the optical system together with the option of changing support stiffness for both degrees of freedom. In this paper experimental results from the range of Reynolds numbers Re = (2.63–2.83) 10⁵ are published. The identified eigenvalues and eigenmodes for zero flow velocity are compared with measured flutter properties (frequency, modes and time evolutions) of the airfoil.     

夹芯梁的精确解法

夹芯梁与普通梁的本质区别在于剪切引起芯层横截面严重的而又不均匀的翘曲变形,其应力分布已远非初等理论所能描述,而正在广泛应用的经典夹层理论却都建立在平面假设基础上,尤其不能正确反映弱芯的轻质夹层结构的行为,本文放弃了不合理的假设,将夹芯梁视为一般层状弹性体,严格按弹性理论导出了既满足控制方程又同时满足全部边界条件、层间的应力及位移的连续条件的封闭解.它可确切地反映夹芯梁的位移形态和应力分布,并从不同角度,包括多种实验和FEM数值解,验证了它的正确性.     

Adjoint Sensitivity Analysis of a Fluid-Structure Interaction Problem

A fluid-structure mathematical model usually includes parameters whose actual values are known only approximately or can vary around some reference values. The objective of the sensitivity analysis is to determine quantitatively the behavior of the responses of a fluid-structure system locally around a chosen point of the trajectory in the phase-space of parameters and dependent variables. In this work, the response considered is the total mechanical energy of the structure. The sensitivities with respect to all the parameters the fluid-structure system depends on are useful in many situations as well as for optimization purposes. We present the theoretical developments necessary for the application of the adjoint sensitivity analysis methods (ASAM) for the fully coupled governing equations of an aeroelastic system. The algorithm is general and can be applied for any kind of fluid-structure interaction problems. Illustrative numerical examples are presented for the case of typical section with two degrees of freedom. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

带控制面机翼结构基于弧长数值连续法的颤振特征研究

以三自由度二元机翼为研究对象,将浮沉位移和俯仰位移方向的非线性刚度简化为立方非线性,对于存在间隙的控制面采用双线性刚度代替.考虑准定常气流,建立气动弹性运动方程,通过数值模拟构造峰值-峰值图,反映其在不同气流速度下的振动特征.通过弧长数值连续法构造系统的分岔图,结合Floquet算子研究其稳定性及其分岔类型,所得分岔图和数值模拟的结果相吻合.由分岔图可得系统由于控制面双线性的存在,导致机翼结构振动形态多变,存在多个分岔点和多个不稳定区间,不仅存在极限环振动和非光滑准周期振动,而且在某些不稳定区间出现混沌现象.     

Modelling of Shape Memory Alloys and Experimental Verification

Prestrained shape memory alloys change their length when heated above their transformation temperature. This effect can be used to generate high forces in a small workspace, which has particular advantages in actuator design. The optimization and control of the shape memory actuator requires a comprehensive simulation of the material behavior. However, many of the existing models are limited to specific load cases or offer rough approximations only. A material model for shape memory alloys from Seelecke [1] is examined in this paper. This model describes the behavior of a shape memory wire, which is heated by electric current. It is implemented in a simulation program to investigate the actuator output and to improve the performance. Finally, the parameters of the simulation are adapted to experimental results.     

High-order sliding mode controller with backstepping design for aeroelastic systems

A nonlinear system for controlling flutter in an aeroelastic system is proposed. The dynamic model describes the plunge and pitch motion of a wing. Interacting nonlinear forces such as structural and aerodynamic forces cause destabilizing phenomena such as flutter and limit cycle oscillation on the wing. Aeroelastic models have a wing section with only a single trailing-edge control surface for suppressing limit cycle oscillation. When modeling a single control surface, the controller design can achieve trajectory control of either plunge displacement or pitch angle, but not both, and internal dynamics describe the residual motion in closed-loop systems. Internal dynamics of aeroelasticity depend on model parameters such as freestream velocity and spring constant. Since single control surfaces have limited effectiveness, this study used leading- and trailing-edge control surfaces to improve control of limit-cycle oscillation. Moreover, two control surfaces were used to provide sufficient flexibility to shape both the plunge and the pitch responses. In this study, high order sliding mode control (HOSMC) with backstepping design achieved system stability and eliminated limit cycle phenomenon. Compared to the conventional sliding mode control design, the proposed control law not only preserves system robustness, but also avoids chatter phenomenon. Simulation results show that the proposed controller effectively regulate the response to origin in state space even under saturated controller input.     

Computational modeling of shape memory fibers in conforming and non-conforming compound structures

In this work a material model for shape memory alloy (SMA) fibers is presented. A constitutive model is provided which aims for computational use. The presented model incorporates all relevant material nonlinear phenomena. It takes pseudoplasticity into account as well as pseudoelasticity and further the shape memory effect (SME). The constrained SME (CSME) and the two-way SME are covered by the presented material model. The constitutive model is implemented in a one-dimensional truss formulation and in a 3D-rebar element. Both formulations are used to model fiber composite structures. Those are described by the use of a non-conforming and a conforming mesh on the mesoscale. The numerical examples show the capability of the formulation. Different meshing strategies for the fiber–matrix compound are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The method of fundamental solutions with eigenfunction expansion method for nonhomogeneous diffusion equation

In this article we describe a numerical method to solve a nonhomogeneous diffusion equation with arbitrary geometry by combining the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunction expansion method (EEM). This forms a meshless numerical scheme of the MFS‐MPS‐EEM model to solve nonhomogeneous diffusion equations with time‐independent source terms and boundary conditions for any time and any shape. Nonhomogeneous diffusion equation with complex domain can be separated into a Poisson equation and a homogeneous diffusion equation using this model. The Poisson equation is solved by the MFS‐MPS model, in which the compactly supported radial basis functions are adopted for the MPS. On the other hand, utilizing the EEM the diffusion equation is first translated to a Helmholtz equation, which is then solved by the MFS together with the technique of the singular value decomposition (SVD). Since the present meshless method does not need mesh generation, nodal connectivity, or numerical integration, the computational effort and memory storage required are minimal as compared with other numerical schemes. Test results for two 2D diffusion problems show good comparability with the analytical solutions. The proposed algorithm is then extended to solve a problem with irregular domain and the results compare very well with solutions of a finite element scheme. Therefore, the present scheme has been proved to be very promising as a meshfree numerical method to solve nonhomogeneous diffusion equations with time‐independent source terms of any time frame, and for any arbitrary geometry. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Numerical modelling of subcritical open channel flow using the K-ε turbulence model and the penalty function finite element technique

A numerical model has been developed that employs the penalty function finite element technique to solve the vertically averaged hydrodynamic and turbulence model equations for a water body using isoparametric elements. The full elliptic forms of the equations are solved, thereby allowing recirculating flows to be calculated. Alternative momentum dispersion and turbulence closure models are proposed and evaluated by comparing model predictions with experimental data for strongly curved subcritical open channel flow. The results of these simulations indicate that the depth-averaged two-equation k-ε turbulence model yields excellent agreement with experimental observations. In addition, it appears that neither the streamline curvature modification of the depth-averaged k-ε model, nor the momentum dispersion models based on the assumption of helicoidal flow in a curved channel, yield significant improvement in the present model predictions. Overall model predictions are found to be as good as those of a more complex and restricted three-dimensional model.