Micro‐Mechanical Modelling of the Constitutive Behaviour of NiTi Shape Memory Alloys

The superelasticity and shape memory effect in NiTi alloys are examined on the basis of micromechanics within the energy minimization framework. We describe the behaviour of polycrystalline shape‐memory alloys via orientation‐distribution of the various martensite‐variants (domains) present in the material. Stress‐strain curves are presented and special attention is payed to the volume fraction of martensite for specific NiTi alloys (Nitinol) specimen under uniaxial tension. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

FE Modelling of NiTi‐Composed Structures

The present contribution focuses on the finite element modelling of NiTi‐based shape memory alloys. For this purpose, the concept of Helm [1] has been further developed and implemented into a finite element formulation. The model is able to describe the multiaxial behaviour of SMA and therefore useful for the simulation of complex problems. Additional emphasis is put on the modelling of the shape memory effect in composites where the interaction between the alloy and other materials like e.g. polymers plays an important role. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Simulation of the Application of NiTi Alloys in Medical Technologies

Shape memory alloys are nowadays already established as a material which is able to solve exceptional tasks in practical applications. Particularly, its utilization in the field of medical technologies increases steadily. For example micro tools (staple, catheters) and implants (coronary stents) are made out of Nickel-Titanium well known as a basic shape memory alloy. Apart from the advantages like the avoidance of auxiliary components and joints in the system and to utilize the high volume specific work of shape memory alloys, NiTi alloys exhibit a good biocompatibility. This property is necessary with regard to either permanent or temporary implants. To optimize the use of NiTi alloys in the scope of medical technologies, the support of the development of applicable tools by numerical simulations is highly recommended. However the complex material behaviour containing a profoundly thermomechanical coupling poses indeed a big challenge to the material modeling and its implementation into a finite element code. Particularly, the material model proposed by Helm [1] proves to be a firm model containing the most common properties of shape memory alloys, as the pseudoelasticity, the shape memory effect and the two-way effect. In the present contribution the FE modelling of a medical staple used in foot surgery is presented by considering the model of Helm which was investigated by the authors to improve its performance in the finite element method [2]. The foot staple, produced by a group of members of the SFB 459 which is funded by the DFG, avails the shape memory effect to excite the desired clamping effect [3]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study on the thermo-mechanical behavior of superelastic NiTi wires

The strong coupling of thermal and mechanical properties and the highly inhomogeneous strain distribution in tensiontests motivate for thorough investigations on NiTi shape memory alloys. For these tests a complex experimental set-up has been developed which allows for the simultaneous measurement of stress, strain, and temperature with high spatial and temporal resolution. The experimental results show the influence of strain rate, number of cycles, and deformation level on the progress of stress induced phase transformation in the specimens. A critical evaluation of the experimental results in view of a potential constitutive modeling is given. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Phenomenological and Numerical Simulation of Shape Memory Alloys at Finite Strains

A phenomenological material law for pseudo elastic NiTi shape memory alloys (SMA) is presented. The model was derived from a thermodynamical framework and is well-suited to describe the thermomechanical coupled behaviour of the material. The material law, which was originally derived for small deformations, was extended to finite deformations using the Eulerian frame, in particular Hencky's logarithmic strain and the logarithmic rate. A first emphasis is on the physical interpretation of the material parameters and their identification. A second focus lies in the presentation of a structural example for the implementation of the material law into a commercial Finite Element code. Additionally a comparison of the numerical and experimental data of the presented example is performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damping Behaviour of Vibrating Shape Memory Alloy Rods Investigated by a Novel Constitutive Model

Hysteretic behaviour of shape memory alloys (SMAs) is highly important for design and applicability of these materials in active structural elements like rods. Especially the damping performance of SMAs depend strongly on their hysteretic characteristics. Experimental investigations show the influences of stress on the hysteretic cycle. The current study shows some computational results of a constitutive model which is capable to investigate the effect of an external applied stress field on the hysteretic cycle according to a recently developed method on the basis of statistical mechanics method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Composite beams with shape memory alloy fibres

We are concerned with the bending problem of fibrous composite beams in which fibres are made of shape memory alloys. These are alloys that may undergo a stress‐induced martensitic phase transformation. The matrix is treated as an elastic medium, and perfect bonding between matrix and fibres is supposed. In our model, the beam is decomposed into layers and the hysteretic behaviour of the shape memory fibres is taken into account. The boundary value problem is formulated in the form of an evolution variational inequality which, after finite element discretization, can be solved incrementally as a sequence of linear complementarity problems. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A micromechanical model for single‐crystal shape‐memory‐alloys

This work is dealing with solid to solid phase transformations in shape‐memory‐alloys and the simulation of the corresponding characteristic phenomena, e.g. pseudoelasticity and the shape‐memory‐effect. In particular it focuses on the micromechanical behaviour of the material and the appearance of microstructures. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Functional Fatigue in polycrystalline Shape Memory Alloys

Shape memory alloys show the well known effect of pseudo-elasticity associated with the formation of two stress plateaus in the stress/strain diagram for tension tests. Due to cyclic loading, the stress plateaus decrease with every load cycle, particularly the upper one. This important effect of functional fatigue results from plastic deformations that are produced during solid-solid phase transformations between the austenitic and martensitic state. Outgoing from a polycrystalline approach for shape memory alloys we develop a micromechanical material model that is based on the Principle of the Minimum of the Dissipation Potential and predicts the evolution of plastic strains. Therefore, only a small number of material parameters is necessary and additionally, only a few assumptions are sufficient to model the effect of functional fatigue. We present yield functions as well as evolution equations for the volume fractions of austenite and martensite, and the plastic strains. Furthermore, we show an exemplary calculation for Nickel Titanium and compare it with experimental measurements to demonstrate the ability of our model. (© 2014 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 pseudo-plasticity in shape-memory-alloys

The name shape memory originates from the material's capability to recover its original shape after an apparent plastic deformation. The secret of this property lies in the specific microstructure. During mechanical loading, alloys of this particular kind change their crystallographic structure from randomly orientated martensite to ordered martensite. With austenite as high-temperature inter-state induced by heat supply, a recovery from the ordered to the unordered martensite is possible. This is accompanied by a macroscopic "healing" process. We apply our material model for shape-memory alloys to this special property and present numerical results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Sachs bound in stress-induced phase transformations in polycrystalline scalar shape-memory alloys

We consider stress–induced transformations of polycrystalline shape–memory alloys which are so–called scalar materials. In this case the Sachs bound on the phase transformation yield stress turns out to be sharp. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一个新的形状记忆合金模型

借助于Tanaka用一维形核动力学方程导出的指数形式的相变百分数,建立了一个新的形状记忆合金本构模型.提出了不同相变条件下的可恢复形状记忆应变的表达式;考虑了材料在变形过程中马氏体的重定向作用;克服了Tanaka系列模型不能描述当材料为完全马氏体状态时的力学行为的缺点.本模型较现有的形状记忆合金本构模型均简单,便于应用,实验证明了模型的正确性.     

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.     

Optimal control of thermomechanical phase transitions in shape memory alloys: Necessary conditions of optimality

The necessary conditions for the optimality of an optimal control problem associated with soiid–solid phase transitions in shape memory alloys are established.     

Global attractor for thermoelasticity in shape memory alloys without viscosity

We consider a nonlinear system of thermoelasticity in shape memory alloys without viscosity. The existence and uniqueness of strong and weak solutions and the existence of a compact global attractor in an appropriate space are proved. Copyright © 2015 John Wiley & Sons, Ltd.     

On the thermo-mechanically coupled simulation of poly-crystalline Shape Memory Alloys

We present a thermo-mechanically coupled model for poly-crystalline shape memory alloys which accounts both for the localized phase transformations and the resulting heat production. The model is based on the physical principles of energy conservation and entropy maximization. Choosing an appropriate ansatz for the entropy production the evolution equation for the phases can be derived as well the heat conduction equation. The results show good agreement to experimental findings. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

形状记忆合金相变过程三维大变形有限元模拟

形状记忆合金（SMA）一直被作为智能材料开发,并被用于阻尼器、促动器和智能传感器元件．形状记忆合金（SMA）的一项重要特性,是它具有恢复在机械加卸载周期下产生的大变形而不表现出永久变形的能力．该文旨在介绍一种由应力产生的相变且可以描述马氏体和奥氏体之间的超弹性滞回环现象本构方程．形状记忆合金的马氏体系数假设为应力偏张量的函数,因此形状记忆合金在相变过程中锁定体积．本构模型是在大变形有限元的基础上执行的,采用了现时构型Lagrange大变形算法．为了方便地使用Cauchy应力和线性应变本构关系,使用了与旋转无关的Jaumann应力增率计算应力．数值分析结果表明,相变引起的超弹性滞回环可以有效地通过该文提出的本构方程和大变形有限元模拟．