Journal of Intelligent Material Systems and Structures OnlineFirst, published on May 30, 2007 as doi: / x

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1 Journal of Intelligent Material Systems and Structures OnlineFirst, published on May 3, 27 as doi:.77/45389x Constitutive Model of Shape Memory Alloys for Asymmetric Quasiplastic Behavior TADASHIGE IKEDA* Department of Aerospace Engineering, Nagoya University, Chikusa, Nagoya , Japan ABSTRACT: A simple constitutive model of shape memory alloys for analyses of tension compression quasiplastic behavior is derived. Here, three martensitic variants are considered; namely, thermal-induced, tensile stress-induced, and compressive stress-induced martensitic variants. Reorientation from one variant to another variant is assumed to take place according to a reorientation energy criterion based on grain-based micromechanics. Stress strain hysteresis loops for a bar under tension compression cyclic loading are simulated and they are compared with available experimental data. Results show that this constitutive model can capture asymmetric stress strain behavior for tension and compression and a strain rate effect on stress strain temperature relationship quite well. Key Words: shape memory alloys, quasiplasticity, constitutive equations, reorientation, tension compression asymmetry. INTRODUCTION QUASIPLASTIC behavior of shape memory alloys (SMAs) is important as well as pseudoelastic behavior, where the term quasiplasticity is defined as the deformation behavior due to reorientation because stress strain behavior of the reorientation is similar to that of plastic deformation. In particular, it is the case when SMAs in martensitic phase are used as structural elements to perform damping or shock absorption (e.g., Graesser and Cozzarelli, 99; Adachi and Unjoh, 999). In such a case, since a form of the structural elements is not only a wire but also a bar or beam, both tensile and compressive behavior must be taken into account at least. On the contrary to the needs, experimental and theoretical studies of the tension compression quasiplastic behavior are not carried out so much. Liu and van Humbeeck (997) and Liu et al. (998) studied tension compression behavior of martensitic SMAs systematically. Their result showed that stress strain curves of martensitic SMAs for compressive loading were different from tensile loading. It was observed with a transmission electron microscope (TEM) that martensitic variants were partially reoriented and no significant plastic deformation occurred inside martensitic twin bands under tension to 4% strain, while under compression to 4% strain, a high density of dislocations was generated in the martensitic * ikeda@nuae.nagoya-u.ac.jp. twin bands and no significant martensitic reorientation occurred. This fact explained the asymmetric behavior in stress strain relationship for tension and compression. Moreover, it was also shown that strain rate had slight influence on quasiplastic stress strain behavior, although it had significant influence on temperature change. There are many constitutive models that capture pseudoelastic behavior (e.g., Tanaka, 986, 99; Liang and Rogers, 99; Mu ller and Xu, 99; Ortı n, 99; Raniecki et al., 992; Brinson, 993; Ivshin and Pence, 994; Leclercq and Lexcellent, 996; Kamita and Matsuzaki, 998; Gall and Sehitoglu, 999; Matsuzaki et al., 2, 22; Nae et al., 23; Ikeda et al., 23, 24a,b) and some of the models can also capture asymmetry of stress strain behavior (e.g., Gall and Sehitoglu, 999; Nae et al., 23). However, for quasiplastic behavior there are fewer models (e.g., Bertram, 983; Falk, 983; Graesser and Cozzarelli, 99; Seelecke, 996; Huang and Brinson, 998; Huo and Zu, 998). Bertram (983) extended classical plasticity theory to describe both the quasiplastic and pseudoelastic behavior of SMAs. Falk (983) found an adequate Helmholtz free energy density as a function of strain and temperature, and obtained stress strain relationship by differentiating the energy function in terms of strain. The above models did not explicitly take into account austenitic and martensitic phases. Seelecke (996) extended Mu ller s model (99), where a pair of symmetric martensitic variants and austenitic phase were considered, and conditions for JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES, Vol X/7/ 8 $./ DOI:.77/45389X ß 27 SAGE Publications + [Ver: A3B2 8.7r/W] [ :29am] [ 8] [Page No. ] REVISED PROOFS {SAGE_REV}Jim/sofa papers-may/jim d (JIM) Paper: JIM Keyword Copyright 27 by SAGE Publications.

2 2 T. IKEDA two-phase equilibria and a three-phase equilibrium state were determined by minimizing total free energy composed of free energies of the three phases and an interfacial energy between the phases. His model is good for understanding a mechanism of equilibrium state of the mixed phases from the energy point of view. These three models could capture both the pseudoelastic and quasiplastic behavior depending on values of model parameters or material constants. However, they could not capture the features such as the asymmetric stress strain relationship and the strain rate effect as observed in the experiments. Accordingly, they may not be good for designing smart structural elements with SMAs. Therefore, in this article, a simple yet accurate constitutive model for analyses of asymmetric quasiplastic behavior is proposed, where three martensitic variants are considered. This model is based on the same concept as proposed in our constitutive model for pseudoelasticity (Ikeda et al., 24a,b). This pseudoelastic model is derived from the grain-based micromechanical model (Ikeda et al., 23; Nae et al., 23), where required energy for phase transformation was approximated by a sum of two exponential functions, and to express partial transformation cycles, the required energy for complete transformation was shifted and already transformed regions were skipped in partial transformation energy function, from a microscopic point of view. Here, this shift skip partial transformation model is applied in part to reorientation appearing in the quasiplastic behavior. In the next section, the quasiplastic model is derived based on the shift skip model. In the third section, numerical simulations of SMA bar under tension compression cycles are carried out and it is shown that the derived model can capture the features of the observed quasiplastic behavior such as the asymmetric stress strain loops and the effect of the strain rate on the stress strain temperature relationship. To recall the shift skip partial transformation model, a brief summary of the model is shown in Appendix. CONSTITUTIVE MODELING In a similar way to the phase transformation in the pseudoelastic case (Appendix), the reorientation criteria is derived. The quasiplastic deformation behavior is a result of combinations of 24 variants in NiTi SMAs and the mechanism becomes more complicated in the polycrystalline SMAs because grains interact with their neighbor grains and the direction of grains is different from each other. However, here the tension compression deformation behavior is considered, and the deformation behavior is assumed to be approximated by a result of combinations of three martensitic variants. This assumption is similar to the assumption in the pseudoelastic models, where only the two phases of the austenitic phase and the martensitic phase are considered (e.g., Tanaka, 99; Liang and Rogers, 99; Brinson, 993; Ikeda et al., 24b). One of the variants is assumed to be generated by thermal-induced transformation and named here variant N, another by tensile stress-induced transformation and named variant T, and the other by compressive stress-induced transformation and named variant C. Variants N, T, and C may be a single variant or may be a combination of some variants. It is assumed that all variants have the same mechanical properties except for the intrinsic strain due to difference in lattice structure and the Young s modulus. The reorientations from variant N to T or C, from T to C, and from C to T are assumed to occur, but the reorientation from variant T or C to N is not assumed to occur, because variant N is generated through self-accommodation of some martensitic variants by cooling the austenitic phase. The driving energy,!, becomes! ¼ 2 2 E E þ ð" " Þ, for the reorientation from variant to variant, where, E, and " denote the stress, the Young s modulus of variant, and the intrinsic strain of variant, respectively. Accordingly, the reorientation criteria from variant N to T, from N to C, from C to T, and from T to C are given by N!T ¼ 2 2 þ ð" T " N Þ¼ N!T, ð2:þ E T E N N!C ¼ 2 2 þ ð" C " N Þ¼ N!C, E C E N ð2:2þ C!T ¼ 2 2 þ ð" T " C Þ¼ C!T, E T E C ð2:3þ T!C ¼ 2 2 þ ð" C " T Þ¼ T!C, E C E T ð2:4þ where! is the required energy for the reorientation (required reorientation energy: RRE) from variant to variant. It is noted that each reorientation driving energy is described separately, although the two-phase transformation driving energy can be described by one form for both the forward and reverse transformations as in Equation (A-). To express partial reorientation cycles, the shift skip model is modified. Here, RRE orders for infinitesimal grains are assumed to be the same in all reorientation directions. To explain this, let us consider a specimen composed of grains in series as shown in Figure, where the grains are arranged in the RRE order. It is noted that the model to be derived is a continuous ðþ + [Ver: A3B2 8.7r/W] [ :29am] [ 8] [Page No. 2] REVISED PROOFS {SAGE_REV}Jim/sofa papers-may/jim d (JIM) Paper: JIM Keyword

3 Shape Memory Alloys for Asymmetric Quasiplastic Behavior 3 Table. Variant border volume fractions at the states illustrated in Figure. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) z T þz C Z NT Z NC z CT z TC Figure. Schematic explanation of partial reorientation rule using the -grain model. model, although the -grain model is used to make it easier to image how the variants reorient at a grain level. Initially, all the grains are assumed to be in variant N (Figure a). When a tensile force is assumed to be applied to this specimen, grain # reorients to variant T first, because it has the smallest RRE (Figure b). Then grain #2 follows grain #, grain #3 follows grain #2, and so on. After grains # to #6 reorient to variant T (Figure c), the specimen is assumed to be unloaded and compressed. Here, reorientation from T to N is assumed never to occur and grain # reorients to variant C first (Figure d). Then grains #2 to #4 follow grain # in number order (Figure e). If the RRE from variant N to C of grain #7 is less than that from T to C of grain #5, then reorientation from N to C of grain #7 takes place before grain #5 reorients from T to C (Figure f ). Further compression makes all the grains variant C (Figure g, h). After this state, variant N never appears. During subsequent tension, compression, tension, and compression, the grains reorient in a similar way to the shift skip model (Figure i l). Formulating this partial reorientation rule, the RRE are written as N!T ¼, N!Tðz T þ z C Þ, ð3:þ C!T ¼ T!C ¼ 8 >< >: 8 >< >: N!C ¼, N!Cðz T þ z C Þ, ð3:2þ, C!TðÞ when the smallest border is z NC or z TC,, C!Tðz CT Þ when the smallest border is z CT,T!CðÞ when the smallest border is z NT or z CT ð3:3þ,t!cðz TC Þ when the smallest border is z TC ð3:4þ :,! stands for the RRE for complete reorientation. z T and z C denote the volume fractions of variant T and C, and if z N denotes the volume fraction of variant N, then z N þ z T þ z C ¼ ; z N, z T, z C : z NT and z NC are, respectively, the variant border volume fractions for N to T and N to C reorientations, when the grains are arranged in the RRE order. z CT and z TC are the smallest variant border volume fractions for C to T and T to C reorientations. To make the meaning of these variables clear, their values at the states illustrated in Figure are listed in Table. The strain equation and the heat and energy flow equation are, respectively, given by where ð4þ " ¼ E I þ " I þ T ðt T i Þ, ð5þ C _T þ h 4 ð d T T sþ ¼ _ T T _, ð6þ ¼ z N þ z T þ z C, E I E N E T E C ð7þ " I ¼ z N " N þ z T " T þ z C " C, ð8þ _ I ¼ N!T _z N!T þ N!C _z N!C þ C!T _z C!T þ T!C _z T!C : T, T, T i, C, h, d, and T s denote the thermal expansion coefficient, the material temperature, the initial temperature, the specific heat capacity at constant stress per unit volume, the convection heat transfer coefficient, the diameter of a wire specimen, and the surrounding temperature, respectively. The dot stands for the time derivative. z! denotes the volume fraction of variant reoriented from variant. NUMERICAL RESULTS AND DISCUSSION To verify the proposed model, predicted deformation behavior is compared with the available experimental data measured by Liu et al. (998). They measured stress strain loops of a rod with d¼ 6:7 3 m for strain cycles between and %, 2 and 2%, ð9þ + [Ver: A3B2 8.7r/W] [ :29am] [ 8] [Page No. 3] REVISED PROOFS {SAGE_REV}Jim/sofa papers-may/jim d (JIM) Paper: JIM Keyword

4 4 T. IKEDA Stress (MPa) Strain (%) % Amp. steady 2% Amp. steady 4% Amp. steady to 4% + st loop 2nd loop 2 4 Figure 2. Stress strain loops under tension compression cycles (symbols: Liu et al. s experiment (998); curves: prediction). and 4 and 4% at a strain rate of _" ¼ :6 2 s at room temperature. The room temperature is assumed to be 2 C as it is not mentioned in their paper. First, from the data for monotonic tension and compression test and cyclic tension compression test, the Young s moduli, E N, E T, and E C, and the intrinsic strains, " N, " T, and " C were estimated at 35, 2, and 55 GPa, and,.4, and.3, respectively. Next, the RRE functions for C to T and T to C reorientations were determined. To this end, their 4% strain loop at a steady state was used, since the loop shape changed much during the first several cycles, as shown with triangles in Figure 2; the first, the second, and the steady loops after about cycles for 4% strain amplitude are shown with open down triangle, closed down triangle, and open up triangle, respectively. Substituting the stress strain data, represented by up triangles in Figure 2, into Equations (2) and (5), the relationships between RRE and the volume fraction for C to T and T to C reorientations were calculated, where the thermal expansion term was neglected. Symbols in Figure 3 represent the RREs for complete reorientation estimated from the experimental data. These RRE data were approximated by a sum of two exponential functions in terms of z! and z! as (Ikeda et al., 24a,b) n o,! ¼ c,! a,! z! þ b! a 2,! ð z! Þ, ðþ where c,!, a,!, b!, and a 2,! are the material constants. These constants were determined by trial and error and are listed in Table 2. The approximation curves are shown in Figure 3 and they are seen to agree well with the estimated RRE data represented by the symbols. It is noted that this process is not a simulation but a kind of evaluation of material constants. RRE Ψ (MJ/m 3 ) Exp. C to T Exp. T to C Approx. C to T Approx. T to C Volume fraction Z C T, Z T C Figure 3. Required reorientation energies for C to T and T to C reorientations estimated from Liu et al. s data (998) (symbols) and approximation curves. Table 2. Material constants for RREs (unit of ) c,a!b is MJ/m 3 ). ) c,c!t a,c!t b C!T a 2,C!T ) c,t!c a,t!c b T!C a 2,T!C ) c,n!t a,n!t b N!T a 2,N!T c,n!c a,n!c b N!C a 2,N!C The material constants for RRE for N to T and for N to C reorientations were also determined from the data of the first loop in the cyclic test, and are also listed in Table 2. Here, the reorientation model is applied for both the tension and compression, although it was observed in Liu et al. s experiment (998) that the reorientation is dominant for tension but the plastic deformation is dominant for compression. This is because generally stress strain behavior due to reorientation is similar to that of due to plasticity as long as the phase transformation does not occur, and that the phase transformation did not appear in Liu et al. s experiment. The specific heat capacity at constant stress per unit volume, the convection heat transfer coefficient, and the thermal expansion coefficient were assumed as C ¼ 3: 6 J=ðm 3 KÞ, h ¼ 5 W=ðm 2 KÞ, and T ¼ : 5 K. Predicted stress strain curves for monotonic tension and monotonic compression are shown in Figure 4. In this simulation, the strain rate was.6 2 s. Asymmetry of the stress strain curves for tension and compression can be captured by using different material constants between tension and compression. It is noted that N to T and N to C reorientations only take place for monotonic tension and monotonic compression, respectively. Curves in Figure 2 shows predicted stress strain hysteresis loops for tension compression cycles with + [Ver: A3B2 8.7r/W] [ :29am] [ 8] [Page No. 4] REVISED PROOFS {SAGE_REV}Jim/sofa papers-may/jim d (JIM) Paper: JIM Keyword

5 Shape Memory Alloys for Asymmetric Quasiplastic Behavior 5 2 Stress (MPa) Tension Compression Variant border volume fraction N T T C C C C C 2 T 2 3 Strain (%) Figure 4. Predicted stress strain curves for monotonic tension and monotonic compression. 2 3 Time (s) 4 5 Figure 5. Variation of variant border volume fractions during the tension compression cycles. amplitudes of, 2, and 4% strain at a strain rate of.6 2 s. In this figure, those for the first five cycles are shown for each strain amplitude. To compare the prediction with the experiment, the data traced from Liu et al. s paper (998) are plotted with symbols. In their experiment, the stress strain loops changed much during the first several cycles. In particular, the first and the second cycles have significant difference. Hence, for 4% strain amplitude cycles, the first, the second, and the steady loops are shown with open and closed down triangles and up triangles, respectively. For and 2% strain amplitude cycles, only the steady loops are shown with squares and circles, respectively. Being similar to the monotonic tension and compression, the loop shapes are asymmetric for tension and compression. The predicted curve for the first 4% strain in the 4% strain amplitude cycle is the same as that of the monotonic tension in Figure 4. Since the RREs for C to T and T to C reorientations were estimated from the steady 4% strain amplitude loop, the predicted steady 4% strain amplitude loops are in quite good agreement with the experiment. The proposed model can also capture the difference between the first loop and the loops in and after the second cycle. This difference of the loop shapes is explained by using variation of predicted variant border volume fractions shown in Figure 5, where the thick full, thick broken, full, and broken curves represent N to C reorientation border, N to T border, T to C border, and C to T border. During the first tensile loading process, N to T reorientation takes place. At 4% strain (2.5 s), the volume fractions of variants N, T, and C are approximately.3,.7, and, respectively. During the unloading process ( s), only thermoelastic deformation takes place and no reorientation occurs. The subsequent compression process makes variant T reorient to C first, and then N to C reorientation starts taking place at approximately 2.8% strain (6.8 s) because the RRE for N to C reorientation becomes smaller than the driving energy. As its results, a stress slope becomes smaller in the strain range between 2.8% and 3.5% of the first cycle. At 4% strain (7.5 s), the volume fractions of variants N, T, and C are approximately.2,, and.98, respectively. After this state, only C to T or T to C reorientation takes place; except that, N to C reorientation takes place between 3.8 and 4.% strain in the second compression process ( s). Accordingly, the difference of loop shapes between a cycle and the next cycle after the second cycle is much smaller than that of between the first and the second cycles. The small change of loop shapes observed in the experiment during the several cycles after the second cycle is considered to be caused by so-called training effect, which is not considered in this model, and accordingly cannot be captured. The predicted hysteresis loops for 2 and % strain amplitudes can approximately capture Liu et al. s data (998). The difference may come from the assumptions that the reorientation order is the same for all reorientation directions and that residual stresses due to unconformity at interfaces between grains are not considered. If these assumptions would be relaxed and degrees of freedom for the reorientation order would be increased by using Preisach model (Ortı n, 99; Matsuzaki et al., 22), etc., this behavior could be captured. However, using such a model would make the reorientation rule much more complicated and make it difficult to determine the RRE as a simple function. + [Ver: A3B2 8.7r/W] [ :29am] [ 8] [Page No. 5] REVISED PROOFS {SAGE_REV}Jim/sofa papers-may/jim d (JIM) Paper: JIM Keyword

6 6 T. IKEDA Next, effect of strain rate is investigated. Predicted stress strain hysteresis loops for 4% strain amplitude cycles at a strain rate of.6 2 s and s are shown in Figure 6 with thin full curve and thick broken curve, respectively. It is not easy to distinguish between them. Predicted temperature change during the cycles is shown in Figure 7, where simulations were carried out up to the 5th cycle. The temperature change increases as increasing strain amplitude and strain rate. Moreover, the temperature increases by 5 C for 4% strain amplitude at a strain rate of s. From these results, it can be seen that the strain rate affects the stress strain relationship little but the temperature change significantly for the reorientation, although it Stress (MPa) (s ).32 (s ) Strain (%) Figure 6. Effect of strain rate on stress strain relationship. Temperature ( C) %,.6 (s ) %,.6 (s ) 4%,.32 (s ) 2 3 Time (s) 4%,.6 (s ) 4 5 Figure 7. Effect of strain amplitude and strain rate on temperature change. would play an important role on both the stress strain relationship and the temperature change for the phase transformation. This feature was also observed in Liu and van Humbeeck s experiment (997), where the temperature increased by approximately, 2, 25, and 4 C for, 2, and 4% strain amplitudes at.6 2 s, and for 4% strain amplitude at s, respectively. The NiTi bar used in this measurement underwent a little different annealing treatment from the bar in the tension compression cyclic test being compared with the present prediction. However, the temperature change for the latter bar is considered comparable with that for the former bar. This shows that the proposed model can also capture the temperature change during the tension compression cycles quite well. CONCLUSION A new constitutive model for describing quasiplastic behavior was proposed by considering three martensitic variants. This model was based on the same concept as our constitutive model for describing pseudoelastic behavior. Here, the thermodynamic driving energy and required reorientation energy pair, the shift skip partial reorientation model, and the required reorientation energy formulated with a sum of two exponential functions were used. Numerical simulation showed asymmetry stress strain loops for tension and compression and significant different stress strain paths between the first and the second loops, which were in quite good agreement with observed data. Moreover, a strain rate had a slight influence on stress strain behavior but a significant influence on temperature change, where the temperature increased by 5 C for 4% strain amplitude at a strain rate of s in the simulation. This strain rate effect on stress strain temperature relationship also agreed with the observed data quite well. Therefore, this constitutive model is considered to be available for explanation of the quasiplastic behavior of SMAs and for designing a structural element including SMAs. However, the temperature increase by 5 C may accompany with the phase transformation. Accordingly, it may be necessary to consider the austenitic phase in this three-martensitic-variant reorientation model to treat the quasiplastic behavior for higher strain rates. APPENDIX: BRIEF REVIEW OF PSEUDOELASTIC MODEL FOR TWO-PHASE TRANSFORMATION The transformation criterion is given by ¼, ða Þ + [Ver: A3B2 8.7r/W] [ :29am] [ 8] [Page No. 6] REVISED PROOFS {SAGE_REV}Jim/sofa papers-may/jim d (JIM) Paper: JIM Keyword

7 Shape Memory Alloys for Asymmetric Quasiplastic Behavior 7 where is the thermodynamical driving energy for phase transformation and given by the following formula: ¼ 2 2 þ " M þ sðt T A$M Þ: ða-2þ E M E A, E M, E A, " M, s, T, and T A$M denote the stress, the Young s moduli for martensitic and austenitic phases, the intrinsic transformation strain of the martensitic phase, the difference in entropy between the two phases, the material temperature, and the temperature at reference state. The reference state is defined as the state where neither stress nor dissipation due to the internal friction is considered. is the required energy for the phase transformation (required transformation energy: RTE). To describe partial transformation cycles, the shift skip model was proposed, where the RTE order of infinitesimal grains is assumed to be the same for forward and reverse transformations. Accordingly, the RTE is given by a function in terms of history of martensitic volume fraction, z, as ðz, _z,z f,i,z r,i ;i ¼,,...,N s Þ 8 f ðz z r,ns Þ for _z > and z r,ns z < z f,ns f ðz z r,k Þ for _z > and z f,k z >< < z f,k, k ¼,2,...,Ns ¼ rðz þð z f,ns ÞÞ for _z < and z r,ns z < z f,ns rðz þð z f,k ÞÞ for _z < and z r,k 2 z >: < z r,k, k ¼ 2,3,...,Ns: ða-3þ: The dot stands for the time derivative. f and r denote the RTE for complete forward and reverse transformations, respectively. Here, the complete transformation is defined as the transformation process where a single phase state is transformed into another single phase state completely. N s is the turn number to be considered. z f,i and z r,i are a pair of memorized volume fractions at the i-th turn for forward and reverse transformations. z f, ¼ and z r, ¼, and when the specimen is loaded until z > z f,k or when the specimen is unloaded until z<z r,k, the memories of z f,i and z r,i with i k are cleared. Here, it is noted that z r,ns does not exist and is not also used when _z<. As is seen from Equation (A-3), the RTE for partial transformation cycles is obtained by shifting the RTE for complete transformation to the turn volume fractions and by skipping energy regions of already transformed grains. Hence, this partial transformation model was named the shift skip model. This assumption is based on Tobushi et al. s experimental result (2). They found through a tensile test of a NiTi SMA wire that the interface between the austenitic phase and the martensitic phase started at the both ends in the gripping parts of the wire and propagated toward the center part both for the martensitic transformation during the loading process and the reverse transformation during the unloading process. The strain is assumed to be approximated by a sum of the elastic, transformation, and thermal strains, and given by where " ¼ E I þ z" M þ T ðt T i Þ, ða-4þ ¼ð zþ þ z, E I E A E M ða-5þ T and T i denote the thermal expansion coefficient and the initial temperature. The heat and energy flow equation for a thin wire is given by C _T þ h 4 ð d T T s Þ ¼ st þ ðz, z f, i, z r, i Þ _z T T _, ða-6þ where C, h, d, and T s denote the specific heat capacity at constant stress per unit volume, the convection heat transfer coefficient, the diameter of a wire specimen, and the surrounding temperature, respectively. AUTHOR BIOGRAPHY Tadashige Ikeda is an associate professor of Nagoya University and specializes in active/passive vibration suppression of smart structures and mechanics of speech production. He received his BS, MS, and PhD from Nagoya University. He became a technical official of Mechanical Engineering Laboratory in 993. Then he became an assistant professor of Nagoya University in 995 and has been an associate professor since 998. He was a visiting researcher at the University of Cambridge in 997 and at Pennsylvania State University in 998. He is a member of the Japan Society for Aeronautical and Space Sciences, the Japan Society of Mechanical Engineers, American Institute of Aeronautics and Astronautics, etc., and received Seguchi Award from the Bioengineering Division of the Japan Society of Mechanical Engineers. REFERENCES Adachi, Y. and Unjoh, S Development of Shape Memory Alloy Damper for Intelligent Bridge Systems, Proc. SPIE Smart Struct. Mater, 367:3 42. Bertram, A Thermo-mechanical Constitutive Equations for the Description of Shape Memory Effects in Alloys, Nuclear Engineering and Design, 74(2): [Ver: A3B2 8.7r/W] [ :29am] [ 8] [Page No. 7] REVISED PROOFS {SAGE_REV}Jim/sofa papers-may/jim d (JIM) Paper: JIM Keyword

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