Hisashi Naito

Constitutive model of shape memory alloys for unidirectional loading considering inner hysteresis loops

A specimen-based macroscopic constitutive model of shape memory alloys for unidirectional loading, which is simple yet accurate and has a physical background, was derived from a grain-based microscopic model. To consider the inner hysteresis loops of a stress?strain?temperature relationship, a new inner loop model called the shift and skip model was proposed. This model is based on microscopic aspects and includes the memory effect of deformation history. Stress?strain relationships were simulated for some representative strain cycles. Numerical results showed that the proposed simple model could capture corresponding experimental results accurately enough to be applied for smart structural design. Comparison with major specimen-based macroscopic models was also discussed, under a unifying approach based on the driving energy and required transformation energy pair.

Thermo-mechanical behavior associated with pseudoelastic transformation of shape memory alloys

We have performed a simulation analysis of the pseudoelastic behavior of a NiTi shape memory alloy wire placed in air, subjected to tensile cyclic loads over a range of low strain rates. Thermomechanical interactions, such as energy dissipation, latent heat and heat transfer, are accounted for in a one-dimensional thermomechanical model based on the phase interaction energy function which was introduced in our previous analyses. The interaction energy function was numerically determined so as to make an analytical constitutive relationship fit available experimental stress-strain curves. Numerical results show that the loading strain rate is influential on changes in the stress-strain characteristics and the temperature of the wire. Good agreement between experiment and analysis was obtained, and the effectiveness of the thermomechanical model proposed here has been confirmed.

Geometric measures of finite carbon nanotube molecules: a proposal for length index and filling indexes

Abstract The structural chemistry of carbon nanotube molecules has been of increasing interest, as molecular entities with fundamental structures of finite nanotube molecules have emerged. For the new field to be developed further, appropriate structural descriptors are necessary as the basis for discussion. In this paper, we propose new geometric descriptors for finite nanotube molecules. Based on popular existing descriptors, these new descriptors provide geometric measures for length and bond- and atom-filling in tubular molecular structures.

Analytical Study on Training Effect of Pseudoelastic Transformation of Shape Memory Alloys in Cyclic Loading

With increasing number of loading cycles, stress-strain hysteresis loops of pseudoelasticity of a shape memory alloy vary continuously in experiments. To account for such characteristic variance observed during phase transformations, the effect of residual martensite is taken into account in a thermomechanical model based on the phase interaction energy function which we proposed in our previous studies. A functional form of volume fraction of the residual martensite which monotonically increases with increasing loading cycle has been determined using experimental stress-strain loops. It is shown that a simple function of the volume fraction of the residual martensite may model complicated behavior of the transformations in the cyclic loading.

Inner loops of pseudoelastic hysteresis of shape memory alloys: Preisach approach

Shape memory alloys (SMA) show very complicated thermomechanical behavior due to phase transformations and rearrangements, including large bounding hysteretic stress-strain loops as well as their inner loops. In our previous analyses, incorporating the phase interaction energy function (PIEF) as a dissipation potential with the free energy of the alloy, we proposed a macroscopic model of SMA for the pseudoelasticity and shape memory effect. Analytical bounding loops derived could accurately model experimental results of a wire subjected to cyclic loads up to 1Hz, including the temperature change. In the present paper, to further extend the concept of the PIEF, we propose a microscopic approach by taking into account the pseudoelastic hysteresis in single crystal grains of polycrystalline SMA. In each grain, we assume that the hysteretic behavior is represented by the Preisach model. Again, incorporating the PIEF with the free energy of the grain, and summing up over the whole material, we have derived the stress-strain relationship in which the Cauchy distribution function is used for the probability of the martensitic and the reverse transformation. We will show that the analytical stress-strain model which has been determined using experimental data of a bounding loop can well describe its inner loops.

Macroscopic and microscopic constitutive models of shape memory alloys based on phase interaction energy function: A review

This paper presents a summary of a series of our macroscopic and microscopic constitutive models for pseudoelasticity and shape memory effect of a shape memory alloy wire or strip based on a general function of the dissipation potential, called phase interaction energy function. Our model may well predict in a unified way complex stress–strain relationships among austenitic, martensitic and rhombohedral phases, including inner hysteresis loops appearing in a bounding loop, effect of loading cycles accompanying rapid change in temperature of the alloy due to dynamic loadings, etc. Some comment on existing constitutive models is given for comparison. A future research direction of shape memory alloys will briefly be addressed.

ON A LOCAL HOLDER CONTINUITY FOR A MINIMIZER OF THE EXPONENTIAL ENERGY FUNCTIONAL

(0.1) E(u):= fedx for u : Ω —• R, where n > 2. For minima of certain functionals with suitable growth conditions, many authors have established regularity results [1,5,7,12]. For example, in [7], Hardt and Lin proved that mappings minimizing the L -norm of the gradient between compact Riemannian manifolds are smooth except singular sets with finite (dim M — [p] — 1)-dimensional Hausdorff measure. If a functional has sufficiently rapid growth, we can expect full regularity of minima. In fact, quite recently, Due and Eells [2], Eells and Lemaire [3] show that, in the case of n = 1, a minimizer u of E satisfies u ^ C°° (Ω) for any smooth boundary data provided that Ω c R is a strictly convex bounded domain. In this paper, we consider a local regularity of minima of E for the case of n > 2. Our main theorem is stated as follows:

A unified constitutive model of phase transformations and rearrangements of shape memory alloy wires subjected to quasistatic load

In our previous studies, we proposed a lumped-parameter quasistatic model for martensitic transformations of shape memory alloys, by introducing a general function of the dissipation potential for the irreversible process, called the phase interaction energy function. It has been proved that a thermodynamic analysis coupled with the quasistatic model may predict well pseudoelastic behaviors of shape memory alloy wires subjected to cyclic loadings up to 1 Hz. In the present analysis, therefore, using the phase interaction energy function, we propose a unified quasistatic thermomechanical model for phase rearrangements and transformations associated with austenitic, martensitic and rhombohedral phases. A numerical analysis is carried out to compare with available quasistatic experimental results on the shape memory effect and pseudoelasticity associated with the three crystal phases and to confirm the effectiveness of the unified approach based on the phase interaction energy function.

Global solution for the Yang-Mills gradient flow on

In this paper, we will study a global weak solution for the Yang-Mills gradient flow on a closed (i.e., compact without boundary) 4-manifold. Let us explain some notion briefly to be able to state our results. Let M be a closed 4-manifold, G a compact Lie group embedded as a subgroup of 5O(/), or SU(l) and P be a principal G-bundle over M. We now assume the universal covering G of G is compact. Denote by g the Lie algebra of G and denote also by gP and ®P the adjoint and automorphism bundles of P, respectively. Using the metric on G induced by the Killing form, we fix a metric on P compatible with the action of G. Let Ω (gP) be the space of smooth g-valued Λ-forms, i.e., β*(gP) = C°°(M; gP ® Λ*Γ*itf). Here, for the space β*(gP) of gP-valued /c-forms, we can define Sobolev spaces W > L with norms || \\wm.p, || \\p in usual way. Connections on P are explained by taking an open covering {Ua} on M; we trivialize P on Ua via a trivialization: P\u = Ua X G. A connection D on P is, by definition, given by D = d + Aa on Ua, where Aa is a g-valued 1-form on Ua. Moreover, for a set of transition functions {gaβ} of P associated with the trivialization for {f/α}, where gaβ: Ua Π Uβ—+G,D satisfies

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We performed an experiment of pseudoelastic ity of a NiTi shape memory alloy wire for measuring stress-strain-temperature relations at loading frequency of from 0.001 to 1.0 Hz and determined numerically the phase interaction energy function proposed in our previous studies on a onedimensional thermodynamic model of shape memory alloys. Then, using the phase interaction energy function determined, we carried out a simulation analysis of pseudoelastic transformation of the wire, in which thermomechanical interactions such as latent heat, energy dissipation and heat transfer are accounted for. Numerical results show that the loading frequency is influential to the change in the stress-strain-temperature of the wire. A good agreement between the experiment and numerical results is obtained, and the effectiveness of our thermodynamic model of pseudoelastic ity proposed in the previous studies has been confirmed.