A Simplified Multivariant SMA Model Based on Invariant Plane ...

We propose that a major obstacle in many of these models has been an overly large
estimation of interaction energy provided by the micromechanics methods.
In next section a summary of the original <strong>Multivariant</strong> model is given, then difficulties
for the <strong>Multivariant</strong> model are reviewed. The simplified <strong>Multivariant</strong> model is then
derived, motivated by reasonable interaction energies based on experimental observations
and implementations in previous micromechanical models. Finally, results predicted by
both the original and revised <strong>Multivariant</strong> models are compared to experimental results.
2. SUMMARY OF THE ORIGINAL MULTIVARIANT MODEL
In this section, the previously developed <strong>Multivariant</strong> <strong>Model</strong> will be briefly summarized
for both the single crystal and polycrystal forms. Although this introduction is intended to
be short, some details are still given so that readers can understand the basis of the
simplified model development. The readers are also referred to previous work on the
<strong>Multivariant</strong> <strong>Model</strong> (Gao et al., 2000; Huang et al., 2000; Huang and Brinson, 1998).
2.1. Single Crystal <strong>Model</strong> <strong>Based</strong> on Micromechanics
The <strong>Multivariant</strong> model begins with the complementary free energy of the material
n
ΨΣ ( , T, f ) = − [ ∆G + W + W − Σ E ]
(1)
ij
ch mech sur ij ij
the rate of change of which is set equal to the rate of change of the dissipation energy
dΨ | Σ ij ,T = dW d ≥ 0 (2)
For the chemical free energy, ∆G ch , a standard expression is used, linearly proportional
to temperature change; the surface energy, W sur , is small in comparison to other terms and
is neglected. The mechanical energy, W mech , is approximated by a micromechanics
technique in which the formation of martensitic variants in a shape memory alloy under
loading is viewed as a superposition of the external loading acting on a homogeneous
material and a set of transforming inclusions (see figure 1). In the simplified model, this
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