Finite Element Method of Functionally Graded Shape Memory Alloy Based on UMAT

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Abstract
Functionally graded shape memory alloy (FG-SMA) is widely used in practical engineering regions due to it possessing the excellent properties of both FG material and SMA material. In this paper, the incremental constitutive equation of SMA was established by using the concept of a shape memory factor. On this basis, the secondary development function of the ABAQUS software 2023 was used to write the user-defined material subroutine (UMAT). The phase transformation and mechanical behavior of transverse and axial FG NiTi SMA cantilever beams under concentrated load at free ends were numerically simulated by discrete modeling. Numerical results show that the stress and shape memory factor were distributed asymmetrically along the thickness direction of the transverse FG-SMA cantilever beam, while the stress and the shape memory factor distributed symmetrically along the thickness direction of the cross section of the axial FG-SMA cantilever beam. The bearing capacity of the axial FG-SMA cantilever beam is stronger than the SMA homogeneous cantilever beam, but weaker than the transverse FG-SMA cantilever beam. The load-bearing capacity of the transverse FG-SMA cantilever beam is twice that of the axial FG-SMA cantilever beam under the same functionally graded parameters and deflection conditions. The discrete modeling method of FG-SMA beams proposed in this paper can simulate the phase transformation and mechanical behavior of an FG-SMA beam well, which provides a reference for the practical application and numerical calculation of FG-SMA structures.

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