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Comparison of methods for calculating phase and structural transformation strains in sma structures on example of a beam bending problem

Tikhomirova K.A.

#### Abstract:

In this article, three methods for calculating the phase and structural transformation strains of shape memory alloy structures are considered and their performance is compared using as an example the problem of cantilever beam deflection. All methods are based on the hypothesis of equivalence of phase and structural transformation strains as regards the further deformation behavior of a material at the macroscopic level. Phase deformation is understood to be the deformation of oriented martensite caused by cooling the austenitic phase under load, and structural deformation is the deformation of oriented martensite caused by the isothermal reorientation of chaotic martensite. The first method involves the construction of three-dimensional constitutive equations of continuous medium mechanics and their implementation by the finite element method. The constitutive equations include two material functions: the direct transformation and martensitic inelasticity diagrams – the dependence of phase and structural transformation strains on the stress responsible for their initiation. The second method is applicable to structures whose deformation is characterized by one kinematic and one force parameter: for example, beam deflection under the action of the applied force. This method uses the structural diagrams of direct transformation and martensitic inelasticity – the dependences of phase and structural components of the kinematic parameter on the force parameter, which allows making calculations in the one-dimensional formulation. The third method can be applied only for calculating the bending of beams and plates. It involves breaking the beam into several layers, each of them experiencing only normal forces, while transverse and shear forces being neglected. The phase and structural transformation strain in each layer is calculated using the constitutive equations of the first method, but in the one-dimensional case. In the context of the beam bending problem, it has been shown that all methods give similar results. The computational efficiency of each method is estimated.

#### Keywords:

BEAM BENDING,

direct transformation diagram,

martensitic inelasticity diagram,

MARTENSITIC TRANSFORMATION,

phase and structural transformation strains,

SHAPE MEMORY ALLOYS,

диаграмма мартенситной неупругости,

диаграмма прямого превращения,

изгиб балки,

мартенситное превращение,

сплавы с памятью формы,

фазово-структурная деформация
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