Abstract
It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy (SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements. To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software. This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation. Two scalars, named by phase-transition modulus and equivalent stiffness, are defined to make it easy to establish and implement the finite element method for a SMA structure. An incremental constitutive equation is developed to formulate the relationship of stress, strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness. A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus, stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition. A finite element equation is established to express the incremental relationship of nodal displacement, external force and temperature change in a finite element discrete structure of SMA. The incremental constitutive equation, phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure. Two SMA structures, which undergo large and uneven deformation, are numerically simulated by the supposed finite element method. Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation, and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.
Highlights
Shape memory alloys (SMAs) have been widely used in many various engineering fields [1,2,3,4] because they possess two special thermo-mechanical characters, shape memory effect and super-elasticity [5,6,7,8]
The super-elasticity and shape memory effect of shape memory alloy (SMA) bar and cirque are respectively simulated by the supposed finite element method
1) The concisely incremental constitutive equation describing the relationship of stress, strain and temperature in a SMA material is developed based on phase-transition modulus and equivalent stiffness
Summary
Shape memory alloys (SMAs) have been widely used in many various engineering fields [1,2,3,4] because they possess two special thermo-mechanical characters, shape memory effect and super-elasticity [5,6,7,8]. There are four characteristic temperatures in a SMA at a freestress state. They are named as martensitic starting temperature, indicated by Ms, martensitic finishing temperature, indicated by Mf, austenitic starting temperature, indicated by As and austenitic finishing temperature,. Both shape memory effect and super-elasticity are the macroscopic phenomena of martensitic phase transition and martensitic inverse
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