Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method. (English) Zbl 1113.74432

Ren, J.; Liew, K. M.; Meguid, S. A.

Int. J. Mech. Sci. 44, No. 12, 2393-2413 (2002).

Summary: This paper is concerned with the application of the element-free Galerkin method to simulate the superelastic behaviour of shape memory alloys (SMA). The meshfree shape functions are derived from a moving least-squares interpolation scheme. A thermomechanical SMA constitutive law is used to describe the superelastic effect. The incremental displacement-based formulation for large deformation is developed by employing the meshfree shape functions and the continuum tangent stiffness tensor in the weak form of the equilibrium equations. By eliminating the unknown constrained nodal variables from the discrete equations, an effective approach is developed for the imposition of the essential boundary conditions. The numerical tests show that the proposed meshfree scheme can successfully reproduce the superelastic behaviour of shape memory alloys.

MSC:

74S30	Other numerical methods in solid mechanics (MSC2010)
74N99	Phase transformations in solids
74C15	Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)

Keywords:

Superelasticity; Large deformation; Shape memory alloy; Return mapping; algorithm; Numerical simulation; Meshfree