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SUMMARYA new computational approach is developed based on the mesh-free method for the numerical simulation of shape memory alloys. A thermomechanical constitutive model is used to describe the complex material response. The incremental displacement-based mesh-free formulation is constructed in a total Lagrangian description by employing the moving least square shape function and rate form of the shape memory alloy constitutive model in the variational equations. This mesh-free formulation is not only applicable to large deformation problems, but also accounts for both stress and thermally induced phase transformation. Moreover, the newly developed mesh-free codes can deal with complex loading paths and multiple temperature cycles in numerical simulation. The performance of the proposed mesh-free scheme for the simulation of shape memory alloys is demonstrated in several numerical examples.

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