This study proposes a novel triangular added damping and stiffness (TADAS) damper that uses the shape memory effect (SME) of iron-based shape memory alloy (Fe-SMA) to provide a self-centering system to recover the initial shape of a structure after significant inelastic deformation induced by nonlinear response of fused elements, without the need for difficult and expensive replacement procedures of conventional TADAS systems. Unlike most studies which consider simplified uniaxial behavior of Fe-SMAs, the present non-linear finite element simulations cover the full 3D material non-linearity of Fe-SMA component based on the SMA constitutive law to capture both flexural and shear behavior in various coupled thermomechanical loadings, including the mechanical loading/unloading, the heating, and the final cooling (as the recovering process). Simulations performed on a one-bay steel frame for different drift ratios reveal that although the dissipation energy of the new device is at most 10% less than the ordinary one, it enjoys the self-centering property to recover the initial shape of the frame before loading, showing that the proposed damper is an effective alternative to ordinary TADAS yielding dampers to achieve the self-centering characteristics.