Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free Galerkin method

Recovery stresses in SMA wires for civil engineering applications: experimental analysis and thermomechanical modelling

“…In 2000, a shape memory alloy thermomechanical constitutive model using mapping algorithms was presented by Qidwai and Lagoudas [21]. The element-free Galerkin method was used for the modelling and simulation of SMA two years later [22]. Thereinafter, a general inelastic framework for the derivation of general three-dimensional thermomechanical constitutive laws for materials undergoing phase transformations was proposed [23].…”

Application of the higher‐order Cauchy–Born rule in mesh‐free continuum and multiscale simulation of carbon nanotubes

“…The integrals in (42) and (43) can be evaluated in virtue of the background cells [27][28][29]. In this work, we use the background cells that coincide with the nodal arrangements [28,29], and the Gaussian quadrature is used in each cell.…”

“…The integrals in (42) and (43) can be evaluated in virtue of the background cells [27][28][29]. In this work, we use the background cells that coincide with the nodal arrangements [28,29], and the Gaussian quadrature is used in each cell. At each iteration step, we need to calculate the first-and second-order deformation gradients using (38)-(41) for each quadrature point and then to use the minimizing method in Section 3.1 to determine the stresses and tangent modulus.…”

“…However, atomistic simulation consumes a tremendous amount of computational time and resources and is restricted to the the interpolation functions. Recently, Tang et al [26] applied the mesh-free method [27][28][29][30] to simulate materials with strain-gradients effects. A distinct advantage of this approach is that the mesh-free approximations possess non-local properties and satisfy the higher-order continuity requirement [27].…”

Dynamic analysis of laminated composite plates with piezoelectric sensor/actuator patches using the FSDT mesh-free method

“…Lancaster and Salkauskas [4] introduced the MLS interpolants to replace the smooth particle-hydrodynamics (SPH) interpolant to deÿne a new particle volume, which ensures thermodynamic compatibility. The mesh-free methods were also employed for modeling of human proximal femur [5], elasto-plasticity [6], structural dynamics [7][8][9], shape memory alloys [10] and large deformation [11] problems. All these meshless methods were reported and veriÿed to provide convincing results.…”