Co-rotational thermo-mechanically coupled multi-field framework and finite element for the large displacement analysis of multi-layered shape memory alloy beam-like structures

Abstract

A thermo-mechanically coupled finite element (FE) for the simulation of multi-layered shape memory alloy (SMA) beams admitting large displacements and rotations (LDRs) is developed to capture the geometrically nonlinear effects which are present in many SMA applications. A generalized multi-field beam theory implementing a SMA constitutive model based on small strain theory, thermo-mechanically coupled governing equations and multi-field kinematic hypotheses combining first order shear deformation assumptions with a sixth order polynomial temperature field through the thickness of the beam section are extended to admit LDRs. The co-rotational formulation is adopted, where the motion of the beam is decomposed to rigid body motion and relative small deformation in the local frame. A new generalized multi-layered SMA FE is formulated. The nonlinear transient spatial discretized equations of motion of the SMA structure are synthesized and solved using the Newton–Raphson method combined with an implicit time integration scheme. Correlations of models incorporating the present beam FE with respective results of models incorporating plane stress SMA FEs, demonstrate excellent agreement of the predicted LDRs response, temperature and phase transformation fields, as well as, significant gains in computational time.

Effect of shape memory alloy actuator geometric non-linearity and thermomechanical coupling on the response of morphing structures

“…Similarly, Faroughi et al (2017) implemented a co-rotational formulation to develop a geometrically non-linear rod element for SMA structures, neglecting the simultaneous solution of the thermal and the mechanical equations. More recently, Solomou et al (2017) presented a multi-field SMA beam FE, which included the geometric non-linear effects into the thermomechanically coupled equations of motion using the co-rotational description of motion.…”

“…The equations are solved for each time increment inside each Newton-Raphson (NR) iteration of the Abaqus global solver in order to determine the values of stress, temperature, and volumetric heat generation associated with the latent heat due to the martensitic transformation, as well as the values of the adopted internal state variables. Furthermore, during the aforementioned process, the derivatives of stress and volumetric heat generation terms are also calculated as they are required for the convergence of the NR process of the global solver (Solomou et al, 2017).…”

“…Due to the LDR that a SMA actuator is foreseen to experience, the aforementioned beam FE has been enhanced by the implementation of the co-rotational description of motion (Solomou et al, 2017). In summary, the polar decomposition theory is considered to split the structure deformation into a rigid body motion and a relative small deformation.…”

“…The solution of the above equations and the determination of the equilibrium thermomechanical state is performed considering the iterative Newton-Raphson method. Detailed description of the beam finite element formulation adopting the co-rotational framework can be found in Solomou et al (2017).…”

Analysis, optimization and testing of morphing structures employing shape memory alloy actuators

“…The work presented in this dissertation focuses on the design of actively morphed structures using shape memory alloy actuators. It constitutes a second phase of research in the field of morphing structures employing shape memory alloy actuators, using the previously developed numerical tools for the prediction of the SMA response (Solomou, MacHairas and Saravanos, 2014;Solomou et al, 2016aSolomou et al, , 2017. A step forward is presented in the current dissertation proposing a systematic design methodology aiming to promote the development of morphing structures addressing challenges associated with the: i.…”