Peridynamic modeling of shape memory polymer Timoshenko beam under thermomechanical loading

In this study, Peridynamic (PD) modeling of Shape Memory Polymer (SMP) for two-dimensional (2D) Timoshenko beams is prepared. The constitutive equation of the SMP is adopted and converted to the nonlocal form to produce the PD-SMP governing equations. Three coupled equations for the motion of PD material points in the axial, lateral, and rotational directions are obtained. Stress and strain in the beam are calculated based on the displacement vector captured using PD nonlocal theory. Quasi-static solutions based on the explicit adaptive dynamic relaxation method and implicit method are introduced, and thermomechanical behavior of the beam under uniaxial, transversal, and thermal loading is examined. It is shown that the PD method is able to accurately monitor the thermomechanical response of the SMP Timoshenko beam. The accuracy of the proposed method is verified by comparing the results with analytical and experimental data, demonstrating a good fit between them.