Thermally nonlinear thermoelasticity of a one-dimensional finite domain based on the finite strain concept

This research examines the application of finite strain theory to the generalized coupled thermoelasticity of isotropic 1D structures. The energy equation is derived based on the Lord-Shulman theorem to adapt to the temperature behavior of the structure due to rapid heating. Furthermore, the thermally nonlinear concept is utilized because the variation between the structure temperature and the reference temperature compared to the reference temperature cannot be overlooked. The nonlinear theory of finite strain is employed in the equation of motion, which is ideal for large deformations and rotations in the configuration. The second Piola-Kirchhoff stress and the Green-Lagrangian strains are applied in the formulation. Two nonlinear coupled partial differential equations of energy and dynamic are displayed in nondimensional version for better interpretation. Next, these equations are turned into discrete ordinary differential time-dependent equations through the generalized differential quadrature method. Newmark time marching integration methods and Picard iterative algorithm solve the resulting nonlinear equations. After validating the results with available papers, the effect of various nonlinearities, boundary conditions, and other parameters on the temporal evolution and wave propagation of deformation, temperature, and stress is investigated. It is demonstrated that the effect of nonlinear terms remarkably depends on the material type. The authors also show that utilizing the nonlinear formulation can change the wavefront speed of displacement, temperature, and stress in the domain.