Novel ideas for analytical dynamic stress and large deformation analyses of thick hyperelastic cylindrical pressure vessels under sudden magneto-thermo-mechanical loads

The present work investigates analytically the time-dependent distributions of the stresses and large displacements in abruptly pressurized thick-walled magneto-thermo-hyperelastic cylinders exposed to a magnetic field and radial temperature gradients that vary with the instantaneous large thickness variations of the pressure vessel. The governing equations are derived through the definition of an augmented free energy density function that accounts for the mechanical, thermal, and magnetic energies, analytical incorporation of the mechanical incompressibility condition, and employing a Mooney-Rivlin-type hyperelastic constitutive model. Since the resulting highly nonlinear analytical integrodifferential equations that govern the instantaneous configuration of the cylinder contain both the time derivatives and spatial integrals of the instantaneous radii, the resulting coupled nonlinear time-dependent governing equations are solved by utilizing an iterative scheme that engages the second-order Runge-Kutta time-marching and trapezoidal spatial integration (based on nonuniform distribution of the grid points) techniques. The results reveal that when the ends of the soft cylinder are confined, the magnetic actuation leads to through-thickness contraction and Poisson's-ratio-inspired radial expansions and tensile hoop stresses, increases in the structural rigidity, and reductions in the magnitudes and fluctuations of the displacement and stress components. The impact of the magnetic field on the responses diminishes asymptotically for thicker cylinders. Moreover, the temperature gradient leads to releases in both displacements and stresses.