Hygrothermal Creep and Stress Redistribution Analysis of Temperature and Moisture Dependent Magneto-Electro-Elastic Hollow Sphere

In this article, the time-dependent stress redistribution analysis of magneto-electro-elastic (MEE) thick-walled sphere subjected to mechanical, electrical, magnetic and uniform temperature gradient as well as moisture concentration gradient is presented. Combining constitutive equations of MEE with stress-strain relations as well as strain-displacement relations results in obtaining a differential equation in which there are the creep strains. At the first step, discounting creep strains in the mentioned equation, an analytical solution for the hygro-thermo-magneto-electro-elastic behavior is achieved at the initial state. After that, the creep stress rates can be achieved by keeping only the creep strains in the differential equation for the steady-state condition. The analysis is done by applying the Prandtl-Reuss equations as well as Norton’s law in creep behavior modeling. Finally, the history of stresses, displacement as well as magnetic and potential field, at any time, is achieved using an iterative method. Results show that the increase in tensile hoop stress resulted from creep progress must be considered in design progress. Also, the effect of hygrothermal loading is more extensive after creep evolution.