THE LIMITATIONS OF LINAER THEORY AND IMPROVED QUADRATIC THEORY FOR SUPERPOSING ADDITIONAL DEFORMATION UPON THE CONFIGURATION WITH INITIAL STRESSES

The linear theory of superposing additional deformation upon the configuration with initial stresses must satisfy two preconditions-the infinitesimal of the additional deformation and the hyperelasticity of the material. This paper attempts to eliminate the two preconditions and provides a more general theory. To this end, the paper starts from the continuum mechanics. The controlling equations and boundary conditions are described with the increment Lagragian stresses. The applicability of the linear theory and an improvement of the linear theory—the development of a quadratic theory by use of the order-of-magnitude analysis are examined. An example is given to compare the quadratic theory and the linear theory. Computational results of the example clearly show that the quadratic theory is applicable under few limits and can lead to a more rational solution.