Identification of the Failure Load of a Hyperelastic Body Considering the Location of the Failure

In recent years, the definition and analysis of inverse hyperelastic problems due to the wide use of these materials in various industries and also in manufacturing of artificial tissues of the body, has received more attention than before. In mechanical analysis of hyperelastic materials, both material behavior and material deformation are considered nonlinear. In this article, an inverse problem related to the failure of hyperelastic bodies is defined and two different methods are proposed to solve it. The inverse analysis of hyperelastic bodies that have failed, can be useful to prevent the recurrence of failure in these materials. In the inverse problem, it is assumed that a two-dimensional hyperelastic solid is failed and the place of its failure is known. The distribution of the load (boundary conditions) in a part of the boundary is considered unknown and is calculated by solving the inverse problem. By defining an appropriate objective function, the defined inverse problem is converted to an unconstrained optimization problem. To solve the optimization problem, a zero-order method based on the equal interval search method and a first-order method based on the steepest descent method are used. To make the problem more practical, the inverse problem input data, which are the location of failure and the critical equivalent strain, are used with some error. Finally, considering the location of the failure and the critical equivalent strain, the load causing failure is identified. It can be seen that the performance of the first-order method is better than the zero-order method.