A Simple Heuristic Algorithm to Determine the Set of Closed Surfaces of the Cubic Tensor Polynomial

摘要

A simple heuristic algorithm, which determines the set of closed surfaces of the cubic tensor polynomial, is proposed. The algorithm is based on the requirement of positive Gaussian curvature (Stoker’s Theorem) for closed surfaces, excluding domains of tensor values, which do not provide closed surface solutions, and focus the search in the remaining domains. The identification of the closed surfaces is an important factor in both theory and applications, such as the failure behavior of anisotropic bodies. An example of applying successfully the algorithm to a material, which has a distinct anisotropic behavior, is presented.