Nonlinear analysis based on homogeneous incremental systems Original Research Article

The performance of path-following techniques depends on so-called constraint equations, which are used in the augmented incremental systems. It is common practice in the literature, that these equations are explicitly defined following the arbitrary geometrical or physical ideas. In the present paper, their role is discussed in order to establish a reliable method of augmentation. It is shown that the explicitly defined constraint equation is not necessary. The implicit formulation is proposed, which is based on the rank analysis performed on the rectangular matrix of the homogeneous incremental system. The proposed method allows to solve problems, where the well-known continuation schemes fail. The theoretical considerations are illustrated by the numerical examples.