Peak Load Determination in Linear Fictitious Crack Model

Abstract

The linear fictitious crack model with linear softening law is a very important special case of the general fictitious crack model proposed by Hillerborg. When the traction‐separation softening curve is assumed linear, the peak load can be determined through the proposed linear eigenvalue problem formalism, referred to as the boundary eigenvalue problem. A detailed description is given of the finite element implementation of the proposed algorithm. It is shown that the first eigenvector can be used to calculate the peak load of the linear fictitious crack model. Furthermore, the first eigenvalue can be related to the critical nondimensional specimen size. Finally, it is elucidated that in the linear fictitious crack model, the peak‐load solutions can be presented in a nondimensional fashion with proper consideration of material properties and specimen sizes. The nondimensional peak‐load solution graphs can be used effectively for quantifying the size effect in the linear fictitious crack model.