A computational strategy for improving efficiency in finite element analyses with non-linear zero-thickness interface elements

Abstract

Zero-thickness interface elements are widely used in Finite Element modelling of fracture, debonding, and displacement discontinuities in rock masses and heterogeneous materials. Their effectiveness in capturing localized non-linear behaviour has led to extensive use in simulations of quasi-brittle materials, multi-material interfaces and meso-scale descriptions of heterogeneous media. However, their introduction requires the duplication of nodes along potential discontinuity surfaces, resulting in a significant increase in the number of degrees of freedom and computational cost, which severely limits the size of problems that can be addressed, especially in large-scale three-dimensional simulations. This work proposes a novel solution strategy to improve the computational efficiency of Finite Element analyses combining linear continuous elements and non-linear zero-thickness interface elements. The method exploits the natural separation between the elastic response of the continuum and the non-linear behavior localized at the interfaces. A substructuring formulation based on the Schur complement is used to condense, at the beginning of each load increment, the degrees of freedom associated with the linear continuum, leading to a reduced system defined only on the interface degrees of freedom, where the non-linear iterations are performed. The continuum domain is further partitioned into independent blocks separated by interface elements, enabling block-wise condensation. The proposed approach preserves full consistency with the original Finite Element formulation while significantly reducing the size of the system solved during non-linear iterations. Implemented in a Finite Element research code, the method is assessed through two-dimensional benchmark problems with increasing mesh size and number of interface elements. The results show substantial reductions in computational time, particularly for large-scale analyses characterized by extensive interface networks. Although particularly advantageous in such cases, the method remains general and applicable to any Finite Element model in which non-linear behavior is confined to interface elements within an otherwise predominantly linear domain.