Hybrid equilibrium element with interelement interface for the analysis of delamination and crack propagation problems

Abstract

This article proposes a formulation for the analysis of delamination and fracture propagation problems at the interelement interface, with perfect adhesion at the pre-failure condition and with linear softening at the post-failure regime. The proposed formulation is based on the hybrid equilibrium element (HEE) model, with stress fields which strongly verify the homogeneous equilibrium equations and interelement equilibrium equations. The HEE can easily model high-order stress fields and can implicitly model the initially rigid behavior of an extrinsic interface at the element sides. The interface model is defined as a function of the same degrees of freedom of the HEE (generalized stresses) and the preand post-failure behavior of the interface can be modeled without any additional degree of freedom. The proposed formulation is developed for a nine-node triangular HEE with quadratic stress fields. This article also proposes an extrinsic cohesive model, rigorously developed in the damage mechanics framework.

Hybrid equilibrium element with high‐order stress fields for accurate elastic dynamic analysis

“…The two‐dimensional static equilibrium formulation considered in the present article follows the same reasoning path as proposed in References 10,18. The two‐dimensional domain is discretized by a set of nonoverlapping triangular subdomains , with .…”

“…The typical drawback of the HEE is the possible occurrence of spurious kinematic modes, which must be controlled or restrained by means of one of the different available strategies. [18][19][20][21] The finite element formulation of the elastic-dynamic problem in the framework of stress-based approaches, such as the hybrid equilibrium element method, 10,18 was addressed a few decades ago in References 22,23 and it currently remains a topic of great interest, as evidenced by recent articles. [24][25][26][27][28][29] In Reference 25 three alternative hybrid finite element formulations (hybrid-mixed, hybrid, and hybrid-Treftz) are presented and compared for solution of linear elastodynamic problems in the frequency domain, and these formulations are developed both in the displacement-based (DB) form and in the stress-based one.…”

“…The great accuracy of the stress fields in HEE provides a powerful numerical tool for modeling of the interelement fracture propagation, as proposed by the author in Reference 10, where an extrinsic (initially rigid) cohesive interface is embedded at any element side without any remeshing and without additional degrees of freedom. In this case the analysis is limited to elastic static problems and its application to dynamic analysis of fracture and fragmentation phenomena would be of great interest.…”

Inter-Element Crack Propagation with High-Order Stress Equilibrium Element

“…( 6) can be derived by the stationarity condition of the complementary energy functional of the partially cracked solid, as proposed in Ref. 17 . In the proposed formulation the interface can be embedded at one or more sides of an hybrid equilibrium element without any additional degrees of freedom, simply considering the additional interface compliance matrix C Γ e defined in Eq.…”

“…The numerical modelling of nonlinear behaviours in brittle materials can be approached in the framework of continuum damage mechanics, by using suitable regularization techniques to avoid pathological mesh dependency, or by adopting discrete crack models, such as the zero-thickness interface element, strong or embedded discontinuity (EFEM) approaches 1,2,3,4 and the eXtended-generalized FEM (XFEM, GFEM) 5,6,7,8 . Discrete crack models are often combined with Cohesive Zone Models (CZMs) 9,10,11,12,13,14,15,16,17,18,19,20 , which describe the Traction Separation Law (TSL) at the discontinuity surface.…”