Strain localization and crack propagation in finite elements augmented with embedded interphases

Abstract

Many engineering problems present the need to model discontinuities that arise when materials are outside their elastic limit. In quasi-brittle materials strains progressively localize in narrow bands, usually leaving elastic the surrounding bulk material. In the framework of FE models, considerable progresses have been done in order to correctly model strain localization and damage propagation; they could be mainly divided into two groups: discrete crack models and smeared crack models. In the ambit of discrete crack models, we propose a computational methodology which is based on the Augmented-Finite Element Method (A-FEM) [1]. Our formulation consists in the implementation of an intra-element weak discontinuity, modelled through a zero-thickness interphase model (IPH, [2,3]). A general finite element that has reached its elastic strain limit is split into three elements, two elastic sub-elements with an interposed IPH element simulating the crack, then assembled by condensing internal additional degrees of freedom at the equilibrium level. Bulk material and interphases are governed by the same isotropic damage constitutive model proposed by Jirásek [4]. The crack is inserted on the basis of values of principal strains at the integration points, while its orientation is evaluated on the basis of the spectral analysis of the fracture tensor built at the element level. A crack-tracking algorithm is proposed to follow crack propagation within near elements, grouped into as many clusters as fractures present. Numerical applications are reported, on some relevant cases, in terms of load-displacement curves and fracture patterns. Results evidence their independence on mesh-size and mesh-bias. References [1] Liu, W., Yang, Q.D., Mohammadizadeh, S., Su, X.Y., “An efficient augmented finite element method for arbitrary cracking and crack interactions in solids", Int. J. Num. Meth. Engng., Vol. 99(6), pp. 438-468, 2014. [2] Giambanco, G., Mróz, Z., “The interphase model for the analysis of joints in rock masses and masonry structures”, Meccanica, Vol. 36, pp. 111-130, 2001. [3] Giambanco, G., Fileccia Scimemi, G., Spada, A., “The interphase finite element”, Comput. Mech., Vol. 50(3), pp. 353-366, 2012. [4] Jirásek, M., “Damage and smeared crack models”, in Numerical modelling of concrete cracking, Springer, pp. 1-49, 2011.