Cohesive surface model for fracture based on a two-scale formulation: computational implementation aspects

Abstract

Keywords: multi-scale cohesive models, computational homogenization, heterogeneous material failure, Embedded Finite Elements (EFEM). AbstractThe paper describes the computational aspects and numerical implementation of a two-scale cohesive surface methodology developed for analyzing fracture in heterogeneous materials with complex microstructures. This approach can be categorized as a semi-concurrent model using the Representative Volume Element (RVE) concept.A variational multi-scale formulation of the methodology has been previously presented by the authors. Subsequently, the formulation has been generalized and improved in two aspects: i) cohesive surfaces have been introduced at both scales of analysis, they are modeled with a strong discontinuity kinematics (new equations describing the insertion of the macro-scale strains, into the micro-scale and the posterior homogenization procedure have been considered); ii) the computational procedure and numerical implementation have been adapted for this formulation. The first point has been presented elsewhere, and it is summarized here. Instead, the main objective of this paper is to address a rather detailed presentation of the second point.Finite element techniques for modeling cohesive surfaces at both scales of analysis (FE 2 approach) are described: i) finite elements with embedded strong discontinuities (EFEM) are used for the macroscale simulation, and ii) continuum-type finite elements with high aspect ratios, mimicking cohesive surfaces, are adopted for simulating the failure mechanisms at the micro-scale.The methodology is validated through numerical simulation of a quasi-brittle concrete fracture problem. The proposed multi-scale model is capable of unveiling the mechanisms that lead from the material degradation phenomenon at the meso-structural level to the activation and propagation of cohesive surfaces at the structural scale.

Multi-scale analysis of the early damage mechanics of ferritized ductile iron

“…Finite element discretization of the RVE consists of 10393 quadrilateral elements with average size of 5 µm and cohesive band thickness of about 0.04 µm. SeeToro et al (2016b) for additional details about the design of micro-cell finite element mesh.…”

Computational Methods for Ductile Fracture Modeling at the Microscale

“…It must be pointed out that Massart et al (2007) did not propose applications to ductile materials or 3D examples, and neither did most studies on this topic (Loehnert and Belytschko (2007); Toro et al (2016)). Belytschko et al (2008) proposed an application to a ductile material where particle debonding and matrix micro-cracking were modeled in fine scale 2D RVE problems and related to a coarse scale 2D crack propagating in a zig-zag pattern due to the microstructure's influence.…”

A computational homogenization framework with enhanced localization criterion for macroscopic cohesive failure in heterogeneous materials

“…The subsequent additional boundary conditions (BC) applied over the localized domain for those RVEs lead to the objectivity of the formulation. This work has been further extended by Toro et al (2016a) and Toro et al (2016b) to cases where microscopic failure mode is a set of cohesive cracks forming a dominant failure path. By establishing a direct scale transition relation between the macroscopic and equivalent microscopic displacement jump terms, Coenen et al (2012a) and Bosco et al (2015) proposed a framework in which the macroscopic traction is included in the macroscopic problem as Lagrange multipliers.…”