FEMME: A multi-scale Finite Element Microstructure MEshfree fracture model for quasi-brittle materials with complex microstructures

Abstract

Please cite this article as: Mora, L.S., James Marrow, T., FEMME: A multi-scale Finite Element Microstructure MEshfree fracture model for quasi-brittle materials with complex microstructures, Engineering Fracture Mechanics (2015), doi: http://dx. AbstractIn this paper we develop a very efficient Finite Element Microstructure MEshfree (FEMME) method to account for the effect of microstructure on quasi-brittle properties within finite element simulations of damage, improving the accuracy and computational cost of calculations at engineering length-scales. This method provides two sets or layers of elements representing the finite element model and the microstructure. The first is used to link the engineering scale problem with the microstructure, obtaining the stress and strain fields of the macro-mechanical problem; from these, we compute the micromechanical fields using the second set of elements, which describes explicitly the microstructure.

Observation and simulation of indentation damage in a SiC–SiCfibre ceramic matrix composite

“…This method is described in detail in reference [22,35,36], and a brief summary is provided here only. The Meshfree framework has been developed to simulate fracture development, using the CA to calculate the damage in the microstructure.…”

“…Once the displacements of the microstructural features are calculated with the MAM layer by solving equation 1, the displacements are mapped to the cells of the CA model. This is done with the exponential shape functions of the IPD or PD that interpolate the domain [22]. With the displacements of the cells, the strains are computed and evaluated against the critical strain of the material phase that it represents.…”

“…In this paper we apply the novel FEMME model [22,35,36] in a case study for microstructure-sensitive damage development in a quasi-brittle material: Hertzian indentation in a SiC-SiC fibre composite. FEMME is a multi-scale Finite Element Microstructure MEshfree fracture model for materials with complex microstructures.…”

“…To address this, various multiscale modelling approaches such as Homogenization, Monte Carlo, Cellular Automata and Molecular dynamics [e.g. 20,21,22] have been proposed as methods to reproduce microstructure within a larger continuous element or Representative Volume Element (RVE); this introduces microstructure into a continuous FEM model. Nonetheless, there remain challenges due to high computational cost and mathematical complexity that hinder the application of these methods for different loading conditions in complex geometries, or more detailed 3D representation of the microstructure.…”

Integrated experiment and modelling of microstructurally-sensitive crack growth

“…More recent methods include mesh-free approaches [15,16] where Barbieri et al [15] introduced new weight-functions for node enrichment and Nguyen et al [17] demonstrated the potential of phase field methods to simulate crack nucleation and propagation.…”