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

In 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 micro-mechanical fields using the second set of elements, which describes explicitly the microstructure.