Method for the explicit insertion of microstructure in Cellular Automata Finite Element (CAFE) models based on an irregular tetrahedral Finite Element mesh: Application in a multi-scale Finite Element Microstructure MEshfree framework (FEMME)

• The novel methodology presented creates the cells for cellular automata (CA) models.
• It proceeds through the subdivision of an irregular tetrahedral finite element (FE) mesh.
• Complex heterogeneous microstructures can be simulated using mathematical descriptions of their features.
• The method is coupled with a FEMME simulation of the strain field in a porous microstructure.

Multiscale models are needed in simulations of mechanical and thermal properties that consider the microstructural heterogeneity of materials, in which a coupling is essential between the numerical models that deal with the different scales. In the class of cellular automata-finite element (CA-FE) or CAFE models, the use of a regular FE mesh restricts the model versatility due to the limited variety of engineering problems that can be simulated with such meshes. A novel methodology is proposed to create the homogeneous cells of the CA model from a mesh that is formed by irregular tetrahedrons. The result is more versatile and capable of modelling complex geometries, improving its applicability. The problem is solved through a subdivision algorithm that creates homogeneous tetrahedral cells, using a methodology to insert microstructures that can be described by particles, pores or fibres. Its use is demonstrated in a multi-scale Finite Element Microstructure MEshfree (FEMME) framework to calculate the elastic strains caused by microstructural features (pores); the method is shown to have a significantly lower computational cost than finite element simulations of equivalent levels of discretization.