Because of their complex microstructure, the continuum approach can be too simple for these materials, and needs a finer discretization to obtain satisfactory results. Quasi-brittle fracture is an emergent characteristic, and this cannot be treated satisfactorily with the numerical methods based on macromechanics. With this method, we can study the development of discontinuous cracking and fracture, and its sensitivity to microstructure. A mesh-free framework has been developed to compute the fracture development through the microstructure, using cellular automata to calculate the damage to the microstructure. The influence of the initial finite element mesh is erased during the development of the microstructure. Graded microstructures, textures and particle anisotropy can be readily simulated in microstructures with multiple phases. By this topological approach we obtain sets of cells with variable properties to model the microstructure (rules are enforced during the selection of the seeds to avoid overlap between particles). The heterogeneous microstructure is created from key cells, called seeds, from which particle-like regions may be grown with defined characteristics. Here the microstructure is modeled explicitly by subdividing a finite element into small elements called cells. A selected 2D triangular CA is applied on an imported triangulated 3D model.In this paper we use the Cellular Automata integrated with Finite Element method (CAFE) to account for the effect of microstructure on quasi-brittle properties within a finite element simulation. An implementation is performed on a regular triangular grid, irregular triangular grid and an imported triangulated 3D mesh which is irregular and has holes. A brief study covers the entities of neighborhood, type of rules (semi-totalistic and general), rule encoding and search for rules that meet given criteria. Two-dimensional (2D) CA in the triangular tessellation is discussed and implemented. The concept of an ‘organic’ pattern in the context of CA is also brieﬂ y discussed. The concept of CA on a triangular tessellation is discussed followed by discussion about the entities of irregularity of a grid, called ‘holes’ and ‘edges’. Therefore, it is possible to control to some degree the state of the whole surface taking advantage of the emergent behavior of the CA. As with a CA, every element of a triangulated surface can be individually assigned with characteristics such as color or transparency level, which is analogous to a CA ‘state’. With the exception of boundary conditions, applicable to the elements positioned at the edge of the surface or around holes, every triangle in the grid has exactly three neighboring triangles. This means that it can become a grid of topologically identical elements.

Such an intelligent ‘skin of a building’ can have any shape and a certain ‘organic’ appearance which can be dynamically controlled in response to the changes of the external conditions or users’ requirements. Cellular automata (CA) can be applied in controlling the state of a free-form building envelope. This paper presents the application of semi-totalistic, also called outer totalistic cellular automata on any three-dimensional (3D) surface.

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3d cellular automaton