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This paper proposes a general method for ab-initio modelling and representation of heterogeneous objects that are associated with complex material variation over complex geometry.  Heterogeneous objects like composites and naturally occurring objects (bones, rocks and meteorites) possess multiple and often conflicting properties (like high hardness and toughness simultaneously), which are associated with random and irregular material distribution. Modelling such objects is desired for numerical analysis and additive manufacturing to develop bio-implants, high-performance tools etc. However, it is difficult to define and map the arbitrary material distribution within the object as the material distribution can be independent of the shape parameters or form features used to construct its solid model.  This paper represents the source of random and irregular material distribution by mixed-dimensional entities with a focus on modelling compositional heterogeneity. The domain of effect of each material reference entity is defined automatically by using Medial Axis Transform (MAT), where the material distribution can be intuitively prescribed, starting from the material reference entity and terminating at the medial axis segment bounding the corresponding domain. Within such a domain, the spatial variation of the material is captured by a distance field from the material reference entity, which can be controlled locally and independently. These domains are stored using the neighbourhood relation for efficient operations like altering material distribution across the material reference entity and material evaluation for a given geometric location. Results from an implementation for 2.5D objects are shown and the extension to 3D objects is discussed.

Modelling multiply connected heterogeneous objects using mixed-dimensional material reference features