Additive manufacturing (AM) has enabled control over heterogeneous materials and structures in ways that were not previously possible, including functionally graded materials and structures. This paper presents a novel method for representing and communicating heterogeneous materials and structures that include tolerancing of geometry and material together. The aim of this paper is to propose a means to specify nominal materials, nominal structures and allowable material variations in parts, including (a) explicit material and structural transitions (implying abrupt changes) and (b) functional transitions to support single and multiple material and structural behaviors (implying designed function-based gradients). The transition region combines bounded regions (volumes and surfaces) and material distribution and structural variation equations. Tolerancing is defined at two levels, that of the geometry including bounded regions and that of the materials. Material tolerances are defined as allowable material variations from nominal material fractions within a unit volume at a given location computed using material distribution equations. The method is described thorough several case studies of abrupt transitions, lattice-based transitions, and multimaterial and structural transitions.

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