Additive manufacturing (AM) has enabled control over heterogeneous materials in ways that were not previously possible. This paper presents a novel method for representing and communicating heterogeneous materials based structures that include tolerancing of geometry and material together. AM has expanded design possibilities to include specified material heterogeneities, including functionally graded materials. The aim of the paper is to propose a means to specify nominal materials and allowable material variations in parts, including (a) explicit material transitions and (b) functional transitions to support single and multiple material behaviors. The transition region combines bounded regions (volumes and surfaces) and material distribution 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 multi-material transitions.

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