Method of creating a component via transformation of representative volume elements

A method of forming a component comprising:

• defining a component volume discretized by a target mesh having a plurality of volume elements, wherein each volume element of the plurality of volume elements is defined, at least in part, by a shape function and a plurality of volume nodes, and wherein the shape function is a quartic or higher order shape function;
• defining a parting surface within a representative volume element, wherein an intersection of the parting surface and boundary faces of the representative volume element define boundary edges of the parting surface;
• discretizing the parting surface using a surface mesh that includes a plurality of surface elements defined by a plurality of surface nodes, wherein the plurality of surface nodes includes boundary surface nodes located along one of the boundary edges of the parting surface;
• mapping the surface mesh into each volume element of the plurality of volume elements according to the shape function of each volume element of the plurality of volume elements to produce a component surface structure;
• and
• forming a component based on the component surface structure.