We propose a universal approach to the problem of computer modeling of shapes with continuously varying material properties satisfying prescribed material conditions on a finite collection of material features and global constraints. The central notion is a parameterization of space by distances from the material features -- either exactly or approximately. Functions of such distances provide a systematic and intuitive means for modeling of desired material distributions as they arise in design, manufacturing, analysis and optimization of components with varying material properties.

The Core Product Model (CPM) was developed at NIST as a high level abstraction for representing product related information, to support data exchange, in a distributive and a collaborative environment. In this paper, we extend the CPM to components with continuously varying material properties. Such components are becoming increasing important and popular due to progress in design, analysis and manufacturing techniques. The key enabling concept for modeling continuously varying material properties is that of distance fields associated with a set of material features, where values and rates of material properties are specified. Material fields, representing distribution of material properties within a component, are usually expressed as functions of distances to material features, and are controlled with a variety of differential, integral or algebraic constraints. Our formulation is independent of any particular platform or representation, and applies to most proposed techniques for representing continuously varying material properties. The proposed model is described using system independent Unified Modeling Language (UML) and is illustrated through a number of specific examples.