A New Method for Modeling 3D Constitutive Relation Based on Orientational Components

A new method for modeling 3D constitutive relation based on orientational components was investigated. Improved representations of stress/strain vectors and of Euler angles as orientational parameters were proposed. Some principles which should be complied with by mechanical units were introduced. According to these, four basic units for simulating primary mechanical properties of material at local orientations were introduced. As a new concept, orientational component, used to simulating micro-mechanical properties of materials at local orientation, was presented by superposing basic units. Then a frame composed of orientational components was created, of which the ratio of component at each orientation was quantified by orientation density function. The integral representation for building macroscopic stiffness matrix was derived. Moreover, the sufficiency of the units, the general forms of components, the universality of the orientational constitutive relations, and the aspects of the further research, were discussed.