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In continuum mechanics, stress concept plays an essential role. Forcomplicated materials, different stress concepts are used with ambiguity ordifferent understanding. Geometrically, a material element is expressed by aclosed region with arbitral shape. The internal region is acted by distancedependent force (internal body force), while the surface is acted by surfaceforce. Further more, the element as a whole is in a physical background(exterior region) which is determined by the continuum where the element isembedded (external body force). Physically, the total energy can be additivelydecomposed as three parts: internal region energy, surface energy, and thebackground energy. However, as forces, they cannot be added directly. Afterformulating the general forms of physical fields, the deformation tensor isintroduced to formulate the force variations caused by deformation. As theforce variation is expressed by the deformation tensor, the deformation stressconcept is well formulated. Furthermore, as a natural result, the additivedecomposition gives out the definition of static continuum, which determinesthe material parameters in constitutive equations. Through using the exteriordifferentials, the constitutive equations are formulated in general form.Throughout the paper, when it is suitable, the related results are simplifiedto classical results for easier understanding.

Formulation of Deformation Stress Fields and Constitutive Equations in Rational Mechanics