  In continuum mechanics, stress concept plays an essential role. For
complicated materials, different stress concepts are used with ambiguity or
different understanding. Geometrically, a material element is expressed by a
closed region with arbitral shape. The internal region is acted by distance
dependent force (internal body force), while the surface is acted by surface
force. Further more, the element as a whole is in a physical background
(exterior region) which is determined by the continuum where the element is
embedded (external body force). Physically, the total energy can be additively
decomposed as three parts: internal region energy, surface energy, and the
background energy. However, as forces, they cannot be added directly. After
formulating the general forms of physical fields, the deformation tensor is
introduced to formulate the force variations caused by deformation. As the
force variation is expressed by the deformation tensor, the deformation stress
concept is well formulated. Furthermore, as a natural result, the additive
decomposition gives out the definition of static continuum, which determines
the material parameters in constitutive equations. Through using the exterior
differentials, the constitutive equations are formulated in general form.
Throughout the paper, when it is suitable, the related results are simplified
to classical results for easier understanding.
