Balance Laws

Abstract

The basic laws of mechanics can all be expressed, in general, in the following form,

$$ \frac{d}{{dt}}\int\limits_{Pt} {\psi dv = \int\limits_{\partial Pt} {{\phi _\psi }nda + \int\limits_{Pt} {{\delta _\psi }dv} } } $$

(2.1)

, for any bounded regular subregion of the body, called a part P ⊂ B and the vector field n, the outward unit normal to the boundary of the region Pt in the current configuration. The quantities Ψ and σΨ are tensor fields of certain order m, and σΨ is a tensor field of order m + 1, say m = 0 or m = 1, so that σ is a scalar or vector quantity, and, respectively, σΨ is a vector or second-order tensor quantity.