ABSTRACT
We consider a body that at some instant occupies the region B of Euclidean three-dimensional space E3. In what follows, unless specified to the contrary, B will denote a bounded regular region [119]. We let B denote the closure of B, call ∂B the boundary of B, and designate by n the outward unit normal of ∂B. The deformation of the body is referred to the reference configuration B and a fixed cartesian coordinate frame. The cartesian coordinate frame consists of the orthonormal basis {e1, e2, e3} and the origin O. We identify a typical particle x of the body B with its position x in the reference configuration. Letters in boldface stand for tensors of an order p ≥ 1, and if v has the order p, we write vij...k (p subscripts) for the rectangular cartesian components of v. We shall employ the usual summation and differentiation conventions: Greek subscripts are understood to range over the integers (1, 2), whereas Latin subscripts, unless otherwise specified, are confined to the range (1, 2, 3); summation over repeated subscripts is implied and subscripts preceded by a comma denote partial differentiation with respect to the corresponding cartesian coordinate. The inner product of two vectors a and b will be designated by a ·b. We denote the vector product of the vectors a and b by a× b.
