3.3.1 Continuous Aligned Isotropic Fibers

Consider a material reinforced with unidirectionally aligned continuous fibers elastically loaded in the fiber direction. The isostrain (or parallel connected) model specifies that the strain in the fibers equals the strain in the matrix. The load in the fiber direction is shared:

(3.10)

Since P = ? A,

(3.11)

Dividing by the total cross section A _C, and noting that the length of the fibers equals that of the matrix, so that A _f / A _c = V _f, then

(3.12)

Now divide each term by the strain ?, and invoke Hooke's law:

(3.13)

The transverse case can be considered as applying a load perpendicular to the plane of a series of layers of equal area. This is the isostress or series model, so that ? _C = ? _f + ? _m. In this case the strains are shared or additive;

(3.14)

Again noting ? = ?/ E and dividing each term by the (equal) stress;

(3.15)

The subscript i refers to each constituent. These "rule of mixtures" type of...