Laminate Theory with Hygral Effects:

In this study, the total strain is assumed to be superimposition of mechanical and hygral strains.

(5.113)

where,  is the hygral strain in laminate. The stress in global direction is given as

(5.114)

The resultant in-plane forces are given as

(5.115)

where,

(5.116)

is defined as the resultant in-plane forces per unit length due to hygral strains.
In a similar way, we can give the resultant moments as

(5.117)

where,

(5.118)

is defined as resultant moments per unit length due to hygral strains. Combining Equation (5.116) and Equation (5.118), we write

(5.119)

The inverse of this equation is written as

(5.120)