The solution of nonhomogeneous state of stress strain and swelling problem in amorphous polymer networks

Abstract

The total free energy a swollen and deformed amorphous cross-linked polymer network is given as ... where .. is the free energy of mixing of polymer and solvent; ... indicates the first part of elastic energy by representing ideal conditions called as "Phantom Case; ... covers the local constraints and completes the total free energy as a second part of elastic free energy. The explicit form of all free energies are obtained from molecular theory of rubber elasticity by including their recent developments. Expressions for stress in terms of strain and swelling ratio are obtained from free energy. Bending of a cross-linked amorphous cuboid is formulated as a boundary value problem and the distribution of solvent and stresses are numerically calculated for six distinct solvents. The magnitude of bending moments are found for different degrees of flexures up to 180. Results are compared with each other and also with their linear solutions. As swelling increases a decrease in elasticity modulus is observed.