A linear-elastic–nonlinear-swelling theory for hydrogels. Part 2. Displacement formulation

We consider the multidirectional swelling and drying of hydrogels formed from super-absorbent polymers water, focusing on elastic deformation caused by differential swelling. By modelling as instantaneously incompressible, linear-elastic materials considering situations in which there can be large isotropic strains (arising swelling) while deviatoric remain small, it is possible to describe accurately a wider range gel states than traditional linear theories allow. An equation derived relating displacement field polymer fraction such hydrogels, permitting shape determined evolves time, using formulation Part 1 find local fraction. discuss boundary conditions applied at surfaces gel, both bulk stress pervadic (pore) pressure interstices. Similarities between for displacements equations classical plate theory are investigated model problem slender cylinder with its base immersed water evaporation into surrounding air. In this problem, along axis cylinder, remains swollen top dries. The results our agree qualitatively experiments that we have conducted, provide physical interpretation forced biharmonic describing field.