Bifurcation of a Swelling Gel with a Mechanical Load and Geometric Constraint

摘要

We present an analysis of the bifurcation phenomenon of a gel in contact with a solvent. When a Mooney-Rivlin form-free energy function is introduced, an asymmetric swelling may appear for a gel swelling under uniaxial constraint or subjected to equal dead loads, which results in an interesting pitchfork bifurcation phenomenon. We present an analytical investigation of this problem based on the classical theory of continuum mechanics. The bifurcation points are obtained for different values of the chemical potential of the solvent molecules. The results demonstrate that the free swelling of the gel under uniaxial constraint will not result in the bifurcation unless further mechanical loads are applied.%We present an analysis of the bifurcation phenomenon of a gel in contact with a solvent.When a Mooney-Rivlin form-free energy function is introduced,an asymmetric swelling may appear for a gel swelling under uniaxial constraint or subjected to equal dead loads,which results in an interesting pitchfork bifurcation phenomenon.We present an analytical investigation of this problem based on the classical theory of continuum mechanics.The bifurcation points are obtained for different values of the chemical potential of the solvent molecules.The results demonstrate that the free swelling of the gel under uniaxial constraint will not result in the bifurcation unless further mechanical loads are applied.Since gels commonly exist in our daily life and engineering society,they have aroused the great interest of a large number of researchers and have been intensely studied over the past few decades.[1-7] Most possible technical and biological applications include medical devices,[8] tissue engineering[9] and actuators responsive to physiological cues.[10,11] Many mechanical models[12-14] have been reported to develop a rigorous description of gels from either an experimental or a theoretical viewpoint.