期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 468, 期 2148, 页码 3824-3841出版社
ROYAL SOC
DOI: 10.1098/rspa.2012.0385
关键词
polymeric gel; visco-poroelasticity; model
资金
- National Science Foundation [CMMI-0900342]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [0900342] Funding Source: National Science Foundation
A polymeric gel can imbibe solvent and swell. Besides the dilatational mode of deformation, which involves long-range solvent migration, a gel may also undergo volume-conserved deformation. For a macroscopic gel with covalent cross-links, the volume-conserved deformation is usually much faster. However, these two modes are coupled for deformation at the microscopic level and for gels containing physical cross-links or large solvent molecules. In this paper, we seek to formulate a unified theoretical framework for the transient behaviour of polymeric gels to account for both solvent migration and viscoelastic deformation. Under this framework, we further develop a simple material model, and implement it into a finite-element code for numerical calculations. By simultaneously tracking the solvent migration and motion of polymer network, we evolve the inhomogeneous fields of stress and chemical potential. Several initial-boundary-value problems are solved as illustrative examples. For macroscopic gels with low viscosity, the time scales for viscoelasticity and poroelasticity are separated, and the long-term behaviour is just as that predicted by a poroelastic model. For structures or processes involving sizes comparable to the intrinsic length of a material, the viscoelasticity and poroelasticity must be considered simultaneously, especially when studying impact responses.
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