scholarly journals A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Min Kyoo Kang ◽  
Rui Huang

A hydrogel consists of a cross-linked polymer network and solvent molecules. Depending on its chemical and mechanical environment, the polymer network may undergo enormous volume change. The present work develops a general formulation based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions along with proper boundary conditions. A specific material model is employed in a finite element implementation, for which the nonlinear constitutive behavior is derived from a free energy function, with explicit formula for the true stress and tangent modulus at the current state of deformation and chemical potential. Such implementation enables numerical simulations of hydrogels swelling under various constraints. Several examples are presented, with both homogeneous and inhomogeneous swelling deformation. In particular, the effect of geometric constraint is emphasized for the inhomogeneous swelling of surface-attached hydrogel lines of rectangular cross sections, which depends on the width-to-height aspect ratio of the line. The present numerical simulations show that, beyond a critical aspect ratio, creaselike surface instability occurs upon swelling.

Author(s):  
Xiao Wang ◽  
Wei Hong

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.


2020 ◽  
Author(s):  
Danuta Miedzińska

The paper deals with numerical simulations of materials printed with SLA technology. SLA (stereolitography) is an additive manufacturing technique, which main idea is printing with the use of a photocurable resin, e.g. epoxy or acrylic. The crosslinking is carried out under UV exposition. The chosen resin was experimentally tested and then numerical analyses were carried out using material models available in LS Dyna library (MAT_24, MAT_168, MAT_081). The results were compared. The best convergence was achieved for MAT_168.


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