A finite strain framework for the simulation of polymer curing. Part II. Viscoelasticity and shrinkage

Abstract

A phenomenologically inspired, elastic finite strain framework to simulate the curing of polymers has been developed and discussed in the first part (Hossain et al. in Comput Mech 44(5):621-630, 2009) of this work. The present contribution provides an extension of the previous simulation concept towards the consideration of viscoelastic effects and the phenomenon of curing shrinkage. The proposed approach is particularly independent of the type of the free energy density, i.e. any phenomenologically or micromechanically based viscoelastic polymer model can be utilised. For both cases the same representatives that have been used for the elastic curing models, i.e. the Neo-Hookean model and the 21-chain microsphere model, are reviewed and extended accordingly. The governing equations are derived as well as the corresponding tangent operators necessary for the numerical implementation within the finite element method. Furthermore, we investigate two different approaches-a shrinkage strain function and a multiplicative decomposition of the deformation gradient-to capture the phenomenon of curing shrinkage, i.e. the volume reduction induced by the polymerisation reaction which may lead to significant residual stresses and strains in the fully cured material. Some representative numerical examples conclude this work and prove the capability of our approach to correctly capture inelastic behaviour and shrinkage effects in polymers undergoing curing processes.

A Survey of Computational Models for Adhesion

“…In some sense adhesion corresponds to "the other side of contact"-describing the FIGURE 4 FE analysis of a liquid bridge for different contact angles [111]. 94 Roger A. Sauer interaction of solids as they are pulled apart instead of pushed together. A survey of contact formulations and corresponding computational models has been provided recently by [114].…”

“…Corresponding models have been considered by [90] and [91]. Thermodynamically derived computational curing models for finite deformations have been formulated recently by [92] and [93,94]. The modeling has also 2 A simple model for shrinkage and swelling due to concentrational changes ▵c, is given by model (31) or (32), respectively, when ▵T is replaced by ▵c.…”

Shape change of cured 2D and 3D nanostructures from imprint lithography

“…Hossain et al developed isothermal elastic and viscoelastic strain models which included shrinkage effects for the curing of epoxy resins. [3][4][5] Ye et al analyzed the effect of exposure time on NIL resist behavior during demolding with a spring and dashpot model where the spring represents the elasticity of the resist, the dashpot represents its viscosity, and the break contact represents its plasticity. This study identified the impact of exposure time on resist moduli and feature defects.…”

Experimental study of cohesive strain prior to crack initiation in constant force single cantilever beam test

“…In terms of mechanical properties, such interphases may extend up to some 100 μm from the substrate and they may be modified significantly by mechanical stresses frozen in during the preparation of the adhesive joint. [19][20][21][22][23][24][25][26][27][28][29] Current fracture mechanics approaches start from two general assumptions. Firstly, the larger part of the sample volume responds elastically to the external mechanical load, thus storing mechanical energy in the field of elastic deformation.…”