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A skeleton-and-bubble model of elastic open-cell foams for finite element analysis at large deformations

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Title: A skeleton-and-bubble model of elastic open-cell foams for finite element analysis at large deformations
Author(s): Sabuwala, Tapan
Director of Research: Gioia, Gustavo
Doctoral Committee Chair(s): Gioia, Gustavo
Doctoral Committee Member(s): Phillips, James W.; Sottos, Nancy R.; Jasiuk, Iwona M.
Department / Program: Mechanical Sci & Engineering
Discipline: Theoretical & Applied Mechans
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Open-cell foams unit-cell model phase transition polyether polyurethane foams.
Abstract: We formulate a new unit-cell model of elastic open-cell foams. In this model, the conventional skeleton of open-cell foams is supplemented by fitting a thin-walled bubble within each cavity of the skeleton, as a substitute for the membranes that occlude the openings of the skeleton in elastic polyether polyurethane foams. The model has 9 parameters, and the value of each parameter may be readily estimated for any given foam. We implement the model as a user-defined material subroutine in the finite-element code ABAQUS. To calibrate the model, we carry out fully nonlinear, three-dimensional finite-element computational simulations of the experiments of Dai et al., in which a set of five polyether-polyurethane EOC foams covering the entire range of commercially available relative densities was tested under five loading conditions: compression along the rise direction, compression along a transverse direction, tension along the rise direction, simple shear combined with compression along the rise direction, and hydrostatic pressure combined with compression along the rise direction. We show that, with a suitable choice of the values of the parameters of the model, the model is capable of reproducing the most salient trends evinced in the experimental stress-strain curves. We also show that the model can no longer reproduce all of these trends if the bubbles be excluded from the model, and conclude that the bubbles play a crucial role at large deformations, at least under certain loading conditions. Next, we turn our attention to the stretch fields. Of special interest to us are the two-phase stretch fields associated with a phase transition. These fields consist of mixtures of two configurational phases of the foam, a high-deformation phase and a low-deformation phase. We show that the stretch fields that obtain in our computational simulations are in good accord with the digital-image-correlation measurements of Dai et al., except for simple shear combined with compression along the rise direction. For this loading condition, Dai et al. concluded that the stretch fields remained continuous and there was no evidence of distinct configurational phases in the foam. And yet, Dai et al. might have concluded otherwise had they probed the stretch fields close to the lateral faces of the specimen, where according to our computational simulations they would have found circumscribed nuclei of the high-deformation phase. To settle the matter, we subject a foam specimen to simple shear combined with compression along the rise direction, measure the stretch fields via a digital-image-correlation technique, and find discontinuities in the stretch fields--but only close to the lateral faces of the specimen, just as expected on the basis of our computational simulations. All of the major features of the stretch fields turn out to be well reproduced in the computational simulations. In the last part of this thesis, we assess the capacity of the new model to yield reliable predictions of the mechanical response of foams under punching, a common type of loading in applications of elastic polyether polyurethane foams. In punching problems the geometry is complex, the stress fields are highly spatially heterogeneous, the deformations are very large, and the use of finite-element simulations is indispensable. We have recourse to data from numerous punching experiments in which tall and short specimens of foams of three low values of relative density were penetrated by a wedge-shaped punch and a conical punch. For each experiment we run a fully nonlinear, three-dimensional finite-element computational simulation and find the simulated force--penetration curve to be in good accord with the corresponding experimental force--penetration curve. Wedge-shaped punches and conical punches lack an intrinsic characteristic length, a fact that has been exploited to carry out a simple but powerful theoretical analysis of the mechanical response of foams under punching. Some of the assumptions and simplifications of this theoretical analysis have remained inaccessible to direct experimental verification, and we use our computational simulations to show that these assumptions and simplifications are justified. Our results on punching serve to underscore the importance of phase transitions in the mechanics of EOC foams. The force-penetration curves display a number of striking features, and we can relate each one of these features to the presence of two configurational phases in the foam. Feature by feature the relation is so specific and intricate that we are lead to conclude that the force-penetration curves could be taken by themselves as proof of the occurrence of phase transitions, even in the absence of any direct experimental evidence of the stretch fields. A number of models of EOC foams might not allow for the occurrence of phase transitions and still be able to account for numerous stress-stretch curves measured under compression along the rise direction, for example. But the force-penetration curves are inextricably linked to the prevalence of two-phase stretch fields, and it is likely that no model can account for these curves unless it allows for the occurrence of phase transitions.
Issue Date: 2012-02-06
URI: http://hdl.handle.net/2142/29725
Rights Information: Copyright 2011 Tapan Sabuwala
Date Available in IDEALS: 2012-02-06
Date Deposited: 2011-12
 

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