In this work, we derive a governing equation for web tension in a span by
employing a Neo-Hookean material model that is applicable for transport of web
materials under both small and large strains. This governing equation may be
employed to study the evolution of tension within a span as well as propagation of
tension variations from span to span as the web is transported in the machine.
First, we find the stretch in a web span and relate it to web tension via a
Neo-Hookean material model; the Neo-Hookean model is linear for small strain
and nonlinear otherwise. Second, we conduct a dimensional analysis by defining
several key coefficients that aid in grouping the machine and web material
parameters separately in order to obtain a compact system of governing equations;
this representation may be utilized to efficiently study the impact of web and
roller properties on transport behavior.
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Analysis of the compressible, isotropic, neo-Hookean hyperelastic model
The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.
more » « less- NSF-PAR ID:
- 10389295
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Meccanica
- Volume:
- 58
- Issue:
- 1
- ISSN:
- 0025-6455
- Page Range / eLocation ID:
- p. 217-232
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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