 Award ID(s):
 1635636
 NSFPAR ID:
 10110994
 Date Published:
 Journal Name:
 Proceedings of the Fifteenth International Conference on Web Handling
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A comparative study is presented to solve the inverse problem in elasticity for the shear modulus (stiffness) distribution utilizing two constitutive equations: (1) linear elasticity assuming small strain theory, and (2) finite elasticity with a hyperelastic neoHookean material model. Assuming that a material undergoes large deformations and material nonlinearity is assumed negligible, the inverse solution using (2) is anticipated to yield better results than (1). Given the fact that solving a linear elastic model is significantly faster than a nonlinear model and more robust numerically, we posed the following question: How accurately could we map the shear modulus distribution with a linear elastic model using small strain theory for a specimen undergoing large deformations? To this end, experimental displacement data of a silicone composite sample containing two stiff inclusions of different sizes under uniaxial displacement controlled extension were acquired using a digital image correlation system. The silicone based composite was modeled both as a linear elastic solid under infinitesimal strains and as a neoHookean hyperelastic solid that takes into account geometrically nonlinear finite deformations. We observed that the mapped shear modulus contrast, determined by solving an inverse problem, between inclusion and background was higher for the linear elastic model as compared to that of the hyperelastic one. A similar trend was observed for simulated experiments, where synthetically computed displacement data were produced and the inverse problem solved using both, the linear elastic model and the neoHookean material model. In addition, it was observed that the inverse problem solution was inclusion sizesensitive. Consequently, an 1D model was introduced to broaden our understanding of this issue. This 1D analysis revealed that by using a linear elastic approach, the overestimation of the shear modulus contrast between inclusion and background increases with the increase of external loads and target shear modulus contrast. Finally, this investigation provides valuable information on the validity of the assumption for utilizing linear elasticity in solving inverse problems for the spatial distribution of shear modulus associated with soft solids undergoing large deformations. Thus, this work could be of importance to characterize mechanical property variations of polymer based materials such as rubbers or in elasticity imaging of tissues for pathology.more » « less

Abstract The most widelyused representation of the compressible, isotropic, neoHookean 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 groundstate 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 snapback feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this nonunique solution is determined in terms of the groundstate 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, neoHookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameterfitting procedure needed to characterize this standard, compressible, isotropic neoHookean model in terms of experimental data.

In this paper we derive spatially dependent transfer functions for web span lateral dynamics which provide web lateral position and slope as outputs at any location in the span; the inputs are guide roller displacement, web lateral position disturbances from upstream spans, and disturbances due to misaligned rollers. This is in sharp contrast to the existing approach where only web lateral position response is available on the rollers. We describe the inherent drawbacks of the existing approach and how the new approach overcomes them. The new approach relies on taking the 1D Laplace transform with respect to the temporal variable of both the web governing equation and the boundary conditions. One can also obtain the web slope at any location within the web span with the proposed approach. A general span lateral transfer function, which is an explicit function of the spatial position along the span, is obtainedfirst followed by its application to different intermediate guide configurations.more » « less

The lateral deformations of webs in rolltoroll (R2R) process machines can affect the quality of the manufacturing process. Webs can enter a cylindrical roller normally if the forces required to sustain normal entry and do not exceed the available friction forces. Webs with simple nonuniform length variation across their width (camber) will steer toward the long side, affecting the steady state lateral deformation and hence registration. Most previous studies have focused on tests and modeling a cambered web span in a free span between two rollers. Often these studies assume some displacement and slope boundary conditions are known and seek the remaining condition(s) that would dictate the steady state lateral deformation of the cambered web in the free span. In many spans in a process machine there may be no known boundary conditions and no steady state deformation of the cambered web. The web may travel toward the long side continually from one web span until the next until a web guide attempts to return the web to an acceptable lateral location in the process machine. The simplest case of multiple span cambered web lateral behavior is that of a cambered web belt transiting two aligned rollers which is the focus of the current work. Dynamic simulation (Abaqus/Standard) has been used to better understand the response of cambered webs under tension that has been witnessed in tests.more » « less

The length of web in a wound roll is one mark of roll quality. The available web length in a roll is a concern for many who process webs and those who convert webs. There are algorithms that estimate the length of web and layers in a wound roll based on simple geometry and inputs of inside and outside radius and web thickness. If webs were infinitely stiff in the machine and outofplane directions such calculations could be accurate but this is not the case. Webs deform as the result of winder operating conditions such as winding tension and the contact pressures and stresses due to winding. Length calculations based on geometry will err as a result of web deformation in the length and radial directions. Webs are generally subject to tension during transport through process machines, the apparent deformed web length will vary with transport tension. The mission of this paper is to describe means by which the available deformed web length and the number of layers in a wound roll can be accurately predicted. The accuracy of the predictions will be verified by winding trials in the laboratory. The winding trials will demonstrate the levels of accuracy that can be realized on laboratory and production machines.more » « less