This paper provides a comprehensive description of the mechanical response of freestanding circular elastic films subjected to point and pressure loads. Regimes of behavior, such as plate, linear membrane, and nonlinear membrane, are identified in terms of two dimensionless variables that allow the creation of a single map that indicates appropriate closed-form solutions. This map provides a theoretical framework to design experiments and interpret film behavior for all orders of magnitude of: film thickness-to-span ratio, deflection, loads, prestretch, and elastic properties. The normalization approach provides the means to quickly identify appropriate simplifications to the nonlinear governing equations, and identify applicable analytical solutions. Numerical results are used to illustrate behavior in transition regions, e.g., the transition for a given plate thickness from small to large deflections under increasing load. Critical loads, thickness and prestretch are identified which indicate when asymptotic plate or membrane solutions are accurate. Asymptotic and numerical results are presented which illustrate finite-sized regions of bending-influenced deformation near point loads and clamped edges. Theoretical predictions for the width of these regions enable us to estimate the validity of analytical strain distributions, and in turn the maximum strains in the film. These results help avoiding brittle fracture or ductile yielding of the film by identifying physical parameters that limit strains to an acceptable level.
The Mechanical Response of Freestanding Circular Elastic Films Under Point and Pressure Loads
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, May 23, 2003; final revision, June 17, 2004. Associate Editor: Z. Suo. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California—Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Komaragiri , U., Begley, M. R., and Simmonds, J. G. (March 15, 2005). "The Mechanical Response of Freestanding Circular Elastic Films Under Point and Pressure Loads ." ASME. J. Appl. Mech. March 2005; 72(2): 203–212. https://doi.org/10.1115/1.1827246
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