Construction of Nonlinear Monotonic Functions With Selectable Intervals of Almost Constant or Linear Behavior

[+] Author and Article Information
E. P. Cernocky, E. Krempl

Department of Mechanical Engineering, Aeronautical Engineering, and Mechanics, Rensselaer Polytechnic Institute, Troy, N. Y. 12181

J. Appl. Mech 45(4), 780-784 (Dec 01, 1978) (5 pages) doi:10.1115/1.3424418 History: Received January 01, 1977; Revised June 01, 1978; Online July 12, 2010


A rather general method is given to construct classes of functions with an arbitrary almost constant (linear) initial interval followed by a nonprescribed interval of monotonic nonlinear behavior. This region of nonlinear behavior is succeeded by an unbounded interval of almost constant (linear) behavior. The functions contain not more than four selectable parameters and are synthesized from analytic, monotonic, normalized, and bounded base functions through the introduction of two separate kernel sets, subsequent addition, and integration. As examples we give the special functions based on the error, the hyperbolic tangent, the inverse tangent, a rational, and the incomplete gamma function. Limiting function forms, such as the bilinear form, are derived for limiting values of the parameters. The functions developed herein are primarily used as coefficient functions in a differential constitutive equation for viscoplasticity developed elsewhere. They are indispensible tools for the numerical modeling of stress-strain diagrams, strain (stress)-rate effects, creep and relaxation curves for monotonic, and cyclic loading both in one and three dimensions.

Copyright © 1978 by ASME
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