Nonlinear Monotonic Functions with Selectable Intervals of Almost Constant or Linear Behavior with Application to Total Strain Viscoplasticity.
Abstract
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. They 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. We have found these functions useful in the total strain approach to viscoplasticity, i.e., the analytical modelling of stress-strain diagrams, strain (stress)-rate effects, creep and relaxation curves for monotonic and cyclic loading. Also these functions offer great flexibility in the curve fitting of experimental data generated in the above-mentioned tests. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1977
- Accession Number
- ADA036344
Entities
People
- E. Krempl
- E. P. Cernocky
Organizations
- Rensselaer Polytechnic Institute