Unifying the Basic Phenomenology of Monotonic Unidimensional Plasticity

Resumo

Stress and strain quantities and related characteristic subdomains of a common monotonic stress-strain
diagram are studied. “Component quantities” are explicitly defined, encompassing many components which,
although found throughout the literature —e, p, –Y, –Y—, are not usually comprehensively explored together
from one single source. Those quantities are used to form planes (component, component) defining characteristic
subdomains, which contain an exclusive type of curve to be linearized. An environment is thus constructed,
offering a broad context of subdomains where linearized relations can be worked out. As a specific application,
using such components and a logarithmic linearization it is possible to unify the unidimensional monotonic
solicitation in tension/compression from one single source of equations, comprising classical formulations —
Ramberg-Osgood, Hollomon, Swift, Ludwik— and other ones not widely knwon nor used. Numerically (or
algebraically), there are two independent sets of elastic plus plastic equations relating the quantities , ep=–Y,
, ep=–Y, p=–e=–(/E), plus accumulated quantities acc and acc from a previous plastic deformation.
Diverse formulations —e.g. logarithmic and/or polynomial ones— can be specified for each subdomain or model.
Such final models will comprise series of computer implementable, adjoined numerical expressions. Notice that
with this comprehensive context of variables and equations some small inconsistencies in the basic formulation of
unidimensional plasticity are revealed, which are qualitatively important for the due description of the
phenomenon of plasticity, specially when developping into a more complex equationing.