569 research outputs found
On the Application of Deformation Kinetics to Nonlinear Constitutive Relations at Higher Temperatures
A single phenomenological constitutive equation is derived theoretically from first principles and applied to aluminum, tin and lead. The theory is based on deformation kinetics of steady creep in which the fundamental mechanism is atomic transport over potential barriers whose conformation is distorted by the application of a stress field. The form of the functional dependence of barrier distortion and stress over the entire temperature range is found to be a sigmoidal curve which tends to straight lines of a unit slope in the small and high stress regions. With this form of barrier distortion, the constitutive equation prediction the steady creep behavior of aluminum, tin and lead over a wide range of temperature and stress
Some Recent Developments in the Endochronic Theory with Application to Cyclic Histories
Constitutive equations with only two easily determined material constants predict the stress (strain) response of normalized mild steel to a variety of general strain (stress) histories, without a need for special unloading-reloading rules. The equations are derived from the endochronic theory of plasticity of isotropic materials with an intrinsic time scale defined in the plastic strain space. Agreement between theoretical predictions and experiments are are excellent quantitatively in cases of various uniaxial constant amplitude histories, variable uniaxial strain amplitude histories and cyclic relaxation. The cyclic ratcheting phenomenon is predicted by the present theory
A numerical algorithm for endochronic plasticity and comparison with experiment
A numerical algorithm based on the finite element method of analysis of the boundary value problem in a continuum is presented, in the case where the plastic response of the material is given in the context of endochronic plasticity. The relevant constitutive equation is expressed in incremental form and plastic effects are accounted for by the method of an induced pseudo-force in the matrix equations. The results of the analysis are compared with observed values in the case of a plate with two symmetric notches and loaded longitudinally in its own plane. The agreement between theory and experiment is excellent
Endochronic theory, non-linear kinematic hardening rule and generalized plasticity: a new interpretation based on generalized normality assumption
A simple way to define the flow rules of plasticity models is the assumption
of generalized normality associated with a suitable pseudo-potential function.
This approach, however, is not usually employed to formulate endochronic theory
and non-linear kinematic (NLK) hardening rules as well as generalized
plasticity models. In this paper, generalized normality is used to give a new
formulation of these classes of models. As a result, a suited pseudo-potential
is introduced for endochronic models and a non-standard description of NLK
hardening and generalized plasticity models is also provided. This new
formulation allows for an effective investigation of the relationships between
these three classes of plasticity models
Materials - Man\u27s Essential Link with the Future
(An invited address delivered on the occasion of the commemoration of the 100th anniversary of the Iowa Academy of Science.)
Materials are essential for the support of human life. At the primitive level they provide food, shelter and protection against the natural elements. At the advanced level of the technological civilization of the 20th century they support the luxuries to which we have become accustomed-and which we insist upon calling our needs. Today they are essential to our industry, our economy and our national security
Localization analysis of variationally based gradient plasticity model
The paper presents analytical or semi-analytical solutions for the formation
and evolution of localized plastic zone in a uniaxially loaded bar with
variable cross-sectional area. A variationally based formulation of explicit
gradient plasticity with linear softening is used, and the ensuing jump
conditions and boundary conditions are discussed. Three cases with different
regularity of the stress distribution are considered, and the problem is
converted to a dimensionless form. Relations linking the load level, size of
the plastic zone, distribution of plastic strain and plastic elongation of the
bar are derived and compared to another, previously analyzed gradient
formulation.Comment: 42 pages, 11 figure
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Application of the orthogonality principle to the endochronic and Mroz models of plasticity
A new description of the endochronic and the Mroz model is discussed. It is
based on the definition of a suitable pseudo-potential and the use of the
generalized normality assumption. The key-point of this formulation is the
dependence of the pseudo-potentials on state variables
Pseudo-potentials and loading surfaces for an endochronic plasticity theory with isotropic damage
The endochronic theory, developed in the early 70s, allows the plastic
behavior of materials to be represented by introducing the notion of intrinsic
time. With different viewpoints, several authors discussed the relationship
between this theory and the classical theory of plasticity. Two major
differences are the presence of plastic strains during unloading phases and the
absence of an elastic domain. Later, the endochronic plasticity theory was
modified in order to introduce the effect of damage. In the present paper, a
basic endochronic model with isotropic damage is formulated starting from the
postulate of strain equivalence. Unlike the previous similar analyses, in this
presentation the formal tools chosen to formulate the model are those of convex
analysis, often used in classical plasticity: namely pseudopotentials,
indicator functions, subdifferentials, etc. As a result, the notion of loading
surface for an endochronic model of plasticity with damage is investigated and
an insightful comparison with classical models is made possible. A damage
pseudopotential definition allowing a very general damage evolution is given
Peristaltic Transport of a Couple Stress Fluid: Some Applications to Hemodynamics
The present paper deals with a theoretical investigation of the peristaltic
transport of a couple stress fluid in a porous channel. The study is motivated
towards the physiological flow of blood in the micro-circulatory system, by
taking account of the particle size effect. The velocity, pressure gradient,
stream function and frictional force of blood are investigated, when the
Reynolds number is small and the wavelength is large, by using appropriate
analytical and numerical methods. Effects of different physical parameters
reflecting porosity, Darcy number, couple stress parameter as well as amplitude
ratio on velocity profiles, pumping action and frictional force, streamlines
pattern and trapping of blood are studied with particular emphasis. The
computational results are presented in graphical form. The results are found to
be in good agreement with those of Shapiro et. al \cite{r25} that was carried
out for a non-porous channel in the absence of couple stress effect. The
present study puts forward an important observation that for peristaltic
transport of a couple stress fluid during free pumping when the couple stress
effect of the fluid/Darcy permeability of the medium, flow reversal can be
controlled to a considerable extent. Also by reducing the permeability it is
possible to avoid the occurrence of trapping phenomenon
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