Yannis F. Dafalias

The Plastic Spin

On presente une formulation macroscopique des grandes deformations elastoplastiques avec des variables de structure tensorielles

Plastic spin: necessity or redundancy?

Abstract The plastic spin concept in large deformation anisotropic elastoplasticity theories with tensorial internal variables, is proved to be a necessary constitutive ingredient. Different inaccurate notions about the plastic spin are dispelled, and its presence in the theory is demystified as something very simple and straightforward. To this extent it is necessary to disassociate the plastic spin concept and the conjugate notion of constitutive spin from the foundation of kinematics, which caused confusion in the past, and define it only in relation to the constitutive equations of evolution of the tensorial internal variables. There, the plastic spin is related to the orientation aspect of such constitutive equations, and the multiplicity of the different internal variables suggests the necessity to have a different spin for each variable. In the process, a straightforward constitutive framework is developed which is based on classical hyperelasticity, yield criteria and invariance requirements of the constitutive functions under superposed rigid body rotation. Ad-hoc assumptions about stress corotational or convected rates and other fuzzy suggestions for different spins are not part of this development. Other topics such as the concept and simplifying effect of the spinless unstressed configuration and its comparison with the isoclinic configuration, some computational aspects, and the effect of small elastic strains are discussed, and all along the significance of plastic spin in the different equations is evaluated.

Anisotropic Critical State Theory: Role of Fabric

An Anisotropic Critical State Theory (ACST) for granular media is presented, which accounts for the role of anisotropic fabric at critical state. It enhances the requirements of critical values for the stress and void ratio of the classical Critical State Theory (CST) by an additional requirement of critical value for an appropriate measure of fabric-anisotropy. A fabric tensor and its evolution toward a critical value, norm-wise and direction-wise, is introduced motivated by micromechanical and experimental studies. On the basis of a scalar-valued fabric-anisotropy variable relating the evolving fabric tensor to the loading direction, a dilatancy state line is defined in the void ratio—pressure plane which determines a dilatancy state parameter ζ that characterizes the contracting or dilating trends of the current state. When the fabric-anisotropy variable reaches its critical state value, the dilatancy state line becomes identical to the critical state line and the ζ identical to the well-known state pa...

Cyclic loading for materials with a vanishing elastic region

Abstract Within a plastic internal variables formalism of rate independent plasticity, a recently developed constitutive law for plastic material response under stress reversals is shown to apply to materials with a vanishing elastic region. The concept of the bounding surface introduced earlier, replaces the vanished yield and loading surfaces in defining loading-unloading criteria. Good comparison of the model with experimental data is obtained.

Issues on the constitutive formulation at large elastoplastic deformations, part 1: Kinematics

SummaryThe kinematics at large elastoplastic deformations are analyzed within the framework of a general macroscopic constitutive theory with tensorial structure variables. The key concept is the distinction between the kinematics of the continuum and its underlying substructure. The proper definition of physically plausible corotational and corodeformational rates for the kinematical and state variables, shows the equivalence of the effect that the choice of an unstressed configuration has, on the transformation of these variables and their rates under superposed rigid body rotations. Along these lines, issues debated in the past are given definitive answers, and comparisons of different approaches are presented.

Orientational evolution of plastic orthotropy in sheet metals

Recent experimental findings show that when orthotropic sheet metal samples are subjected to uniaxial tensile loading at an angle to the orthotropic axes, a drastic re-orientation of the axes takes place at moderate tensile strain levels, while orthotropic symmetries are preserved. This phenomenon is explained and simulated within a simple theory of plasticity, which combines Hills quadratic yield criterion for orthotropy with the concept of plastic spin as a necessary constitutive ingredient for the orientational evolution of anisotropic tensorial internal variables. Detailed analytical investigation, corroborated by the experimental data, shows a trend of anisotropic axes rotation towards alignment of a pertinent minimum yield stress with the stretching direction. This imposes a constitutive coupling relation between the anisotropic parameters and the plastic spin coefficient. Similarities and differences with other works as well as unresolved questions are discussed.

The effect of plastic spin on anisotropic material behavior

Abstract The effect of the plastic spin on the behavior of initially anisotropic materials is demonstrated by obtaining in closed analytical form the stress-strain response of orthotropic and transversely isotropic materials subjected to various kinds of homogeneous large inelastic deformations, at different rates and temperatures. The important issue is the evolution of the orientation of the anisotropic axes, which is based on the key aspect of the aspect of the constitutive relations for the plastic spin. In one case, the theoretical results show a remarkable qualitative similarity with experimental data from fixed-end torsion experiments. For other cases, physically plausible interpretations of the theory are discussed.

The plastic spin in viscoplasticity

Abstract The importance of the role of plastic spin in the rate-dependent response of materials at large deformations is the main objective of this work. After a brief presentation of a general constitutive framework for viscoplasticity at large strains, an isotropic/kinematic hardening and an orthotropic viscoplastic model are used to analyze the stress-strain response under simple shear and biaxial loading at different rates. A clear understanding of the role of plastic spin is achieved by obtaining closed-form analytical expressions for different stress values, in which the plastic spin constitutive parameters interrelate with the strain rate and other more conventional model constants. Such analytical expressions allow for a direct evaluation of the capabilities of the models to account for large deformations and rate dependence as exhibited by available experimental data, and provide guidance towards the proper choice of constitutive parameters.

On the microscopic origin of the plastic spin

SummaryConsidering the configuration of a single slip and employing a scale invariance argument, it is possible to deduce a set of “microscopic” plastic flow relations having a direct counterpart in the “macroscopic” formulation of plasticity and viscoplasticity. In particular, a microscopic form of the plastic spin and its macroscopic counterpart for the case of anisotropy induced by kinematic hardening are obtained in terms of elementary physical arguments. Moreover the evolution equation for the back-stress is rigorously derived. Parameters which were assumed to be constant and/or independent from each other in a macroscopic development, are now found to be interrelated and dependent on the accumulated plastic strain. These findings are used for the analysis of the simple shear problem, especially in evaluating the development of the axial stress normal to the shear plane. A preliminary qualitative comparison with available data from fixed-end torsion experiments is discussed.

Distortional and orientational hardening at large viscoplastic deformations

Distortional and orientational hardening, reflecting macroscopically texture development, are combined with standard isotropic and kinematic hardening features in the development of a constitutive model for large viscoplastic deformations of metals. The proper choice of hardening parameters, including those for plastic spin expressions within a multiple spins formulation, allows the realistic simulation of data from fixed-end torsion experiments, in which the axial stress oscillates or changes sign while the shear stress increases monotonically. The model response is examined under reverse loading and different rates and temperatures.