Constitutive equations for cyclic plasticity and cyclic viscoplasticity

A model of workhardening is proposed which generalizes the known rules of isotropic and kinematic workhardening by introducing the concept of a ‘field of workhardening moduli.’ This field is defined by a configuration of surfaces of constant workhardening moduli in the stress space. For any loading history the instantaneous configuration can be determined by calculating the translation and expansion or contraction of all surfaces; the material behaviour can thus be determined for complex loading paths, in particular for cyclic loadings. Several examples for a plane stress state are presented.

On the description of anisotropic workhardening

A number of observations are made on the macroscopic behavior of materials subjected to uniaxial random cyclic loadings. These observations are then generalized to construct a model describing the material behavior for complex multiaxial loadings, in particular for cyclic loadings. This generalization introduces the concept of a bounding surface in the stress space which always encloses the loading surface. A parameter defined by the relative position of the loading and the bounding surface, and the plastic work done during the most recent loading, determine the value of the plastic modulus.

A model of nonlinearly hardening materials for complex loading

A fabric tensor \IF\di\dj\N for three-dimensional assemblies of granular soils is introduced as an index showing the anisotropy due to the preferred orientation of constituent particles and is actually determined by using data derived from a material science approach of soils. Using the fabric tensor, a Drucker–Prager type of yield function is extended so as to take into account the anisotropic yielding behavior of granular soils. Plane strain tests on Toyoura sand are analyzed with a result that the anisotropic shear strength is well fitted by the extended Drucker–Prager yield function. Based on this, it is concluded that this study provides a step to link the material science approach of soils, in which the spatial arrangement of particles and associated voids plays an important role, to the continuum theory of plasticity.

Yield Function for Soil with Anisotropic Fabric

Directional distortional hardening in metal plasticity within thermodynamics

A hardening rule accounting for anisotropy produced by plastic deformations is developed. Transition from an initially isotropic material into an anisotropic one is studied. The proposed rule accounts for translation, rotation and expansion of the initial yield locus.

A. Sawczuk

Papers

A rule of anisotropic hardening