ANALYSIS OF SIMPLE SHEAR ENDOCHRONIC EQUATIONSFOR FINITE PLASTIC DEFORMATION

Jaumann rate, generalized Jaumann rate,Fu rate and Wu rate were incorporated into endochronic equations for finite plastic deformation to analyze simple shear finite deformation. The results show that an oscillatory shear stress and normal stress response to a monotonically increasing shear strain occurs when Jaumann rate objective model is adopted for hypoelastic or endochronic materials. The oscillatory response is dependent on objective rate adopted,independent on elastoplastic models. Normal stress is unequal to zero during simple shear finite deformation.

On Numerical Modelling of Industrial Powder Compaction Processes for Large Deformation of Endochronic Plasticity at Finite Strains

Compaction processes are one the most important par ts of powder forming technology. The main applications are focused on pieces for a utomotive, aeronautic, electric and electronic industries. The main goals of the compaction processes are to obtain a compact with the geometrical requirements, without cracks, and with a uniform distribution of density. Design of such proc esses consist, essentially, in determine the sequence and relative displacements of die and punches in order to achieve such goals. A.B. Khoei presented a gener al framework for the finite element simulation of powder forming processes based on the following aspects; a large displacement formulation, centred on a total and updated Lagrangian formulation; an adaptive finite element strategy based on error estimates and automatic remeshing techniques; a cap model based on a hard ening rule in modelling of the highly non-linear behaviour of material; and the use of an efficient contact algorithm in the context of an interface element fo rmulation. In these references, the non-linear behaviour of powder was adequately desc ribed by the cap plasticity model. However, it suffers from a serious deficiency when the stress-point reaches a yield surface. In the flow theory of plasticit y, the transition from an elastic state to an elasto-plastic state appears more or less abruptly. For powder material it is very difficult to define the locati on of yield surface, because there is no distinct transition from elastic to ela stic-plastic behaviour. Results of experimental test on some hard met al powder show that the plastic effects were begun immediately upon loading. In such mater ials the domain of the yield surface would collapse to a point, so making the di rection of plastic increment indeterminate, because all directions are normal to a point. Thus, the classical plasticity theory cannot deal with such materials and an advanced constitutive theory is necessary. In the present paper, the constitutive equations of powder materials will be discussed via an endochronic theory of plasticity. This theory provides a unifi ed point of view to describe the elastic-plastic behaviour of material since it places no requirement for a yield surface and a ’loading function’ to disting uish between loading an unloading. Endochronic theory of plasticity has been app lied to a number of metallic materials, concrete and sand, but to the knowledge of authors, no numerical scheme of the model has been applied to powder material . In the present paper, a new approach is developed based on an endochronic rate independent, density-dependent plasticity model for describing the isothermal deformation behavior of metal powder at low homologous temperature. Although the concept of yield surface has not been explicitly assumed in endochronic theory, it is shown that the cone-cap plasticity yield surface (Fig.1), which is the m ost commonly used plasticity models for describing the behavior of powder materi al can be easily derived as a special case of the proposed endochronic theory. Fig.1 Trace of cone-cap yield function on the meridian pl ane for different relative density As large deformation is observed in powder compaction process, a hypoelastic-pl astic formulation is developed in the context of finite deformation plasticity. Constitutive equations are stated in unrotated frame of reference that greatly s implifies endochronic constitutive relation in finite plasticity. Constitutive e quations of the endochronic theory and their numerical integration are establish ed and procedures for determining material parameters of the model are demonstra ted. Finally, the numerical schemes are examined for efficiency in the model ling of a tip shaped component, as shown in Fig.2. Fig.2 A shaped tip component. a) Geometry, boundary conditio n and finite element mesh; b) density distribution at final stage of

ENDOCHRONIC ANALYSIS FOR COMPRESSIVE BUCKLING OF THIN－WALLED CYLINDERS IN YIELD REGION

The longitudinal compressive buckling of long and thin-walled cylinders in yield region is analyzed with the incremental and finite forms of the endochronic constitutive equation, respectively. The relations between the critical stress σ_(cr)versus the ratio of R (the radius) versus h (the thickness of the wall) are derived. The critical stress of the thin-walled cylinders made of abuminum alloys AMГ and 1T are analyzed and compared with the experimental data and the analytical results based on traditional theory of plasticity. It is seen that. except that the σ_(cr) of the cylinders made of 1Tpredicted by the finite form of the endochronic theory seems a little more conservative than that by traditional deformation theory of plasticity, in most cases, both forms of the endochornic constitutive equation provide more satisfactory results.

AN ENDOCHRONIC CONSTITUTIVE MODEL FOR RATE-DEPENDENT AND NONPROPORTIONAL CYCLIC PLASTICITY

The total stress response of material is decomposed into a sum of an equilibrium stress response and a non-equilibrium overstress response. Correspondingly, the rate-independent intrinsic time and the rate-dependent intrinsic time are defined respectively. Additional hardening functions for describing the isotropic and anisotropic nonproportional effects are assumed to be related to the accumulation of plastic strain component along the normal of equilibrium stress trajectory, in which the effects of geometry of the loading path are included. An endochronic constitutive model for rate-dependent, nonproportional cyclic plasticity is formulated and applied to simulate the stress responses of stainless steel XCrNil8. 9 for some typical loading programs at different loading rates. A comparison between predicted results and experimental ones by Haupt and Lion shows that the former are in agreement with the latter.

Cyclic behavior of soils and numerical analyses in cold regions and seismic zones

The solutions of boundary value problems involving strain-softening material property contain serious difficulties from both modeling of strain-localization and a viewpoint of numerical procedure. Mesh size-dependent hardening modulus is considered to alleviate the mesh size-dependency of the solution. The elasto-plastic soil model with kinematic hardening model considering the cumulative deformation by cyclic loading is developed. In finite element analyses, the dynamic relaxation method combined with the generalized return-mapping algorithm is applied to the static drained and un-drained tri-axial tests and plane strain tests. The cyclic behavior of retaining wall problems by freeze and thaw in cold regions is also analyzed. Finally the dynamic progressive failure analysis of rockfill dam is carried out.