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Strain-Space Plasticity: Current StatusB. M. Dawari

Lecturer in Applied Mechanics

Stress-space plasticity conceptualized by Naghdi and co-researchers is an alternative formulation and considered to be superior in many ways to conventional stress-

space plasticity. This article is intended to highlight the merits of strain-space formulation as well as current research status.

1. INTRODUCTION

The yield surface in the stress-space can be expressed as ....(1)

However, for any yield surface in stress-space there corresponds a unique yield surface in strain-space

....(2)

2. CONSTITUTIVE RELATIONS IN STRAIN-SPACE

1. Flow rule: ....(3)

where is a proportionality factor which can be determined by the consistency condition.

2. Stress-strain relation: ....(4)

....(5)

3. Plastic loading ....(6)

3. CURRENT STATE OF RESEARCH IN STRAIN-SPACE PLASTICITY

Table 1: Strain-Space Plasticity: Current Research Status

Investigator Investigation Highlights

Naghdi ,Trapp (1975) Concept of strain-space plasticity theory presented.

Han , Chen (1986) General formulation of the strain-space

Simo , Ju (1987) Continuum elasto-plastic damage models

Dawari, Pandey (2007) Implementation for Cyclic plasticity

Dawari (2009) Implementation of three-dimensional plasticity coupled with damage

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4. APPLICATIONS OF STRAIN-SPACE PLASTICITY

A thin square plate of size 210 mm x 210mm subjected to uniaxial stress is analysed with 100 eight noded isoparametric elements. The material properties are E = 210

GPa, = 0.30.

Figure 1. Response of Thin Plate Subjected to Uni-axial TensionFigure 1. Response of Thin Plate Subjected to Uni-axial Tension

It is demonstrated that [4] all three types of beahviour strain-hardening, perfect plasticity and strain-softening can be captured with a single set of constitutive equations.

5. SUMMARY

The current status of strain-space plasticity based on Iliushin postulate is reviewed here. The merits of this formulation are highlighted. It is advocated that strain-space

formulation has great potential in engineering applications particularly for damage-coupled analysis.

References

[1] Naghdi, P. M., and Trapp, J. A. (1975), The significance of formulating plasticity theory with reference to loading surfaces in strain space, Int. J.

Eng. Sci. 13, pp. 785 797.

[2] Han, D. J., and Chen, W. F. (1986), Strain space plasticity formulation for hardening softening materials with elasto-plastic coupling, Int. J. Solids

Structures 22 (8), pp. 935 950.

[3] Dawari, B. M., and Pandey, P.C. (2008), Three-dimensional strain-space plasticity: formulation and implementation, International Conference on

Multiscale Modelling and Simulation, ICMMS-08, Bangalore India.

[4] Dawari, B. M. (2009), Non-linear finite element implementation of strain-space plasticity coupled with damage, Ph.D. thesis (submitted), Indian

Institute of Science, Bangalore India.

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