Geometric Representation of Modified Forms of Seven Important Failure Criteria
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32920
Geometric Representation of Modified Forms of Seven Important Failure Criteria

Authors: Ranajay Bhowmick


Elastoplastic analysis of a structural system involves defining failure/yield criterion, flow rules and hardening rules. The failure/yield criterion defines the limit beyond which the material flows plastically and hardens/softens or remains perfectly plastic before ultimate collapse. The failure/yield criterion is represented geometrically in three/two dimensional Haigh-Westergaard stress-space to facilitate a better understanding of the behavior of the material. In the present study geometric representations in three and two-dimensional stress-space of a few important failure/yield criterion are presented. The criteria presented are the modified forms obtained due to the conditional solutions of the equation of stress invariants. A comparison of the failure/yield surfaces is also presented here to obtain the effectiveness of each of them and it has been found that for identical conditions the Rankine’s criterion gives the largest values of limiting stresses.

Keywords: Deviatoric plane, failure criteria, geometric representation, hydrostatic axis, modified form.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 333


[1] R. Bhowmick, “Solution of Cubic Equation of Stress Invariants for a Particular Condition”, IRJET, vol. 07, pp. 4423 – 4425, 2020.
[2] H. M. Westergaard, “Theory of Elasticity and Plasticity”, John Wiley & Sons, 1952.
[3] W. F. Chen and A. F. Saleeb, “Constitutive Equations for Engineering Materials”, John Wiley & Sons, 1982.
[4] G. C. Nayak and O. C. Zienkiewicz, “Convenient forms of stress invariants for plasticity”, ASCE, Journal of Structural Division, vol. 98, pp. 949 – 954, 1972.
[5] W. Lode 'Versucheueber den Einfluss der mitt lerenHauptspannung auf das Fliessen der Metalle Eisen Kupfen und Nickel', Z, Physik, vol. 36, pp. 913-39, 1926.
[6] R. Bhowmick, “Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories”, International Journal of Mechanical and Mechatronics Engineering, Vol 14 (12), pp. 508 – 511, 2020.
[7] W. J. M. Rankine, “A Manual of Applied Mechanics”, Richard Griffin & Company, 1958.
[8] R. Chatterjee, “Mathematical Theory of Continuum Mechanics”, Narosa Publishing House.
[9] R. von Mises, “Mechanics of Solid Bodies in the Plastically Deformed State”, Nachr. d. Kgl. Ges. Wiss. Göttingen, Math.-phys. Klasse 4 (1913), pp. 582-592.
[10] A. Nadai, “Plastic Behaviour of Metals in the Strain – Hardening Range Part I”, Journal of Applied Physics, vol. 8, pp. 205 – 213, 1937.
[11] S.P. Timoshenko and D.H. Young, “Elements of Strength of Materials”, Affiliated East – West Press.
[12] D. C. Drucker and W. Prager, “Soil Mechanics and Plastic Analysis or Limit design”, Quarterly of Applied Mechanics, vol. 10, pp. 157 – 165, 1952.