Implicit Numerical Integration of Nonsmooth Multisurface Yield Criteria in the Principal Stress Space

There are several different yield surfaces of Drucker-Prager yield criterion which corresponds to Mohr-Coulomb yield criterion in principal stress space. The different yield surfaces are determined by parameters in Drucker-Prager criterion. The influence of the different parameters on computational results is discussed in the paper, and the use of the equivalent Drucker-Prager criterion to Mohr-Coulomb criterion is suggested when elastoplastic analysis is performed in engineering problems.

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Positive and Negative Failure-Shears in Orthotropic Materials

Journal of Reinforced Plastics and Composites ◽

10.1177/073168449201100103 ◽

1992 ◽

Vol 11 (1) ◽

pp. 32-55 ◽

Cited By ~ 5

Author(s):

P. S. Theocaris

Keyword(s):

Principal Stress ◽

Failure Criterion ◽

Fiber Composite ◽

Pure Shear ◽

Failure Surface ◽

Loading Path ◽

Orthotropic Materials ◽

Stress Space ◽

Elliptic Paraboloid ◽

Principal Stress Space

Failure predictions of off-axis loaded fiber composite laminae are given according to the elliptic paraboloid failure criterion for anisotropic solids [1]. The failure condition assumes that for any anisotropic solid a safe triaxial loading path exists, along the hydrostatic compression, and thus the failure surface must be open-ended. By appropriately formulating the failure criterion, it is shown that the geometric interpretation of the failure surface in the principal stress space is an elliptic paraboloid (EPFS) whose axis of symmetry is parallel to the hydrostatic axis in the principal stress space. Because of the shape and position of the EPFS, the intersections by principal stress planes corresponding to loadings of off-axis laminae of a fiber composite are represented by ellipses whose origins are displaced from the origin of the stress reference frame. This fact creates unequal shear yield stresses in the positive and negative sense clearly manifested in a pure shear failure loading. The predictions of the above criterion for plane stress failure loadings of laminae, and especially for pure shear induced failures, are compared with existing experimental data for various fiber composites and are shown to be in satisfactory agreement.

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Failure surfaces in principal stress space

Journal of Polymer Science Part C Polymer Symposia ◽

10.1002/polc.5070320113 ◽

2007 ◽

Vol 32 (1) ◽

pp. 239-267 ◽

Cited By ~ 57

Author(s):

N. W. Tschoegl

Keyword(s):

Principal Stress ◽

Stress Space ◽

Principal Stress Space

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Mögliche Deutungen quadratischer Fließbedingungen bei Isotropie und Anisotropie / Physical Interpretations of Isotropic and Anisotropic Yield-Conditions

Zeitschrift für Naturforschung A ◽

10.1515/zna-1975-0813 ◽

1975 ◽

Vol 30 (8) ◽

pp. 996-1000

Author(s):

A. Troost ◽

J. Betten

Keyword(s):

Shear Stress ◽

Principal Stress ◽

Yield Criterion ◽

Physical Significance ◽

Stress Space ◽

Physical Explanation ◽

Principal Stress Space ◽

Anisotropic Yield Criterion ◽

The Difference ◽

Yield Conditions

Abstract The paper introduces shear stress quantities, which are the difference of two stress tensors, the actual one and one produced by rotating the axes. This quantities have physical significance. In the vectorial representation in the principal stress space and the principal shear stress space the paper give some interesting relations. The authors observe that Hill′s anisotropic yield criterion can be derived from their shear stress quantities by introducing a measure tensor and gave a physical explanation to Hill′s condition.

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