Abstract
Strain localization analysis for orthotropic-associated plasticity in cohesive–frictional materials is addressed in this work. Specifically, the localization condition is derived from Maxwell’s kinematics, the plastic flow rule and the boundedness of stress rates. The analysis is applicable to strong and regularized discontinuity settings. Expanding on previous works, the quadratic orthotropic Hoffman and Tsai–Wu models are investigated and compared to pressure insensitive and sensitive models such as von Mises, Hill and Drucker–Prager. Analytical localization angles are obtained in uniaxial tension and compression under plane stress and plane strain conditions. These are only dependent on the plastic potential adopted; ensuing, a geometrical interpretation in the stress space is offered. The analytical results are then validated by independent numerical simulations. The B-bar finite element is used to deal with the limiting incompressibility in the purely isochoric plastic flow. For a strip under vertical stretching in plane stress and plane strain as well as Prandtl’s problem of indentation by a flat rigid die in plane strain, numerical results are presented for both isotropic and orthotropic plasticity models with or without tilting angle between the material axes and the applied loading. The influence of frictional behavior is studied. In all the investigated cases, the numerical results provide compelling support to the analytical prognosis.
Highlights
Published: 18 April 2021Orthotropic Materials such as wood and masonry have been traditionally used in construction and are very much used today
This paper addresses the analytical determination of the orientation of slip lines in orthotropic elasto-plastic cohesive–frictional materials by extending the strain localization analysis developed in previous works
A general form of the considered yield criteria is given that allows closed-form solutions for the orientation of the slip lines in 2D plane strain and plane stress conditions
Summary
Orthotropic Materials such as wood and masonry have been traditionally used in construction and are very much used today. The authors [44,45] used Maxwell’s compatibility condition and stress boundedness to predict analytically the orientation of shear discontinuities for isotropic von Mises and orthotropic Hill elasto-plastic models. This paper addresses the analytical determination of the orientation of slip lines in orthotropic elasto-plastic cohesive–frictional materials by extending the strain localization analysis developed in previous works. The objectives are fourfold: (i) to extend the strain localization analysis to orthotropic elasto-plastic cohesive–frictional materials; (ii) to derive analytically localization angles in plane stress and plane strain conditions for these models;. (iii) to verify these analytical results via independent numerical simulations; and (iv) to investigate the influence of plastic material properties on strain localization in orthotropic cohesive–frictional materials.
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