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This paper investigates the capacity of solid finite elements with independent interpolations for displacements and strains to address shear, membrane and volumetric locking in the analysis of beam, plate and shell structures. The performance of the proposed strain/displacement formulation is compared to the standard one through a set of eleven benchmark problems. In addition to the relative performance of both finite element formulations, the paper studies the effect of discretization and material characteristics. The first refers to different solid element typologies (hexahedra, prisms) and shapes (regular, skewed, warped configurations). The second refers to isotropic, orthotropic and layered materials, and nearly incompressible states. For the analysis of nearly incompressible cases, the B-bar method is employed in both standard and strain/displacement formulations. Numerical results show the enhanced accuracy of the proposed strain/displacement formulation in predicting stresses and displacements, as well as producing locking-free discrete solutions, which converge asymptotically to the corresponding continuous problems.

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.