von Mises yield criterion

About: von Mises yield criterion is a research topic. Over the lifetime, 4374 publications have been published within this topic receiving 82642 citations. The topic is also known as: Von Mises stress.

Bernstein - von Mises Theorem for growing parameter dimension

Abstract: This paper revisits the prominent Fisher, Wilks, and Bernstein -- von Mises (BvM) results from different viewpoints. Particular issues to address are: nonasymptotic framework with just one finite sample, possible model misspecification, and a large parameter dimension. In particular, in the case of an i.i.d. sample, the mentioned results can be stated for any smooth parametric family provided that the dimension \(p \) of the parameter space satisfies the condition "\(p^{2}/n \) is small" for the Fisher expansion, while the Wilks and the BvM results require "\(p^{3}/n \) is small".

Exact integration of constitutive equations in elasto - plasticity

Abstract: A unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity, assuming the total strain-rate direction to be constant. This unified approach includes all previous exact integration procedures as special cases and, in addition, some new closed-form solutions are derived for combined kinematic and isotropic hardening. Special emphasis is laid on combined kinematic and isotropic hardening for von Mises' material and on isotropic hardening for Mohr-Coulomb and Tresca materials.

A class of generalized mid‐point algorithms for the Gurson–Tvergaard material model

Abstract: SUMMARY We investigate the generalized mid-point algorithms for the integration of elastoplastic constitutive equations for the pressure-dependent Gurson-Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric parts, a formula for explicitly calculating the consistent tangent moduli with the generalized mid-point algorithms is derived for the GursonTvergaard model. The generalized mid-point algorithms, together with the consistent tangent mo.duli, have been implemented into ABAQUS via the user material subroutine. An analytical solution of the GursonTvergaard model for the plane strain tension case is given and the performances of the generalized mid-point algorithms have been assessed for plane strain tension and hydrostatic tension problems and compared with the exact solutions. We find that, in the two problems considered, the generalized mid-point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid-point algorithm (a = 0.5) the most accurate one. Considering the extra non-symmetrical property of the consistent tangent moduli of the algorithms with a < 1, the Euler backward algorithm (a = 1) is, perhaps, the best choice. The integration of constitutive equations is the most important part of any numerical scheme employed for the analysis of elastoplastic problems. Efficient schemes which are both fast and accurate are needed. The algorithms employed for the integration of constitutive equations can be classified into two groups: those based on an explicit technique and those based on an implicit technique. Recently, implicit algorithms, falling within the category of return mapping algorithms, have become more and more popular.'-' Within the framework of operator splitting methodology, Simo and Ortiz6 have proposed a new class of return mapping algorithms applicable to a general class of plastic and viscoplastic constitutive models. In recent years, there has been growing interest in the analysis of plastic flow localization and fracture behaviour of ductile porous metals. Unlike the conventional von Mises model, however, the yield models for porous solids exhibit a dependence on hydrostatic pressure. It is now well established that the fracture of ductile metals results from the initiation, growth and coalescence of microscopic voids. In order to accurately predict the limit to ductility of structural metals, it is necessary to have a constitutive theory which properly incorporates the inelastic straining resulting from the nucleation and growth of voids. Gurson'** has developed a theory of dilatational plasticity for this purpose, which has been modified by Tvergaardg* lo in order to