A unified criterion for yielding behavior of metallic glasses

The yield behavior of metallic glasses was studied. Three yield criteria, including von Mises yield criterion, Mohr-Coulomb yield criterion and the unified yield criterion were used to describe the yield phenomena of the metallic glasses. Two classes of the experimental data were chosen to draw the yield loci using the unified yield criterion. It is shown that the unified yield criterion can be used to describe the yield behavior of the metallic glasses no matter whether the metallic glasses show strength- different effect or non-strength-different effect. Almost all the widely accepted yield criteria are the subsets of the unified yield criterion if the intermediate principle stress and/or the intermediate principle shear stress are not considered at all.

Analysis of plane strain bending of a strain hardening curved beam based on unified yield criterion

The analysis of plane strain elastic-plastic bending of a linear strain hardening curved beam with a narrow rectangular cross section subjected to couples at its end is conducted based on a unified yield criterion. The solutions for the mechanical properties of plane strain bending are derived, which are adapted for various kinds of non-strength differential materials and can be degenerated to those based on the Tresca, von Mises, and twin-shear yield criteria. The dependences of the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane on different yield criteria and Poisson’s ratios are discussed. The results show that the influences of different yield criteria and Poisson’s ratio on the two critical bending moments, the radii of the interfaces between the elastic and plastic regions and the radial displacements of the points at the symmetrical plane of the curved beam are significant. Once the value of bis obtained by experiments, the yield criterion and the corresponding solution for the materials of interest are then determined.

Ultimate end bearing capacity of rock-socketed pile based on generalized nonlinear unified strength criterion

In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end beating capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.

Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines

In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion （USC）. An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USC- based analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By discussion, it is found that for the end-capped pipes, the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes, the burst pressure is independent of the specific form of the strength criterion and strength difference in tension and compression.

An explicit formulation of the macroscopic strength criterion for porous media with pressure and Lode angle dependent matrix under axisymmetric loading

This paper aims to propose an explicit formulation of the macroscopic strength criterion for porous media with spherical voids.The matrix is assumed rigid and perfectly plastic with yield surface described by the three-parameter strength criterion,which is Lode angle and pressure dependent and capable of accounting for distinct values of the uniaxial tensile strength,uniaxial compressive strength(UCS)and equal biaxial compressive strength(eBCS).An exact upper bound of the macroscopic strength is derived for porous media subjected to purely hydrostatic loading.Besides,an estimate of the macroscopic strength profile of porous media under axisymmetric loading is obtained in parametric form.Moreover,a heuristic strength criterion in explicit form is further developed by examining limit cases of the parametric strength criterion.The developed strength criteria are assessed by finite-element based numerical solutions.Compared with the parametric strength criterion which involves cumbersome functions,the heuristic one is convenient for practical applications.For specific values of the matrix’s strength surface,the proposed heuristic strength criterion can recover the well-known Gurson criterion.The present work also addresses the effect of the ratio of matrix’s eBCS to UCS on the macroscopic strength of porous media.For matrix with distinct values of eBCS and UCS,neglecting the difference between eBCS and UCS would result in an underestimation of the macroscopic strength,especially when the pressure is large.

Unified analytical solutions for a circular opening based on non-linear unified failure criterion

Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.

Analysis of Penetration Model for Geo-Material by Rigid Projectile

Based on the cylindrical cavity expansion theory, a plastic-damage-elastic model is proposed for the penetration problem of geo-material. In the model, the unified strength criterion (Yu, 1991) is adopted as the failure criterion. The distributions of the radial stress and velocity are analyzed. According to the Newton's second law, a series results of the final penetration depth and the impedance load are obtained to different parameter b, when a rigid projectile normally impacts and penetrates a semi-infinite geo-material target with an impact velocity of 300-1200 m/s. By comparing with the test data available, it appears that the method can be used in analyzing the final depth and the impedance load of a rigid projectile penetrating into a semi-infinite target with different impact velocities.

Modified unified co-rotational framework with beam,shell and brick elements for geometrically nonlinear analysis

The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis.This paper presents a modified co-rotational framework,unified for beam,shell,and brick elements.A unified zero-spin criterion is proposed to specify the local element frame,whose origin is always located at the centroid.Utilizing this criterion,a spin matrix is introduced,and the local frame is invariant to the element nodal ordering.Additionally,the projector matrix is redefined in a more intuitive way,which is the derivative of local co-rotational element frame with respect to the global one.Furthermore,the nodal rotation is obtained with pseudo vector and instantaneous rotation,under a high-order accurate transformation.The resulting formulations are achieved in unified expression and thus a series of linear elements can be embedded into the framework.Several examples are presented to demonstrate the efficiency and accuracy of the proposed framework for large displacement analysis.