Homogeneous Continuous Medium Research Articles

Secondary development of finite-element method based on the calculation of scale effect of soil particles

Soil, regarded as a homogeneous continuous medium in the classical soil mechanics, actually comprises mineral particles of different scales and has the basic characteristics of a heterogeneous discontinuous medium. During the deformation, particles of different scales contained in the soil demonstrate diverse deformation states and produce scale effects. At the same time, the rotation of the particles significantly changes the deformation and strength characteristics of the soil and produces a rotation effect. However, the current finite-element calculations are lacking in the calculation methods that take into account the effects of scale and rotation. In the previous work, one of the authors of this paper introduced an intrinsic scale factor and established a constitutive relationship according to the particle scale effect. Based on the constitutive formula of soil particle scale effect, the UEL subroutine of ABAQUS is used to express particle rotation by node rotation, and secondary development of the finite-element calculation program is carried out to solve the specific calculation problem of soil deformation scale effect caused by particle rotation. The results of a verification example involving a round hole display that the stress concentration factor of the hole decreases to a stable value with the increase of the intrinsic scale factor of the particles, which conforms to the influence mechanism of soil particle deformation and basically verifies the reliability of the secondary development program. Furthermore, using the secondary development program to calculate the stability of a slope illustrates that the shear band uncertainty and the element sensitivity in slope instability analysis are eliminated by considering the particle scale effect of the soil.

Development of a model of a homogeneous continuous medium based on the material with defects in the form of hollows

In a body of the billet received by casting, inevitably there are defects accompanying this process: blisters, hollows and other discontinuities affecting the deformation and strength properties of the metal. The experience showed that direct calculation of the stress-strain state by the FEM of the body with a defective structure requires the use of supercomputer-level computing power. A medium with multiple randomly distributed discontinuities was schematized by a regular structure formed by a set of elements in the form of a regular tetrahedron with spherical hollows at its vertices. The proposed technique makes it possible to create the model of a continuous homogeneous medium, which is equivalent in its deformation properties to the original discontinuous material. Using this approach was got a power-law approximation of the stress-strain curve of the model medium. The last one represents the basic characteristic of the material, both under single-shot loading and (if we take into account the cyclic hardening) in analyzing the kinetics of the stress and strain fields’ under repeatedly-variable loading. The discontinuity of the material was fixed using the Kolmogorov’s deformation criterion of ductile fracture. This criterion was applied in evaluating the limit state of the valve chamber under operating conditions.

Finite element simulations of the behavior of piled‐raft foundations using a multiphase model

SUMMARYFinite element simulations of the behavior of a piled raft foundation have been carried out using a multiphase model conceived as an improved homogenization approach. According to this model, the ground reinforced by a group of piles is treated as a homogeneous continuous medium. In this approach, no specific interface elements are necessary to account for the mechanical interaction between the piles and the ground: this interaction is described by means of two scalar parameters, one stiffness parameter and one which can easily be derived from the maximum ground‐pile friction. The implementation of the model into a finite element code provides an efficient tool for the analysis of the influence of the pile number or length on the settlement and bearing capacity of a square piled raft foundation and of the way the total applied load is shared between the raft and the piles. Results are compared with a standard 3D finite element analysis. The comparison highlights the fact that the proposed approach remains to be improved to account for tip resistance. Copyright © 2012 John Wiley & Sons, Ltd.

Calculation of dipole fields at interstices of rare-earth metals

An effective method for calculating the sum of dipole magnetic fields of lattice sites is developed using the threefold axial symmetry and performing summation over hexagonal planes. The values of fields in octahedral and tetrahedral interstices of an hcp lattice are determined for spiral structures of heavy RE metals and for samarium. It is shown that the absence of an experimentally observed jump in the dipole field at the point of ferro-antiferromagnetic transition in the disposition is due to the small angle of rotation of the spiral magnetic structure. The problem of interpretation of the Lorentz macroscopic field is discussed on the basis of calculation of microscopic fields in a homogeneous continuous medium.

Texture Transition, Micro Shear Bands and Heterogeneous Plastic Strain in F.C.C. and B.C.C. Metals in Rolling

During the plastic deformation of a metallic polycrystal many kinds of heterogeneous deformation are often observed, both on an intergranular scale and inside the grains. The heterogeneities of the plastic intragranular strains are associated with the latent hardening and with internal stresses.In order to deal with this problem, it is assumed that some regions of simple glide exist inside the grains, separated by plane interfaces. These interfaces are assumed to be habit planes, separating the domain of simple glide and a homogeneous continuous medium, whose deformation is the one imposed on the polycrystal.The compatibility relations between the domain of simple glide and the imposed deformation, enable for determination of the gliding amplitude, normal to the habit plane, and the rotation of the crystal lattice inside this domain.In the case of rolling for F.C.C. and B.C.C. metals, we have analyzed the spin of the crystal lattice in the form of a distribution function. We observe sources and sinks which correspond to the stable orientations, shown by the orientation distribution function. The comparison between these calculations and classical data of rolling texture analysis indicates that a certain number of observed components are due to deformation inhomogeneities, as suggested previously.The comparison of the orientation of the habit planes shows that there exists a definite relation between habit planes and micro shear bands.

Note on the macroscopic elastic constants of materials with a foam-like structure

It is assumed that the materials considered consist of a large number of small elements so that on a macroscopic scale the behaviour approaches that of homogeneous continuous media. Assuming that the small elements follow prescribed strains it is possible to find an expression for the specific energy from which the average elastic constants can be derived.