A generalized Mohr–Coulomb criterion implied by the revised Goodman–Cowin theory

In the present study, the constitutive relations derived in the revised Goodman–Cowin theory for granular matter are shown to imply a generalized Mohr–Coulomb criterion for impending flows. Due to the concept of microcontinuum and the incorporation of the internal friction into the expression of the Cauchy stress tensor, a constrained equilibrium stress state characterized by the Mohr–Coulomb criterion is yet obtained under uniform distributions of the grains.     

Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion

Conventional calculations of static and seismic active earth pressures of soils on a retaining wall are formulated assuming the soils obeying a linear Mohr–Coulomb yield criterion. However, experimental evidences show that the strength envelopes of almost all geomaterials are nonlinear in nature over a wide range of normal stresses. In this paper, the strength envelope of the backfill behind a retaining wall is considered to follow a nonlinear yield criterion. A simple method is proposed for calculating the static and seismic active earth pressures acting against a retaining wall using a nonlinear yield criterion. This method is based on the upper bound theorem of limit analysis. Both translational and rotational fracture surfaces are employed in the formulation for calculating active earth pressures. Quasi-static representation of earthquake effects using a seismic coefficient concept is adopted for seismic active earth pressure calculations. Instead of using directly the actual nonlinear yield criterion, a linear Mohr–Coulomb yield criterion, which is tangential to the nonlinear yield criterion, is used to formulate the active earth pressure problem as a classical nonlinear programming problem. A nonlinear sequential quadratic programming algorithm is used to search for the maximum solution. In order to assess the validity of the proposed method, values of active earth pressures for different values of seismic coefficients and nonlinear parameters in the yield criterion are calculated and compared with solutions obtained using an extended Rankine’s active earth pressure theory. For the case of static active earth pressure, the upper bound solutions using the present method with a translational fracture surface are equal to the extended Rankine’s theoretical solutions and are slightly smaller than those obtained using the present method with a rotational fracture surface. For the case of seismic active earth pressure, numerical results obtained using the present method with a rotational fracture surface is very close to the extended Rankine’s theoretical solutions. A study is conducted to investigate the effects of the parameters in the nonlinear yield criterion on the active earth pressures.     

Rolling friction as a viscoelastic dissipative process

The viscous additions to the stress tensor on the half–space surface over which a ball moves are calculated with the use of a viscosity (dissipative) tensor. The rolling friction force which corresponds to the Coulomb law and which is proportional to the velocity and which is simultaneously the lower estimate for the sliding friction force is found. Expressions for the radial and vertical displacements on the surface of an elastic half–space are given.     

Predicting ductile fracture of low carbon steel sheets: Stress-based versus mixed stress/strain-based Mohr–Coulomb model

Two distinct implementations of the Mohr–Coulomb failure model are used in conjunction with a non-associated quadratic plasticity model to describe the onset of fracture in low carbon steel sheets. The stress-based version corresponds to the original Mohr–Coulomb model in stress space. For the mixed stress/strain-based version, the Mohr–Coulomb failure criterion is first transformed into the space of stress triaxiality, Lode angle parameter and equivalent plastic strain and then used as stress-state dependent weighting function in a damage indicator model. Basic fracture experiments including tensile specimens of different notch radii and a punch test are performed to calibrate the material parameters of the respective models. Subsequently, the models are used to predict the crack initiation in a Hasek test and during the stamping of an anticlastic structure. Unlike for the calibration experiments, the loading history during stamping is highly non-linear. Both models can be calibrated with similar accuracy, but the strain-based model predicts the instant of onset of fracture with greater accuracy in the stamping experiment which is an advantage of the empirical damage accumulation rule.     

Localized viscoelastoplastic strain in mesovolume of heterogeneous medium under different loading types

The localized viscoelastoplastic strain in the mesovolume of heterogeneous media under quasi-static and dynamic loading is investigated. The generalized Bingham–Shwedov model is used; it consists of a combination of Dragon–Mroz's for elastoplasticity and Maxwell's model of viscoelasticity. Any variational finite-difference scheme for solving the quasi-static problem of elastoplastic yielding of a heterogeneous solid can be taken into account. A modified Lagrange's variance equation for analyzing the stress–strain state can be described by the non-symmetric stress tensor. Approximation of spatial derivatives is made by using the twofold partition of spatial domain in tetrahedronal or three-angular (in two-dimensional space) unit cell of mesh-work. Finite difference for deformation is made use of in two or three space dimensions and time. Results for heterogeneous medium with complex form and large number of interior surfaces are obtained for quasi-static and dynamics problems.     

Experimental investigations of the joint-mortar behaviour

An important failure mode of the masonry walls is the shearing process in joint mortar. In order to understand better this phenomenon, an experimental study is carried out on half brick couplet specimen. Load/Unload shear tests are performed to assess the type of the shear behaviour of the joint mortar. The cohesion and the internal friction angle are then derived from linear regression while assuming Mohr–Coulomb criterion. In particular, the influence of holes on the joint behaviour is studied by comparing results obtained with both solid and hollow bricks. In both cases, the experimental results show that there is not any stiffness degradation even in the softening regime. Actually, the shear modulus remains constant. Hence, the joint behaviour is considered to be elastoplastic, independently on the brick type. However, it seems that the presence of holes increases the stiffness but does not affect the internal friction angle of the joint mortar.     

Computational analysis of stress-based forming limit curves

This article, through computational analyses, examines the validity of using the stress-based and extended stress-based forming limit curves to predict the onset of necking during proportional loading of sheet metal. To this end, a model material consisting of a homogeneous zone and a zone that has voids (material inhomogeneity) is proposed and used to simulate necking under plane strain and uni-axial stress load paths. Results of the in-plane loading computations are used to construct a strain-based formability limit curve for the model material. This limit curve is transformed into principal stress space using the procedure due to Stoughton [Stoughton, T.B., 2000. A general forming limit criterion for sheet metal forming. International Journal of Mechanical Sciences 42, 1–27]. The stress-based limit curve is then transformed into equivalent stress and mean stress space to obtain an Extended Stress-Based Limit Curve (XSFLC). When subjected to three-dimensional loading, the model material is observed to display a variety of responses. From these responses, a criterion for the applicability of the XSFLC to predict the onset of necking in the model material when it is subjected to three-dimensional loading is obtained. In the context of straight tube hydroforming, to provide support for the use of the XSFLC, it is demonstrated that the criterion is satisfied.     

Proposition of a general yield function in geomechanics

A general smooth and convex yield function is proposed, able to model the particular behavior of geomaterials, particularly rock materials that are characterized by a linear or parabolic Mohr's envelope, and a particular shape in the deviatoric plane. These characteristics are defined by two functions: the equation of the criterion in the meridian plane and the extension ratio, which are integrated in a general equation ensuring convexity and smoothness of the yield function, whatever the characteristic functions. This expression is interesting, because it allows a straightforward development of a constitutive model based on triaxial tests, in extension and compression. It also allows the development of smooth criteria corresponding to the Mohr–Coulomb criterion and the H?k–Brown criterion, the latter typical of rock mechanics. To cite this article: S. Maïolino, C. R. Mecanique 333 (2005).     

一种横观各向同性强度准则及变换应力空间

考虑岩土介质在自然形成过程中产生的原生各向异性性质,将其简化为一种横观各向同性岩土材料.基于已提出的a强度准则,根据沉积面与有效滑移面在物理空间中位置的相互关系,采用两面的空间夹角作为度量岩土材料原生各向异性在加载条件下发挥强度作用的影响变量.并根据有效滑移面的物理概念,当沉积面与有效滑移面夹角越大,则摩擦特性潜力发挥的越充分,此时对应更高的强度应力比,反之则对应越小的强度应力比.基于上述思想,建立了考虑原生各向异性的强度应力比公式,将其用于修正a准则,进而得到了横观各向同性a准则公式.采用上述横观各向同性a准则公式向各向同性Von-Mises准则公式转换的变换思路,在横观各向同性a准则公式基础上,推导得到了变换应力公式,该公式可由横观各向同性应力空间转变为各向同性应力空间,利用所提出的变换应力方法,可方便的将传统的在偏平面上以Von-Mises准则为基础的二维模型转换为可考虑原生各向异性的三维模型.通过对岩土材料的强度以及真三轴条件下的应力应变关系试验数据预测,验证了所提的横观各向同性a准则及其变换应力公式的有效性及适用性.      

On the non-oscillation criterion for multiplicative anisotropic plasticity at large simple shear deformation

The criterion for non-oscillatory stresses under monotonic large simple shear deformation in the context of multiplicative anisotropic plasticity is discussed. In particular, evolving anisotropy combined with a Hill type of yield criterion is considered. It is shown that a sufficient, but not necessary, criterion for a non-oscillatory stress is ellipticity of the first Piola–Kirchhoff stress. Loss of ellipticity corresponds to a critical value h_cr of the generalized plastic modulus. Similarly, the absence of limit points on the stress–strain relation motivates an alternative criterion in terms of a critical value h_sh  h_cr. Finally, this criterion is demonstrated analytically as well as numerically for an important class of models with evolving anisotropy of the saturation type.     

强度折减有限元在堤防稳定分析中的应用研究

采用强度折减有限元法,研究非均值堤防塑性区的开展特征和失稳破坏过程,并根据堤防应力场分布和临界滑动面的形成来分析堤岸整体失稳破坏的机理。结果表明:把强度折减有限元应用到非均质土层的堤防边坡稳定分析,在理论上、数值模拟实现上都是可行的; 有限元静力平衡和位移计算不收敛作为堤防边坡整体失稳的标志,同时考察滑移面上某些特征点的位移与荷载增量的关系、参考土体内坡脚向坡顶上方贯通的塑性滑动带的形成,可以准确判别堤防边坡失稳破坏状态; 此外,堤防失稳时的应力场分布特征表明,有必要应用张拉-剪切复合屈服准则,以真实反映堤防边坡的临界滑动面形成机理。     

Electroconvective stability of a weakly conducting liquid

In inhomogeneous electric fields, at sufficiently high field strengths, a weakly conducting liquid becomes unstable and is set in motion [1–4]. The cause of the loss of stability and the motion is the Coulomb force acting on the space charge formed by virtue of the inhomogeneity of the electrical conductivity of the liquid [4–13]. This inhomogeneity may be due to external heating [4–6], a local raising of the temperature by Joule heating [2, 7, 8], and nonlinearity of Ohm's law [9–13]. In the present paper, in the absence of a temperature gradient produced by an external source, a condition is found whose fulfillment ensures that the influence of Joule heating on the stability can be ignored. Under the assumption that this condition is satisfied, a criterion for stability of a weakly conducting liquid between spherical electrodes is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–142, July–August, 1979.     

Wedging an Orthotropic Body by a Rectangular Wedge of Finite Length

Galin's method is used to derive equations that relate the basic parameters of the problem on wedging an orthotropic space by a rigid rectangular wedge. To eliminate the stress singularity at the wedging crack tips, a Leonov–Panasyuk–Dugdale prefracture zone is assumed to exist at the crack front. The equations are derived using the COD criterion     

Coupled modeling of damage growth and permeability variation in brittle rocks

This paper presents a coupled model for anisotropic damage and permeability evolution by using a micro–macro approach. The damage state is represented by a second order tensor. The evolution of damage is determined from a crack propagation criterion. The free enthalpy function of cracked material is obtained by using micromechanical considerations. It is assumed that cracks exhibit normal aperture which is coupled with the crack growth due to asperities of crack faces. By using Darcy’s law for macroscopic fluid flow and assuming laminar flow in microcracks, the overall permeability of the RVE is obtained by a volume averaging procedure taking into account crack aperture in each orientation.     

Sufficient Discrete—Integral Criterion of Rupture Strength

The behavior of the atomic structure in the vicinity of the crack tip is modeled. The loss of stability and postcritical deformation of a triatomic cell in a close–packed atomic layer in tension are studied. For macrocracks in single crystals, the concept of the generalized Burgers vector is introduced. A sufficient discrete—integral strength criterion is proposed for normal–rupture cracks in the case where the stress fields have a singular component. In accordance with Novozhilov's hybrid model, this criterion is formulated with the use of a new class of solutions that differs from solutions used in formulating the classical sufficient strength criterion. In the limiting case where the energy characteristics of the postcritical deformation of the cell can be ignored, the sufficient criterion proposed admits a limiting passage to the necessary criterion. The critical loads calculated by means of the sufficient criterion differ substantially from those determined with the use of the necessary criterion; this makes it possible to describe the Rehbinder effect.     

The interplay between boundary conditions and flow geometries in shear banding: Hysteresis, band configurations, and surface transitions

We study shear banding flows in models of wormlike micelles or polymer solutions, and explore the effects of different boundary conditions for the viscoelastic stress. These are needed because the equations of motion are inherently non-local and include “diffusive” or square-gradient terms. Using the diffusive Johnson–Segalman model and a variant of the Rolie-Poly model for entangled micelles or polymer solutions, we study the interplay between different boundary conditions and the intrinsic stress gradient imposed by the flow geometry. We consider prescribed gradient (Neumann) or value (Dirichlet) of the viscoelastic stress tensor at the boundary, as well as mixed boundary conditions in which an anchoring strength competes with the gradient contribution to the stress dynamics. We find that hysteresis during shear rate sweeps is suppressed if the boundary conditions favor the state that is induced by the sweep. For example, if the boundaries favor the high shear rate phase then hysteresis is suppressed at the low shear rate edges of the stress plateau. If the boundaries favor the low shear rate state, then the high shear rate band can lie in the center of the flow cell, leading to a three-band configuration. Sufficiently strong stress gradients due to curved flow geometries, such as that of cylindrical Couette flow, can convert this to a two-band state by forcing the high shear rate phase against the wall of higher stress, and can suppress the hysteresis loop observed during a shear rate sweep.     

The evolution of Hooke's law due to texture development in FCC polycrystals

Initially isotropic aggregates of crystalline grains show a texture-induced anisotropy of both their inelastic and elastic behavior when submitted to large inelastic deformations. The latter, however, is normally neglected, although experiments as well as numerical simulations clearly show a strong alteration of the elastic properties for certain materials. The main purpose of the work is to formulate a phenomenological model for the evolution of the elastic properties of cubic crystal aggregates. The effective elastic properties are determined by orientation averages of the local elasticity tensors. Arithmetic, geometric, and harmonic averages are compared. It can be shown that for cubic crystal aggregates all of these averages depend on the same irreducible fourth-order tensor, which represents the purely anisotropic portion of the effective elasticity tensor. Coupled equations for the flow rule and the evolution of the anisotropic part of the elasticity tensor are formulated. The flow rule is based on an anisotropic norm of the stress deviator defined by means of the elastic anisotropy. In the evolution equation for the anisotropic part of the elasticity tensor the direction of the rate of change depends only on the inelastic rate of deformation. The evolution equation is derived according to the theory of isotropic tensor functions. The transition from an elastically isotropic initial state to a (path-dependent) final anisotropic state is discussed for polycrystalline copper. The predictions of the model are compared with micro–macro simulations based on the Taylor–Lin model and experimental data.