Relationships between hardness, elastic modulus, and the work of indentation

The work done during indentation is examined using dimensional analysis and finite element calculations for conical indentation in elastic-plastic solids with work hardening. An approximate relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work in indentation is found. Consequently, the ratio of hardness to elastic modulus may be obtained directly from measuring the work of indentation. Together with a well-known relationship between elastic modulus, initial unloading slope, and contact area, a new method is then suggested for estimating the hardness and modulus of solids using instrumented indentation with conical or pyramidal indenters.

Scaling approach to conical indentation in elastic-plastic solids with work hardening

We derive, using dimensional analysis and finite element calculations, several scaling relationships for conical indentation in elastic-plastic solids with work hardening. Using these scaling relationships, we examine the relationships between hardness, contact area, initial unloading slope, and mechanical properties of solids. The scaling relationships also provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They may also be helpful as a guide to numerical and finite element calculations of indentation problems.

Plot Erosion Model Using Gray Relational Analysis Method

The main factors affecting interrill erosion-including runoff discharge, rainfall intensity, mean flow velocity, and slope gradient-were analyzed by using a gray relational analysis. An equation for interrill erosion was derived by coupling this analysis with dimensional and regression analyses. The values of erosion rates predicted by this equation were in good agreement with experimental observations.

水位变化引起分层边坡滑坡的实验研究

通过对分层的边坡在水位变化时滑坡的模拟实验,考察了分层坡体的滑坡模式、坡体变形、破坏和渗流引起的滑坡,重点考察了水位涨落速度对坡体稳定的影响,以及坡面从产生张拉裂缝直到形成滑面的整个过程,并对这类滑坡中的现象给出了定性解释.最后用有限元对实验坡体进行了应力和位移的静力场分析,计算结果与实验结果基本一致.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

Experimental Investigation and Numerical Simulation on the Effect of Fissure Water Pressure in Vertical Sliding Surface

This paper studies the effect of fissure water pressure in different fractures on the critical angle of landslide by laboratory investigation and numerical simulation in order to understand the mechanisms of fissure water pressure on landslide stability. Laboratory observations show that the effect of fissure water pressure on the critical angle of landslide is little when the distance between water-holding fracture and slope toe is three times greater than the depth of fissure water. These experimental results are also simulated by a three-dimensional face-to-face contact discrete element method. This method has included the fissure water pressure and can accurately calculate the critical angle of jointed slope when fissure water pressure in vertical sliding surface exists. Numerical results are in good agreement with experimental observations. It is revealed that the location of water-holding structural surface is important to landslide stability. The ratio of the distance between water-holding fissure and slope toe to the depth of fissure water is a key parameter to justify the effect of fissure water pressure on the critical angle of landslide.

A Simulation Model for Unified Interrill Erosion and Rill Erosion on Hillslopes

A mathematical model was developed for simulating runoff generation and soil erosion on hillslopes. The model is comprised of three modules: one for overland flow, one for soil infiltration, and one for soil erosion including rill erosion and interrill er

各向异性非线性强度条件下的边坡稳定性

解释了土体强度各向异性、非线性的物理本质,结合常规直剪试验、三轴试验结果,在前人工作基础上建立了边坡稳定性分析中强度各向异性、非线性的描述方法,其中特别提出了一个各向异性函数.基于Janbu普遍条分法(GPS),运用SPREADSHEET模板程序,提出了一个能将各向异性、非线性强度准则逐点等效到Mohr-Coulomb直线强度准则处理上的迭代方法,准确方便地获得了非线性强度下的边坡稳定性分析.最后的算例展示了方法的使用过程.

边坡稳定分析的三维Spencer法

将边坡稳定分析中的二维Spencer法拓展到了三维。该方法对所有条块满足力的平衡以及整体力矩平衡，克服了其他方法中只适用对称问题的缺点，不需已知滑动方向，还可根据滑面的几何特征，进一步得到各条块局部的稳定性系数及其潜在的滑动方向。此外，给出了该方法的实现步骤，其算法的收敛性也较好。最后以不对称问题为算例，并与其他文献中的结果进行比较，验证了该方法的可行性和有效性。

What is indentation hardness?

Using dimensional analysis and finite element calculations, we derive simple scaling relationships for loading and unloading curve, contact depth, and hardness. The relationship between hardness and the basic mechanical properties of solids, such as Young's modulus, initial yield strength, and work-hardening exponent, is then obtained. The conditions for 'piling-up' and 'sinking-in' of surface profiles during indentation are determined. A method for estimating contact depth from initial unloading slope is examined. The work done during indentation is also studied. A relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work is discovered. This relationship offers a new method for obtaining hardness and elastic modulus. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and 'indentation size effect' is established.

Application of Three-Dimensional Discrete Element Face-to-Face Contact Model with Fissure Water Pressure to Stability Analysis of Landslide in Panluo Iron Mine

Three-dimensional discrete element face-to-face contact model with fissure water pressure is established in this paper and the model is used to simulate three-stage process of landslide under fissure water pressure in the opencast mine, according to the actual state of landslide in Panluo iron mine where landslide happened in 1990 and was fathered in 1999. The calculation results show that fissure water pressure on the sliding surface is the main reason causing landslide and the local soft interlayer weakens the stability of slope. If the discrete element method adopts the same assumption as the limit equilibrium method, the results of two methods are in good agreement; while if the assumption is not adopted in the discrete element method, the critical phi numerically calculated is less than the one calculated by use of the limit equilibrium method for the same C. Thus, from an engineering point of view, the result from the discrete element model simulation is safer and has more widely application since the discrete element model takes into account the effect of rock mass structures.

含弱透水夹层饱和砂土坡体滑坡的实验研究

通过含有细砂夹层的饱和砂土在冲击载荷下的滑坡模拟实验，考察了土层参数不均匀的坡面的滑坡模式、坡体变形、破坏和不均匀渗流引起的滑坡，特别是散体粒径不均匀时出现的含水层和通道与滑坡的关系、各控制参数（载荷的和土体的）对滑坡的影响，并对这类滑坡中的现象给出了定性解释。

三峡库区寨坝变形体的渗流变形有限元耦合分析

三峡库区寨坝民德小学变形体是山前坡积物、崩积物以及滑坡堆积物等的混杂体，中部存在孤立的块碎石含水层，地下水位较高。公路开挖引起了远场集中通道排水疏干和开挖面附近卸载，导致了不均匀变形破坏产生。本文给出了这种开挖卸载与排水疏干共同作用下，边坡饱和-非饱和渗流与变形耦合的有限元分析方法。研究表明，集中通道排水造成了坡体大范围的孔隙水压力下降，从而导致不均匀变形和地面开裂；其中通道排水诱发的不均匀变形将随着排水通道的封堵和地下水位的回升而停止，而纯粹的开挖卸载主要影响开挖面附近的土体变形。这一典型实例所揭示的机理模式，可以解释工程施工区通常出现的因开挖和开挖引起的排水所诱发的远近变形破坏现象的实质。

Two-Dimensional Kinematic Wave Model of Overland-Flow

A two-dimensional kinematic wave model was developed for simulating runoff generation and flow concentration on an experimental infiltrating hillslope receiving artificial rainfall. Experimental observations on runoff generation and flow concentration on irregular hillslopes showed that the topography of the slope surface controlled the direction and flow lines of overland flow. The model-simulated results satisfactorily compared with experimental observations. The erosive ability of the concentrated flow was found to mainly depend on the ratio of the width and depth of confluent grooves.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic–plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a “hold” period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and “hold-at-the-maximum-indenter-displacement” for determining the instantaneous modulus using spherical indenters.