Mohr-Coulomb material

The soil is considered as Mohr-Coulomb material. Table 1 presents the material properties of the soils used in this analysis. 

Ceramics which, when indented, undergo the mechanisms listed above, with the exception of cracking, can be grouped as Mohr-Coulomb materials for which five parameters—E, a-y, v, H, and a—are needed to calculate hardness. Here E, a-y, and i> have their usual meaning while H is the stress hardening rate and a is the densification factor. Clearly if indentation causes densification then a and H must be closely linked. 

Yield in Mohr-Coulomb materials follows a criterion which is the sum of stress terms and the Mises criterion ... 

The most common failure criterion for granular materials is the Mohr-Coulomb failure criterion. Mohr introduced his theory for rupture in materials in 1910. According to his theory, the material fails along a plane only when a critical combination of normal and shear stresses exists on the failure plane. This critical combination, known as the Mohr-Coulomb failure criterion, is given by... 

The Mohr-Coulomb failure criterion can be recognized as an upper bound for the stress combination on any plane in the material. Consider points A, B, and C in Fig. 8.4. Point A represents a state of stresses on a plane along which failure will not occur. On the other hand, failure will occur along a plane if the state of stresses on that plane plots a point on the failure envelope, like point B. The state of stresses represented by point C cannot exist since it lies above the failure envelope. Since the Mohr-Coulomb failure envelope characterizes the state of stresses under which the material starts to slide, it is usually referred to as the yield locus, YL. 

To close the problem, constitutive relations of powders must be introduced for the internal connections of components of the stress tensor of solids and the linkage between the stresses and velocities of solids. It is assumed that the bulk solid material behaves as a Coulomb powder so that the isotropy condition and the Mohr-Coulomb yield condition may be used. In addition, og has to be formulated with respect to the other stress components. 

For these calculations, three different material models were investigated a linear elastic, an elasto-brittle, and elasto-plastic ubiquitous joint model. The ubiquitous joint, elasto-plastic model, is defined by a two-dimensional yield criterion, composed of two Mohr-Coulomb criteria, along two predefined directions characterised by their normal vectors ni and n2. 

LaRC 03 failure criterion The LaRC 03 failure criterion [12] consists of a family of six criteria. It is an extension of the Puck [11] and Hashin [13] failure criteria. Like the Puck criterion, it focuses on the fiacture plane that is determined by maximizing the Mohr—Coulomb stresses. In the LaRC 03 criterion, failure due to matrix compression is the result of local interaction of shear stresses on a fracture plane. This perspective comes from soil mechanics situafions where the compression strength is different than the tension strength. It is parficularly useful in cases where, on a certain plane in the material, there are both normal and shear stresses acting. The interaction line that... 

FLAG has several built-in material behavior models. The failure of rock material is assumed to follow the Mohr-Coulomb criterion as illustrated in Fig. 4 which is used for materials that yield when... 

Finn (1966) presented an analysis of the earthquake stability of an infinite cohesive slope shown in Figure 11.22. This analysis used a Bingham model incorporated in a Mohr-Coulomb failure criteria. Based on this analysis the minimum acceleration coefficient ky to cause yielding of the slope in a c-( ) material is given by the following equation ... 

The idea of plastic yielding is also applied to granular materials, such as soils and powders. In this case, the shear stress required for deformation depends on the packing density, and the particle shape and surfaee characteristics. The shear resistance is commonly described by the Mohr-Coulomb yield criterion, i.e.. 

For a uniaxial compression test, determine the plane on which the maximum shear stress will occur for a material that obeys the Mohr-Coulomb yield criterion. Suggest an approach for measuring the material parameters (d>, Tq) in the Mohr-Coulomb yield criterion. (Hint construct the Mohr s circle (see Fig. 2.23) for various values of the normal stress.)... 

Assumptions of the model (a) plane stress state, (b) The surrounding rocks are uniform and elastic isotropic materials, (c) the fault is assumed as contact element with no thickness., and (d) Mohr-Coulomb failure criterion is chosen for rocks. 

Overburden of the tunnel 100.0 m The rock mass is considered as the idealized elastoplastic material with the Mohr-Coulomb yield criterion, and all the materials of support system are treated as elastic material. The initial stress field of analysis zone is calculated as self-weight... 

The Geogrid was modeled as linearly elastic-perfectly plastic material with Mohr-Coulomb failure criterion. The axial stiffness (J) and the tensile strength (T) were needed in the program and taken J = 620 kN/m and T = 70 kN/m, respectively. The interaction coefficient between the geogrid and cohesive backfill was taken 0.7. 

The geotechnical material was shear failure mainly, and it was adapted to Mohr-Coulomb criterion. Its shear strength was determined by the cohesion (c) and internal friction angle ( ). The limit condition might be reached by decreased the shear strength of material in SRM. It was expressed as follows ... 

The failure criterion of soils was the Mohr-Coulomb equivalent area circle yield criterion that was advanced in reference (Xu G.Ch. and Zheng Y.R., 1990). This criterion was suitable for computing in the 3D space problems, and the material constants a and k were shown in formula (16) and formula (17). 

In this limit analysis of pile foundation, the ANSYS software was used. The finite element model was 1/4 body. The strength criterion of pile body material was linear elastic model, and the criterion of soils was Mohr-Coulomb equivalent area circle criterion. The mechanics characteristic of pile-soil interface was simulated by contact element. The contact surface behavior on the side of pile was the form of Rough. The contact surface behavior on pile toe was the form of No separation. 

To obtain the proper initial geostatic stress state of the slope, static calculation is required before the dynamic analysis (Itasca Consulting Group, 1999). Two procedures are followed in the static calculation (a) set relevant mechanical parameters and take elastic model as material constitutive model, and then make the slope model balanced in gravity field (b) take Mohr-Coulomb model as the material constitutive model (Yan et al., 2011) and reset cohesion and tensile strength to their initial value, and then rebalance the model. This is just the slope model on which the dynamic load will be applied. The contour plot of initial vertical geostatic stresses in the slope (Figure 3) reflects the vertical stress state in which no dynamic load is applied on the slope. 

Model materials the rock and soil mass in the slope is divided into two layers (Figure 2), and the relevant physical and mechanical parameters are listed in Table 1. The parameters are inverted from the drilling data, geophysical data and microtremor in situ testing result of the slope site, so as to guarantee the accuracy of numerical simulation. Mohr-Coulomb plastic model built in the software... 

It is therefore common to assume that the state variables that describe the rapid deformation response of granular materials would border on the parameters that describe the behavior of fluids and Coulomb type dissipation of energy (static). In view of the above it is common to find that the theories governing granular flow are formulated around the assumption of a continuum similar in some regard to viscous fluids however, the equilibrium states of the theories are not states of hydrostatic pressure, as would be in the case of fluids, but are rather states that are specified by the Mohr-Coulomb criterion (Cowin, 1974). The advantage of continuum formulations over alternative particulate (stochastic) formulations is that use of continuum is more capable of generating predictive results. Mathematically one... 

The yield stress of a material is a measured stress level that separates the elastic and inelastic behavior of the material. The magnitude of the yield stress is generally obtained from the results of a uniaxial test. However, the stresses in a structure are usually multiaxial. A measurement of yielding for the multiaxial state of stress is called the yield criterion. For example, the Mohr-Coulomb criterion, the Buyukozturk criterion, and the Drucker-Prager criterion are common yield criteria for concrete, and the von Mises criterion is the widely used yield criterion for steel. 

The standard criteria for yielding developed in elasticity theory for metals, namely the Tresca, von Mises or Mohr-Coulomb, do not apply quantitatively to polymeric materials because these criteria ignore the effect of the hydrostatic component of the stress tensor. This is important in determining the yield behaviour of polymers, not neces-... 

Alternatively, where plastie flow is strongly localized into intense dilatant shear bands, as in the cases of cohesionless granular media (Coulomb 1773 Mohr 1900), the S-D effect has been viewed as the effect of a normal stress On acting across the shear plane and thereby increasing or decreasing the shear resistance of such bands through a friction effect on the shearing material. This alternative explanation results in a Coulomb Mohr-type unsymmetrical yield condition similar to the behavior of cohesionless sand or soils, where, however, the linear dependence of the shear resistance is on is continuous around zero in the form of... 

Figure 11.12 Mohr circle diagram for two states of stress that produce yield in a material satisfying the Tresca yield criterion (a) and the Coulomb yield criterion (h)...

The static failure theory for brittle materials has historically been the Coulomb-Mohr failure theory. A simple definition of a brittle material is that the ultimate compressive strength is greater than the tensile strength, >5 and the yield strengths are approximately eqnal to the nltimate strengths in tension and compression, = S and Cast iron, rock, and concrete are typical materials that are analyzed by... 

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