ABAQUS Analysis User's Manual
11.3.3 Mohr-Coulomb plasticity
Product: ABAQUS/Standard
Mohr-Coulomb plasticity is defined by using the *MOHR COULOMB option together with the *MOHR COULOMB HARDENING option.
References
∙ *MOHR COULOMB
∙ *MOHR COULOMB HARDENING
∙ “Material library: overview,” Section 9.1.1
∙ “Inelastic behavior,09款讴歌mdx” 上海二手车交易Section 11.1.1
Overview
The Mohr-Coulomb plasticity model:
∙ is used to model materials with the classical Mohr-Coloumb yield criterion;
∙ 用于模拟具有典型的莫尔－库仑屈服准则的材料
∙ allows the material to harden and/or soften isotropically;
∙ 容许材料等向硬化和（或）软化
∙ uses a smooth flow potential that has a hyperbolic shape in the meridional stress
∙ 使用光滑流势，在子午面上为双曲线形自行车上路
∙ plane and a piecewise elliptic shape in the deviatoric stress plane;
∙ 在偏应力面上为平面和分段椭圆形
∙ is used with the linear elastic material model (“Linear elastic behavior,” Section 10.2.1); and
∙ 用于线弹性材料；
∙ can be used for design applications in the geotechnical engineering area to simulate material response under essentially monotonic loading.
∙ 可以用于地质工程中的设计，用来模拟材料在常量荷载下的相应
Elastic and plastic behavior www.autohome弹性和塑性行为
The elastic part of the response is specified on the *ELASTIC option. Linear isotropic elasticity is assumed.
弹性响应部分由*ELASTIC选项来指定。假定为线性等向弹性。
The hardening behavior of the material is specified using the *MOHR COULOMB HARDE
NING option. Isotropic cohesion hardening is assumed. The hardening curve must describe the cohesion yield stress as a function of plastic strain and, possibly, temperature and predefined field variables. In defining this dependence at finite strains, “true” (Cauchy) stress and logarithmic strain values should be given.
材料的硬化行为通过*MOHR COULOMH HARDENING选项来指定，假定为等向粘聚硬化。硬化曲线必须将粘聚屈服应力表达为塑性应变和（可能的话）温度及预设定场值的函数。在确定有限应变的可靠性时，必须指定真应力（柯西应力）和有效应变值。
Rate dependency effects are not accounted for in this plasticity model.
Usage: *MOHR COULOMB HARDENING
Yield criterion 屈服准则
标志4008The Mohr-Coulomb criterion assumes that failure occurs when the shear stress on any point in a material reaches a value that depends linearly on the normal stress in the same
plane. The Mohr-Coulomb model is based on plotting Mohr's circle for states of stress at failure in the plane of the maximum and minimum principal stresses. The failure line is the best straight line that touches these Mohr's circles (Figure 11.3.3–1).
莫尔－库仑准则假定破坏发生在材料中任意点的剪应力某一值，该值线性依赖于在该面的法向应力。莫尔－库仑模式基于莫尔圆来判断最大和最小主应力平面上的破坏应力状态。破坏线是与莫尔圆相切的直线。
Figure 11.3.3–1 Mohr-Coulomb failure model.
Therefore, the Mohr-Coulomb model is defined by
where is negative in compression. From Mohr's circle,
Substituting for and , multiplying both sides by , and reducing, the Mohr-Coulomb model can be written as
where
is half of the difference between the maximum principal stress, , and the minimum principal stress, (and is, therefore, the maximum shear stress),
is the average of the maximum and minimum principal stresses, and is the friction angle.
For general states of stress the model is more conveniently written in terms of three stress invariants as
where
is the slope of the Mohr-Coulomb yield surface in the – stress plane (see Figure 11.3.3–2), which is commonly referred to as the friction angle of the material and can depend on temperature and predefined field variables;
is the cohesion of the material; and
is the deviatoric polar angle defined as
and
is the equivalent pressure stress,
is the Mises equivalent stress,
is the third invariant of deviatoric stress,
is the deviatoric stress.
The friction angle controls the shape of the yield surface in the deviatoric plane as shown in Figure 11.3.3–2. The friction angle can range from . In the case of the Mohr-Coulomb model reduces to the pressure-independent Tresca model with a perfectly hexagonal deviatoric section. In the case of the Mohr-Coulomb model reduces to the “tension cut-off” Rankine model with a triangular deviatoric section and 电动车电池价格(this limiting case is not permitted within the Mohr-Coulomb model described here).
While using one-element tests to verify the calibration of the model, it should be noted that the ABAQUS/Standard output variables SP1, SP2, and SP3 correspond to the principal stresses , , and , respectively.
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