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The angle of the intersection with the green plane is the red plane's apparent dip in the northward direction . When measuring or describing the attitude of an inclined feature, two quantities are needed. The angle the slope descends, or dip, and the direction of descent, which can be represented by strike or dip direction. [4]
The Lode angle varies with respect to the middle eigenvalue of the stress. There are many definitions of Lode angle that each utilize different trigonometric functions: the positive sine, [ 5 ] negative sine, [ 6 ] and positive cosine [ 7 ] (here denoted θ s {\displaystyle \theta _{s}} , θ ¯ s {\displaystyle {\bar {\theta }}_{s}} , and θ c ...
Schmid's Law states that the critically resolved shear stress (τ) is equal to the stress applied to the material (σ) multiplied by the cosine of the angle with the vector normal to the glide plane (φ) and the cosine of the angle with the glide direction (λ). Which can be expressed as: [2] =
The angle θ = ε + 90° is used for a mathematical description in a spherical coordinate system. For the approximation of a flat earth – which is usual for airborne radar with short to medium range – the grazing angle and the depression angle can be assumed to be equal γ = ε and the incident angle is β = 180° – θ.
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.
Mohr's circle is used to determine which principal stresses will produce this combination of shear and normal stress, and the angle of the plane in which this will occur. According to the principle of normality the stress introduced at failure will be perpendicular to the line describing the fracture condition.
Stress components on a 2D rotating element. Example of how stress components vary on the faces (edges) of a rectangular element as the angle of its orientation is varied. Principal stresses occur when the shear stresses simultaneously disappear from all faces. The orientation at which this occurs gives the principal directions.
The Schmid Factor for an axial applied stress in the [] direction, along the primary slip plane of (), with the critical applied shear stress acting in the [] direction can be calculated by quickly determining if any of the dot product between the axial applied stress and slip plane, or dot product of axial applied stress and shear stress ...
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