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Stress in a material body may be due to multiple physical causes, including external influences and internal physical processes. Some of these agents (like gravity, changes in temperature and phase , and electromagnetic fields) act on the bulk of the material, varying continuously with position and time.
The formula to calculate average shear stress τ or force per unit area is: [1] =, where F is the force applied and A is the cross-sectional area.. The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.
The stress tensor which automatically obeys the equilibrium equation may now be ... The Airy stress function is a special case of the ... (physics) Elastic modulus ...
This equation implies that the stress vector T (n) at any point P in a continuum associated with a plane with normal unit vector n can be expressed as a function of the stress vectors on the planes perpendicular to the coordinate axes, i.e. in terms of the components σ ij of the stress tensor σ.
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
The hoop stress equation for thin shells is also approximately valid for spherical vessels, including plant cells and bacteria in which the internal turgor pressure may reach several atmospheres. In practical engineering applications for cylinders (pipes and tubes), hoop stress is often re-arranged for pressure, and is called Barlow's formula .
Stress-strain curve: Plot the calculated stress versus the applied strain to create a stress-strain curve. The slope of the initial, linear portion of this curve gives Young's modulus. Mathematically, Young's modulus E is calculated using the formula E=σ/ϵ, where σ is the stress and ϵ is the strain. Shear modulus (G)
The modified power law equation then becomes: = ¯ where A, Q and m can all be explained by conventional mechanisms (so 3 ≤ m ≤ 10), and R is the gas constant. The creep increases with increasing applied stress, since the applied stress tends to drive the dislocation past the barrier, and make the dislocation get into a lower energy state ...