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Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science by Mark F. Horstemeyer

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2.2 STRESS

In continuum mechanics, stress is a measure of the force over an area of a surface within a deformable body on which the forces act. The notion of stress assumes a continuum point, which is typically larger than atomistic distances but less than the total size of a body. Because the loaded, deformable body is assumed as a continuum, the internal forces are distributed continuously within the volume of the material body; that is, the stress distribution in the body is expressed as a piecewise continuous function of space coordinates and time. The definition of stress has its origin from the work of Cauchy [2] in which the stress σ was defined from the traction force t operating on a body tj = σijni. It is interesting that Isaac Newton’s laws of forces were defined approximately 100 years before Cauchy first introduced the notion of stress in 1827. We often discuss stress and forces in the same breath when discussing strength of materials, but the connection historically did not occur for quite a long time. This original definition of stress by Cauchy will be described in this section and essentially represented a continuum point without respect to the smaller length scale items within the continuum. For example, for a metal, the grain size is ignored. Hence, from a purely continuum perspective, Cauchy defined the stress state, which was crucial since investigators were trying to determine how structures fractured. Force, by itself, was not a good indicator. When Cauchy ...

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