Stress is a measure of the local concentration of mechanical force. Consider a body subjected to equal and opposite forces on two faces (Fig.1). If these forces act perpendicular to a face (ie parallel to its face normal), as shown, the stress σ (sigma) is termed a normal stress. This may be tensile (positive) or compressive (negative).
\nUnder simple uniaxial tension or compression, the von Mises stress is equal to the applied stress, while the hydrostatic stress is equal to one third of it. The von Mises stress is always positive, while the hydrostatic stress can be positive or negative. It is not appropriate to think of the von Mises stress as being “tensile”, as one would if it were a normal stress (with a positive sign). It’s effectively a type of (volume-averaged) shear stress. Shear stresses do not really have a sign, but it’s conventional to treat them as positive, as indeed is done for the von Mises stress.
\nIt’s also possible to identify deviatoric and hydrostatic components of the (plastic) strain state. Analogous equations to those above are used to obtain these values. The von Mises strain is often termed the “equivalent plastic strain”. Again, it always has a positive sign, but this does not mean that it is a “tensile” strain. The hydrostatic plastic strain, on the other hand, always has a value of zero. This follows from the fact that plastic strain does not involve a change in volume. (This is not true of elastic strains, which do in general involve a volume change.)
\nMany loading situations create complex stress fields that are not only multi-axial, but also vary with position in the component (sample). These situations can be modelled using the Finite Element Method (FEM), in which the component is divided up into a large number of separate volume elements, with the stress-strain relationship concerning being satisfied in all of them. This can be done using a simple (uniaxial) relationship, provided the von Mises stress and the von Mises strain are used in it.
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