The stresses your design encounters are usually some combination of tension, compression and shear.  What I call “normal” loads are these plus the common cases of flexure and torsion.  “Weird” loads are everything else, like stress concentrations, fatigue, thermal expansion, buckling, impact etc.  There are many other types of “weird” loads that get increasingly esoteric. 
One type of loading I thought we could talk about is triaxial stresses, which can put a small portion of an object at stresses beyond its yield point and produce plastic flow in a tiny portion of your design. This can happen where solids contact at concentrated points such as curved surfaces and rough surfaces.  Most surfaces are rough and the localized stresses are produced between particles where the peaks (asperities) and valleys of the particle surfaces interface.  This contact area is much smaller than would be provided by an apparent contact area of a perfectly smooth surface. Generally, the smallest of these asperity junctions contact one another under highly localized pressure and therefore deform plastically.  With further load however, the larger asperities engage each other and the contact area increases.  These asperities deform elastically because of the large contact area.  With many metals and brittle materials the mechanism of plastic deformation is an anisotropic “slip” in which planes of atoms slip over each other.  As the load increases, a critical shear stress is achieved causing plastic deformation within the zone of elastic deformation.  This can be common on curved surfaces like bearings.  What is strange is that the deformation is constrained by this sphere of plastic deformation that prevents further penetration of the stress into an object.  This cushion of mush can pop out of the surface and/or acts as a bullet proof vest for the underlying material.
To look at this further, consider one of the material yield criteria that can be applied to the asperity contact, based on Tresca’s maximum shear stress, which gives the yield point being one half the yield stress in tension or compression. Another criterion that can be applied here is the von Mises shear strain energy criterion.  This criterion is based on yielding occurring when the distortion energy rises to equal the distortion energy at yield in pure shear or tension.  This is commonly used in finite element analysis results so I'll put the equation here even though I can't get the math functions to work well (sorry) This criterion gives:
(Y^2)/3 = k^2 = (1/6){(σ1-σ2)^2 + (σ2-σ3)^2 + (σ3-σ1)^2}    
 Where,  σ1, σ2, σ3 are the principal stresses, k = shear, and Y = tension or compression. Therefore, the yield stress in pure shear is fifteen percent higher than the yield stress in simple tension than predicted by the Tresca criterion.
For axisymmetric contact of two spheres, the maximum shear stress occurs beneath the surface on the axis of symmetry.  The derivation will not be shown here, however by Hertzian analysis for a Poisson ratio of 0.3, half of the absolute value of σz- σr =  0.31 p at a depth of 0.48 a, where: p= maximum contact pressure and a = contact radius
 Therefore by the Tresca criterion, the yield value is given by,
 (p)   =  1.5(pm) = 3.2 k = 1.60 Y    
Where, pm =  mean contact pressure
 While von Mises gives: (p)y  = 2.8 k = 1.60 Y
Therefore, the load, W, to initiate yield is given by Hertzian analysis.  For a composite modulus of elasticity equal to a ratio of modulii of elasticity (I won't include the equations here).  You can then calculate
Wy =21.17 Y(R^2)[(Y/E)^2], where E is the composite modulus of two materials.
 The distribution of these stresses is interesting to note.  A spherical band of tensile hoop stress develops around the point of contact and prevents the expansion of the plastically deformed material.  This band produces a peak hoop stress at the surface, which delineates the tensile radial forces outside the band and the compressive stresses within it.  This stress distribution is the cause of surface cracking in non-hardening materials.  These stresses are a “weird” load because they produce a tiny area of plastic deformation that only occurs at the surface contacts and no where else.