Privileged optical arrangements for higher order approximations with caustics (Q1116741)

An improved method for the evaluation of the stress intensity factor (SIF) in cracked plates, considering large initial curve caustics, is developed. For this purpose the Muskhelishvili complex potential \(\phi\) (z) was approximated by a four-term series expansion. The influence of the higher than the first terms resulted in the variation of the geometry of caustic as the radius of its initial curve was increased. The introduction of higher terms in the definition of the \(\phi\) (z)- function resulted in a higher accuracy in the formation of shape of caustics and yielded satisfactory results for the SIF evaluated by the caustic even for larger shapes of initial curves. The method is then convenient for applications in nonlinear problems of elasticity and plasticity.