Why are sharp contours stress concentrators?

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SUMMARY

Sharp contours act as stress concentrators due to abrupt geometrical changes that cause stress flow to concentrate at discontinuities. This phenomenon can be quantitatively analyzed using elasticity theory and plate analysis, which involve complex partial differential equations. Alternatively, the finite element method (FEM) can be employed for numerical analysis, although it may lead to infinite stress values in certain scenarios. Understanding these principles is crucial for effective stress analysis in engineering applications.

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intuitively it makes sense but what is the scientific explanation
 
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Stress concentrations are due to abrupt geometrical changes that cause the flow of stress to concentrate (
visualize stress contours tightly packed at the discontinuity). From a theoretical scientific point of view, these stress concentration factors can be calculated using elasticity theory and plate analysis and a lot of messy partial differential equations. Or by computer finite element approach (caution, this sometimes leads to infinities).
 

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