Stress distribution around an elliptic hole in a plate with ‘implicit’ and ‘explicit’ non-local models

Understanding the effects of defects is crucial due to their deliberate or unintentional presence in many materials. Classical theory elasticity may not be best candidate describe behaviour structures with comparable size its underlying material organization, as it lacks internal scale parameters. In this respect, present study focused on comparison two well-established non-local theories; ‘implicit/weak’, micropolar (Cosserat), and ‘explicit/strong’, Eringen’s model, that classical model highlight differences a common case study: infinite plates weakened an elliptic hole different aspect ratios, under remote uniaxial tension. Fraction coefficient, providing identical stress concentration factor plates, searched for two-phase local/nonlocal model. Results are obtained by adopting finite element method quadrilateral elements. To account discontinuities within domain, modified using geodetical distance instead Euclidean one, computationally very efficient procedure developed exploit symmetric character problem without losing long-range interactions. The results suggest effects, reducing maximum stress, become more pronounced increasing geometric discontinuity quantified ratio ellipse which also influences equivalency between characteristic lengths models.