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

Abstract

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