In the present paper, a novel hybrid approach with complex and conformal mapping functions is proposed for the first time.This strain-based approach is based on the special trial functions and the assumed natural strain (ANS) theory, which provides a unified framework for solving fracture problems. In the utilized method, the proposed super-element is divided into perforated and solid domains. For the perforated domain, Muskhelishvili-Kolosov potential function is employed to simulate the perforated discontinuity. For the solid domain, the higher-order strain field is assumed as the enriched interpolation functions. Moreover, the rigid body terms are imposed into the kinematic variables to enhance the convergence ability and the element performance. Numerical examples demonstrate that the proposed element (PHSM20) produces high precision results for both displacement and stresses.

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