Comparative study on finite elements with embedded discontinuities.

*(English)*Zbl 1166.74427Summary: The recently emerged idea of incorporating strain or displacement discontinuities into standard finite element interpolations has triggered the development of powerful techniques that allow efficient modeling of regions with highly localized strains, e.g. of fracture process zones in concrete or shear bands in metals or soils. Following the pioneering work of M. Ortiz, Y. Leroy and A. Needleman [Comput. Methods Appl. Mech. Eng. 61, 189–214 (1987; Zbl 0597.73105)], a number of studies on elements with embedded discontinuities were published during the past decade. It was demonstrated that local enrichments of the displacement and/or strain interpolation can improve the resolution of strain localization by finite element models. The multitude of approaches proposed in the literature calls for a comparative study that would present the diverse techniques in a unified framework, point out their common features and differences, and find their limits of applicability. There are many aspects in which individual formulations differ, such as the type of discontinuity (weak/strong), variational principle used for the derivation of basic equations, constitutive law, etc. The present paper suggests a possible approach to their classification, with special attention to the type of kinematic enhancement and of internal equilibrium condition. The differences between individual formulations are elucidated by analyzing the behavior of the simplest finite element – the constant-strain triangle (CST). The sources of stress locking (spurious stress transfer) reported by some authors are analyzed. It is shown that there exist three major classes of models with embedded discontinuities but only one of them gives the optimal element behavior.

Reviewer: Reviewer (Berlin)

##### Keywords:

Finite elements; Strain discontinuity; Displacement discontinuity; Cracking; Shear bands; Localization; Variational principles; Enhanced assumed strain; Stress locking
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\textit{M. Jirásek}, Comput. Methods Appl. Mech. Eng. 188, No. 1--3, 307--330 (2000; Zbl 1166.74427)

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