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An analysis of embedded weak discontinuity approaches for the finite element modelling of heterogeneous materials

Abstract : This paper analyses in detail the use of the Embedded Finite Element Method (E-FEM) to simulate local material heterogeneities. The work starts by a short review on the evolution of weak discontinuity models within the E-FEM framework to discuss how they account for the presence of multiple materials within a single element structure. A theoretical basis is introduced through some mathematical weak discontinuity definitions and the Hu-Washizu variational principle, for then establishing a set of requirements for retaining variational and kinematic consistency for any weak discontinuity enhancement proposal. From a general definition of a displacement enhancement field, two particular enhancement functions are derived by considering different consistency requirements: one which has been typically used in previous works and other which truly possesses variational consistency. A discussion is held on enhancement stability properties and the impact to global finite element solution processes. In the end, numerical simulations are made to assess the performance of each of these enhancements on the task of modelling a classical bi-material layered 3D tension problem and a more realistic heterogeneous sample having spherical inclusions of different radii. The final discussion evaluates both model performance and ease of implementation.
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https://hal.archives-ouvertes.fr/hal-03778041
Contributor : Emmanuel Roubin Connect in order to contact the contributor
Submitted on : Thursday, September 15, 2022 - 12:27:38 PM
Last modification on : Saturday, September 17, 2022 - 3:05:23 AM

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Alejandro Ortega Laborin, Emmanuel Roubin, Yann Malecot, L. Daudeville. An analysis of embedded weak discontinuity approaches for the finite element modelling of heterogeneous materials. Computers & Structures, 2022, 273, ⟨10.1016/j.compstruc.2022.106894⟩. ⟨hal-03778041⟩

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