Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach

E. Artioli; G. Elefante; A. Sommariva; M. Vianello; E. Artioli; G. Elefante; A. Sommariva; M. Vianello

doi:10.3934/mine.2024021

Mathematics in Engineering

2024, Volume 6, Issue 4: 510-535. doi: 10.3934/mine.2024021

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Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach

1.
Engineering Department "Enzo Ferrari", University of Modena and Reggio Emilia, Modena 41121, Italy
2.
Department of Mathematics "Tullio Levi-Civita", University of Padova, Padova 35121, Italy

Received: 07 December 2023 Revised: 03 June 2024 Accepted: 13 July 2024 Published: 29 July 2024

The paper presents an augmented curvilinear virtual element method to determine homogenized in-plane shear material moduli of long-fibre reinforced composites in the framework of asymptotic homogenization method. The new virtual element combine an exact representation of the curvilinear computational geometry for complex fibre cross section shapes through an innovative two-dimensional cubature suite for NURBS-like polygonal domains. A selection of representative numerical tests supports the accuracy and efficiency of the proposed approach for both doubly periodic and random fibre arrangement with matrix domain.
- material homogenization,
- fibre reinforced composite,
- low-cardinality algebraic cubature,
- PI (Positive Interior) rules,
- curvilinear polygons,
- NURBS,
- virtual element method
Citation: E. Artioli, G. Elefante, A. Sommariva, M. Vianello. Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach[J]. Mathematics in Engineering, 2024, 6(4): 510-535. doi: 10.3934/mine.2024021

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Abstract

The paper presents an augmented curvilinear virtual element method to determine homogenized in-plane shear material moduli of long-fibre reinforced composites in the framework of asymptotic homogenization method. The new virtual element combine an exact representation of the curvilinear computational geometry for complex fibre cross section shapes through an innovative two-dimensional cubature suite for NURBS-like polygonal domains. A selection of representative numerical tests supports the accuracy and efficiency of the proposed approach for both doubly periodic and random fibre arrangement with matrix domain.

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