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A robust local arc-length method for multiscale problems

Akbari Rahimabadi, Ahmad, Kerfriden, Pierre ORCID:, Rabczuk, T. and Bordas, Stephane Pierre Alain ORCID: 2011. A robust local arc-length method for multiscale problems. Presented at: 19th UK Conference of the Association for Computational Mechanics in Engineering (ACME 2011), Edinburgh, UK, 5-6 April 2011. Published in: Laghrouche, O., El Kacimi, A., Woodward, P. and Medero, G. eds. Proceedings of the19th UK Conference of the Association for Computational Mechanics in Engineering (ACME 2011). Edinburgh: Heriot-Watt University, pp. 73-76.

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In this paper, a new local arc-length method has been introduced to follow the snap-back at the microscale as well as in the macroscale for a multiscale problem. First order multiscale computational homogenization (FE2) approach has been employed to study the behaviour of a one dimensional (1D) bar with cohesive cracks in the both scale. The macroscale material properties and constitutive equations are unknown. The local macroscopic constitutive response is determined by solving the related microscale Representative Volume Element (RVE). Each RVE has cohesive cracks whose damage parameters are a function of the displacement jump. The non-damaged part of RVEs are assumed to be linear elastic. In FE2 multiscale methods, the arc-length method is used in the macroscale and the displacement control method is used in the microscale, however, the displacement control cannot follow the snap back. The comparison of the new local arc-length method and conventional local arc-length is presented.

Item Type: Conference or Workshop Item (Paper)
Date Type: Publication
Status: Published
Schools: Engineering
Subjects: T Technology > TJ Mechanical engineering and machinery
Uncontrolled Keywords: multiscale ; local arc-length ; cohesive crack
Publisher: Heriot-Watt University
ISBN: 9780956595119
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Last Modified: 11 Mar 2023 02:12

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