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A coupled finite element approach for the modelling of composites with fibres possessing fibre‐bending stiffness
Author(s) -
Asmanoglo Tobias,
Menzel Andreas
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610138
Subject(s) - finite element method , boundary value problem , stiffness , bending , bending stiffness , partial differential equation , materials science , field (mathematics) , constitutive equation , mathematical analysis , composite material , mathematics , structural engineering , engineering , pure mathematics
The algorithmic implementation of a constitutive model for fibre‐reinforced materials with fibre‐bending stiffness, in addition to the classical directional contributions of the fibres, is presented. Based on theoretical investigations presented in [1], the numerical solution of the underlying non‐linear system of coupled partial differential equations by means of a mixed‐type multi‐field finite element approach is discussed. To this end, additional field variables are introduced to approximate higher‐order gradients which enter the proposed energy function of the extended continuum and, accordingly, introduce a size effect into the model. Concluding, representative boundary value problems are solved to analyse the basic properties of the model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)