Application of periodic boundary conditions on multiple part finite element meshes for the meso-scale homogenization of textile fabric composites

Both micro- and meso-scale structures are involved in the analyses of many composite materials such as filament-wound tubes. In this paper, a unified approach for applying periodic boundary conditions to micro/meso-scale repeated unit cell models in the finite element analysis is presented. As an application example, a two-scale analysis of a ±θ helical filament-wound tube is provided.

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A numerical homogenization technique for unidirectional composites using polygonal generalized finite elements

Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications ◽

10.1177/14644207211046320 ◽

2021 ◽

pp. 146442072110463

Author(s):

Murilo Sartorato

Keyword(s):

Finite Element ◽

Finite Elements ◽

Boundary Conditions ◽

Computational Efficiency ◽

Periodic Boundary ◽

Deformation Gradient ◽

Reaction Force ◽

Periodic Boundary Conditions ◽

Unit Cell ◽

Unit Cells

The present study proposes a computational methodology to obtain the homogenized effective elastic properties of unidirectional fibrous composite materials by using the generalized finite-element method and penalization techniques to impose periodic boundary conditions on non-uniform polygonal unit cells. Each unit cell is described by a single polygonal finite element using Wachspress functions as base shape functions and different families of enrichment functions to account for the internal fiber influence on stresses and strains fields. The periodic boundary conditions are imposed using reflection laws between two parallel opposing faces using a Lagrange multiplier approach; this reflection law creates a distributed reaction force over the edges of the [Formula: see text]-gon from the direct application of a given deformation gradient, which simulates different macroscopic load cases on the macroscopic body the unit cell is part of. The methodology is validated through a comparison with results for similar unit cells found in the literature and its computational efficiency is compared to simple cases solved using a classic finite-element approach. This methodology showed computational advantages over the classic finite elements in both computational efficiency and total number of degrees of freedom for convergence and flexibility on the shape of the unit cell used. Finally, the methodology provides an efficient way to introduce non-circular fiber shapes and voids.

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Consistent application of periodic boundary conditions in implicit and explicit finite element simulations of damage in composites

Composites Part B Engineering ◽

10.1016/j.compositesb.2018.12.023 ◽

2019 ◽

Vol 168 ◽

pp. 254-266 ◽

Cited By ~ 15

Author(s):

D. Garoz ◽

F.A. Gilabert ◽

R.D.B. Sevenois ◽

S.W.F. Spronk ◽

W. Van Paepegem

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Periodic Boundary ◽

Periodic Boundary Conditions ◽

Finite Element Simulations ◽

Explicit Finite Element ◽

Implicit And Explicit ◽

Consistent Application

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The Energetics of Dislocation-Obstacle Interactions by 3-D Quasicontinuum Simulations

MRS Proceedings ◽

10.1557/proc-578-155 ◽

1999 ◽

Vol 578 ◽

Cited By ~ 1

Author(s):

Kedar Hardikar ◽

R. Phillips

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Point Defects ◽

Periodic Boundary ◽

Boundary Effect ◽

Periodic Boundary Conditions ◽

Boundary Effects ◽

Quasicontinuum Method ◽

Finite Element Calculations ◽

Infinite Extent

AbstractThe goal of this work is to study the interaction of dislocations with local obstacles to glide such as point defects, precipitates and other dislocations. The quasicontinuum method is used as the basis of this study. It is demonstrated that two types of boundary effects are of concern in the calculation of hardening parameters using finite sized simulation cells. A recently developed technique to incorporate periodic boundary conditions in the quasicontinuum method is used to eliminate surface effects which were present in earlier implementations and to simulate a dislocation of infinite extent interacting with an array of obstacles. The second type of boundary effect is due to the boundary conditions on the lateral boundaries. A method based on finite element calculations is proposed for quantifying the effect of lateral boundaries in these simulations. Preliminary results for the validation of the method are presented as well as a simulation of the interaction between a conventional edge dislocation in Al with an array of clusters of Ni atoms.

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