A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models

By Jason M. Tyrus, M. Gosz, E. Desantiago. 2007

89 citations recorded by the source corpus.

Recent advances in computational speed have resulted in the ability to model composite materials using larger representative volume elements (RVEs) with greater numbers of inclusions than have been previously studied. Imposing periodic boundary conditions on very large RVEs can mean enforcing thousands of constraint equations. In addition, a periodic mesh is essential for enforcing the constraints. The present study investigates a method that uses a local implementation of the constraints that does not adversely affect the computational speed. The present study demonstrates the method for two-dimensional triangular and square RVEs of periodically-spaced regular hexagonal and square arrays of composite material containing fibers of equal radii. To impose the boundary conditions along the edges, this study utilizes a cubic interpolant to model the displacement field along the matrix edges and a linear interpolant to model the field along the fiber edges. It is shown that the method eliminates the need for the conventional node-coupling scheme for imposing periodic boundary conditions, consequently reducing the number of unknowns to the interior degrees of freedom of the RVE along with a small number of global parameters. The method is demonstrated for periodic and non-periodic mesh designs.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/459e0822c410e8e035baa07efc0288a7e1fbac41

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

Citations in the corpus

Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation (2012, background): “[16] implemented the periodic boundary condition for periodic composite materials, for arbitrary non-periodic mesh by enforcing a linear displacement field at intersection of fibers and RVE sides and a cubic displacement field at”
Computational homogenization of cellular materials (2014, methodology): “For these non–conformal meshes, some methods are available to enforce the periodic boundary condition in first–order schemes, such as the master/slave approach [44], the weak periodicity [41], the local implementation [45] and in a more general way as the interpolation polynomial interpolation [42].”