Special-purpose elements to impose Periodic Boundary Conditions for multiscale computational homogenization of composite materials with the explicit Finite Element Method

Abstract

A novel methodology is presented to introduce Periodic Boundary Conditions (PBC) on periodic Representative Volume Elements (RVE) in Finite Element (FE) solvers based on dynamic explicit time integration. This implementation aims at overcoming the difficulties of the explicit FE method in dealing with standard PBC. The proposed approach is based on the implementation of a user-defined element, named a Periodic Boundary Condition Element (PBCE), that enforces the periodicity between periodic nodes through a spring-mass-dashpot system. The methodology is demonstrated in the multiscale simulation of composite materials. Two showcases are presented: one at the scale of computational micromechanics, and another one at the level of computational mesomechanics. The first case demonstrates that the proposed PBCE allows the homogenization of composite ply properties through the explicit FE method with increased efficiency and similar reliability with respect to the equivalent implicit simulations with traditional PBC. The second case demonstrates that the PBCE coupled with Periodic Laminate Elements (PLE) can effectively be applied to the computational homogenization of elastic and strength properties of entire laminates taking into account highly nonlinear effects. Both cases motivate the application of

Relationship Between Matrix Cracking and Delamination in CFRP Cross-Ply Laminates Subjected to Low Velocity Impact

“…It has been revealed by many researchers that the transverse/parallel shear behavior of composites exhibits high nonlinearity [34,35,36]. When a ply is under the shear loading, the matrix between fibers is under local tensile stress due to the Poisson ratio mismatch of the fiber and matrix.…”

“…For the cross-ply laminates tested in this paper, high-level shear strain γ13 occurred near the impact location during LVI. The widely used Ramberg–Osgood equation with three parameters was adopted to describe the nonlinear τ13-γ13 behavior [36,39,40]:τ13=G130γ13(1+(G130γ13τb)n)1n where G130 is the initial shear modulus, τb is the asymptotic stress level, which is assumed to be equal to S12, and n is the shape parameter for the curve. In this paper, G130, τb, and n were 4.20 GPa, 105 MPa, and 2.0 respectively.…”

High fidelity simulation of the mechanical behavior of closed-cell polyurethane foams

“…It is well known that the accuracy of the effective properties obtained by means of the numerical simulation of a RVE of a heterogeneous microstructure increases (for a given RVE size) with the application of periodic boundary conditions as compared with Dirichlet, Neumann or mixed boundary conditions (Segurado and LLorca, 2002;Kanit et al, 2003). Nevertheless, the implementation of periodic boundary conditions in explicit analysis often leads to spurious displacement oscillations that impairs the numerical analysis (Sádaba et al, 2019). Moreover, the application of periodic boundary conditions requires to develop a periodic microstructure of the foam and the application of these boundary conditions to beam and shell elements is complicated and requires extra mesh manipulations.…”

Boundary Element Method Analysis of Boundary Value Problems With Periodic Boundary Conditions

“…Mixed boundary value problems for elliptic equations with periodic boundary conditions occur in a wide range of engineering applications, such as composite and fluid mechanics [1], [2], vibrations of structural elements [3], crack propagation in elastic mediums [4], fluid-structure interactions [5], [6], cyclically symmetrical structure design [7], and more.…”