Influence of Boundary Conditions on Numerical Homogenization of High Performance Concrete

Abstract

Concrete is the most widely used construction material nowadays. We are concerned with the computational modelling and laboratory testing of high-performance concrete (HPC). The idea of HPC is to enhance the functionality and sustainability of normal concrete, especially by its greater ductility as well as higher compressive, tensile, and flexural strengths. In this paper, the influence of three types (linear displacement, uniform traction, and periodic) of boundary conditions used in numerical homogenization on the calculated values of HPC properties is determined and compared with experimental data. We take into account the softening behavior of HPC due to the development of damage (micro-cracks), which finally leads to failure. The results of numerical simulations of the HPC samples were obtained by using the Abaqus package that we supplemented with our in-house finite element method (FEM) computer programs written in Python and the homogenization toolbox Homtools. This has allowed us to better account for the nonlinear response of concrete. In studying the microstructure of HPC, we considered a two-dimensional representative volume element using the finite element method. Because of the random character of the arrangement of concrete’s components, we utilized a stochastic method to generate the representative volume element (RVE) structure. Different constitutive models were used for the components of HPC: quartz sand—linear elastic, steel fibers—ideal elastic-plastic, and cement matrix—concrete damage plasticity. The numerical results obtained are compared with our own experimental data and those from the literature, and a good agreement can be observed.

FFT‐based homogenization with mixed uniform boundary conditions

“…All tests assumed linear elasticity, but the method can be applied to nonlinear material laws without any changes. 10 Of course, the efficient implementation of the double fine material grid (12) would not be possible.…”

“…In Pahr and Böhm, 10 the authors demonstrate that these boundary conditions yield valid results also for nonlinear material laws. Panyasantisuk et al 11 and Denisiewicz et al 12 confirmed that also in the nonlinear regime, KUBC provide an upper bound to the apparent stiffness and yield behavior, while SUBC lead to a lower estimate of the effective values. PMUBC provide more compliant linear and nonlinear values.…”

“…Especially the coarse resolution does not seem to be sufficient for this type of element. That the staggered grid discretization with DFMG is more robust with respect to coarsely resolved structures can be explained by the fact that it incorporates a material parameter smoothing at the interfaces, compare Equation (12).…”

Multiscale Homogenization Techniques for TPMS Foam Material for Biomedical Structural Applications

“…where ε(u) is the micro strain and x is the position vector on the boundary ∂Ω. This method presents the advantage of having no restriction to its application except that no rigid part must intersect the boundary [32]. Uniform traction boundary conditions consist of applying on the boundary of the RVE the stress vector field that would occur if the stress were uniform inside the RVE…”

A computationally efficient approach for generating RVEs of various inclusion/fibre shapes

“…In a micromechanical analysis of the RVE, applying periodic boundary conditions (PBC) is more advantageous over homogeneous boundary conditions [34,35]. In order to apply PBC, RVE must be continuous across its boundary when it is repeated in the space.…”