Computed Tomography-based Modeling of Structured Polymers

Abstract

A hybrid numerical-experimental approach is proposed to characterize the macroscopic mechanical behavior of structured polymers. The method is based on capturing the details of the material's microstructure using 3D X-ray Computed Tomography (CT). By employing segmentation and voxelconversion, the reconstructed volume is automatically converted into a finite element model that is subsequently used for mechanical analyses. The approach is demonstrated on a 2D polycarbonate (PC) honeycomb. An ideal representative volume element (RVE), with a volume equivalent to the volume of the real X-ray CT-based model, is used to determine the dependence of the macroscopic response of the structure on intrinsic material behavior, strain rate, and cell wall thickness. A nonlinear elasto-viscoplastic constitutive model is used to describe the intrinsic behavior of the PC base material and a comparison with a hyperelastic material model reveals that local plastic deformation significantly influences the macroscopic behavior. A cubic relation between the stiffness of the structure and cell wall thickness is found, whereas the strain rate has a minor influence. The ideal RVE shows a different response compared to the real X-ray CT-based model due to local variations of the cell wall thickness in the latter, causing nonhomogeneous deformations. In addition to the geometric imperfections, jagged edges, as a consequence of voxel conversion, contribute to this local variation in cell wall thickness.

X‐ray computed tomography‐based modeling of polymeric foams: The effect of finite element model size on the large strain response

“…However, in this study, a realistic structure is taken where the cells are randomly distributed, which is a result of their process history. Also, it should be mentioned that previous studies showed that the intrinsic material behavior strongly influences the effective mechanical behavior 9, 27, 28, 34. Plasticity causes localization in the structure, and therefore, one can anticipate that, by incorporating plasticity, larger models may be needed 10, 19, 34.…”

“…To incorporate the effects of the complex structure of foams, finite element (FE) analyses have been used in many studies on foams and composites to determine the structure–property relationship 5, 9–20. In these studies, the artificially generated FE models were based on regular structures,5, 9–14 for example, perfect honeycomb structures and regular Kelvin cells, where others used irregular structures to more realistically represent the microstructure, mostly based on Voronoi tessellation 10, 11, 14–19. These studies conclude that small details of the foam morphology, like cell irregularity, cell wall thickness variations, and cell shape anisotropy strongly influence the mechanical responses of these structures.…”

Modelling the elastic response of a polyurethane open cell foam based on a minimal surface energy approach

“…The morphology of foam is characterised by the number and type of cell faces and the cross sectional area, shape and length of the cell edges. These characteristics were first quantified by the observations of (Matzke [3]) and were confirmed using (electron) microscopy (Gong et al [4], Mills [5]) and CTimaging more recently (Jang et al [6], Wismans et al [7]). In general, a cell with 14 faces and a face with 5 edges proved to be the most abundant.…”

Unified treatment of microscopic boundary conditions and efficient algorithms for estimating tangent operators of the homogenized behavior in the computational homogenization method

“…From 2-dimensional interpolation formulations, the application on 3-dimensional cases can be easily derived using a bilinear patch Coons formulation. The finite element-based interpolation formulation, resulting in the so-called quasi-periodic boundary condition, was considered to apply the periodic boundary condition on a foamed RVE [63]. Finally, the master/slave approach [64] can be considered as a special case of finite element-based interpolation by considering directly the finite element mesh at the RVE boundary as interpolation bases.…”

“…Therefore, the interpolationbased periodic boundary condition is considered with the Coons patch formulation based on Lagrange or cubic spline interpolants [50] and with the finite elementbased formulation [63]. The obtained results are shown in Fig.…”