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

Abstract

The mechanical behavior of closed-cell foams in compression is analyzed by means of the finite element simulation of a representative volume element of the microstructure. The digital model of the foam includes the most relevant details of the microstructure (relative density, cell size distribution and shape, fraction of mass in the struts and cell walls and strut shape), while the numerical simulation takes into account the influence of the gas pressure in the cells and of the contact between cell walls and struts during crushing. The model was validated by comparison with experimental results on isotropic and anisotropic polyurethane foams and it was able to reproduce accurately the initial stiffness, the plateau stress and the hardening region until full densification in isotropic and anisotropic foams. Moreover, it also provided good estimations of the energy dissipated and of the elastic energy stored in the foam as a function of the applied strain. Based on the simulation results, a simple analytical model was proposed to predict the mechanical behavior of closed-cell foams taking into the effect of the microstructure and of the gas pressure. An example of application of the simulation tool is presented to design foams with an optimum microstructure from the viewpoint of energy absorption for packaging.

Microstructure, mechanical properties, corrosion resistance and cytocompatibility of WE43 Mg alloy scaffolds fabricated by laser powder bed fusion for biomedical applications

“…Further deformation led to successive minima and maxima in the load carried by the scaffold, but the maxima were fairly constant up to strains around 40%. An increase in strength due to densification is expected to be found at strains > 60% [31] but this regime was not attained in these tests.…”

Analysis of an open foam generated from computerized tomography scans of physical foam samples

“…The link between these model parameters and geometric characteristics of foams (such as the porosity, the average pore size and the pore size variation) is also far from being trivial and has been the subject of numerous studies. [37][38][39][40][41][42] However, Laguerre tessellations are not able, by construction, to capture nonconvex cells, cells with curved boundaries, and suffer from the inconsistency of presenting seedless cells. 43 Also, when available, a Laguerre tessellation does not fully exploit the voxel-informations present in CT-images.…”

Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional

“…Gibbsringing is well-known and well-documented, for instance in [21,22,18,20,40]. Sharp discontinuity with high phase contrast exacerbates Gibbs-ringing, thus, Gibbs ringing is more pronounced in problems containing phases with high contrast, for instance RVEs containing highly contrasted composites [45] or void in the micro-structure such as foams [41].…”

“…Use of Newton-CG due to its quadratic convergence properties is common in FFT-based solution schemes [19,28,75,81]. However, it is notable that Newton-CG is unable to handle problems with non-convex energy functional (symmetric non-positive semi definite (SNPSD) system matrix) such as homogenization of RVEs containing meta-materials [36] or continuum damage [1,41]. Conventional non-linear FEM solvers are also susceptible to instabilities in modeling nonconvex problems [58].…”