Multiscale modelling of deformation and fracture in metal foams

PhD ceremony: Mr. K.R. Mangipudi, 14.30 uur, Senaatskamer Academiegebouw, Broerstraat 5, Groningen

Dissertation: Multiscale modelling of deformation and fracture in metal foams

Promotor(s): prof. P.R. Onck

Faculty: Mathematics and Natural Sciences

Metal foams are materials that contain both a microstructure on the microscale (the scale of the cell walls) and a micro-mesoscopic structure (on the scale of the cell). These micro-and mesoscopic structures are sensitive to the manufacturing method of the foam and also affect the mechanical properties. The purpose of this thesis is to investigate the influence of these two structural levels on the mesoscopic deformation and damage mechanisms and to understand how they affect the macroscopic mechanical properties.

For this purpose, a multiscale model of a two-dimensional foam has been developed with Voronoi tessellations representing the cellular architecture. The strain hardening behaviour is analysed and an additional hardening mechanism due to the meso-structural changes has been identified. We found that the competition between strain hardening and softening due to damage is important in determining the foam's tensile fracture strength and ductility. Also, increased intrinsic strain hardening enhances foam ductility. In irregular structures with a broad cell size distribution, mescoscopic deformation is not uniform, leading to a reduction in ductility. In structurally anisotropic foams, the foam is stronger and less ductile in the rise direction compared to transverse direction. Based on the numerical results, simple expressions were derived for macroscopic hardening, tensile fracture strength and ductility in terms of the material properties and geometric parameters of the cellular architecture. We have also analysed the tensile response in the presence of internal defects like cracks. Finally, the failure of cancellous bone is also investigated in this thesis, comparing the clinical efficacy of two treatments for osteoporosis.