Department of Mechanics: Seminar: Abstract Benjamin Werner 2022
Modelling Heterogeneities Using the Extended Quasicontinuum Method
28 February 2022, 10:00-11:00 CET, Room B-366 @ Thákurova 7, 166 29 Prague 6
Abstract: Numerical models of discrete lattice networks are beneficial to study the failure behavior of various heterogeneous materials. This includes quasi brittle materials such as concrete, all fibrous material as paper, textiles or woven fabrics. In the case of textiles or fabrics, the struts of the lattice are representing yarns and fibers at the meso-scale level and thus directly allow to incorporate bond failure in a straightforward manner. The downside of such numerical analyses is their excessive computational cost.
The Quasicontinuum (QC) Method is a numerical multi-scale approach for lattices addressing that problem. It was first introduced for crystal lattices on the atomistic level to investigate crack tip dislocations during nanoindentation. It is characterised by two integral parts to reduce the computational demand.
- A linear interpolation is applied to approximate the displacements of the full atomistic arrangement with a triangular mesh.
- To avoid visiting every lattice site to determine the potential energy of the system, summation rules are used to reduce the computational cost.
In the present study, the focus is on further increasing the computational efficiency of the QC method by using enriched interpolation functions motivated by the XFEM to incorporate heterogeneities. The extended QC with enriched interpolation functions is used to investigate lattices with inhomogeneities such as fibers and stiff inclusions embedded in a soft matrix. The outcome is compared to standard QC analyses with conforming meshes resolving the discontinuity boundaries as well as full discrete lattice simulations. The extended QC reveals a similar level of accuracy compared to the standard QC while being computationally much more efficient.
Acknowledgements: This activity was supported by the Ministry of Education, Youth and Sports, program Operational Programme Research, Development, and Education, Project No. CZ.02.2.69/0.0/0.0/18_053/0016980.