Computational Modeling of Moving Boundary Problems
11:00 - 12:00
Prof. Timon Rabczuk
Chair of Computational Mechanics, Bauhaus University Weimar
Max-Planck-Institut für Eisenforschung GmbH
Seminar Room 1
Prof. Dierk Raabe
The focus of this presentation is on computational methods for moving boundary/interface problems and its applications including fracture, fluid structure interaction, inverse analysis and topology optimization. First, two computational methods for dynamic fracture will be presented, i.e. the cracking particles method (CPM) and dual-horizon peridynamics (DH-PD). These methods do neither require a representation of the crack surface and associated complex crack tracking algorithms nor criteria for crack branching and crack interactions. They also do not need to distinguish between crack nucleation and crack propagation. Complex discrete fracture patterns are the natural outcome of the simulation. The performance of these methods will be demonstrated by several benchmark problems for non-linear quasi-brittle dynamic fracture and adiabatic shear bands. Subsequently, a local partition of unity-enriched meshfree method for non-linear fracture in thin shells -- based on Kirchhoff-Love theory -- exploiting the higher order continuity of the meshfree approximation will be presented. The method does not require rotational degrees of freedom and the discretization of the director field. This also drastically simplifies the enrichment strategy accounting for the crack kinematics. Based on the meshfree thin shell formulation, an immersed particle method (IPM) for modeling fracturing thin-structures due to fluid-structure interaction is proposed. The key feature of this method is that it does not require any modifications when the structure fails and allows fluid to flow through the openings between crack surfaces naturally.The last part of the presentation focuses on inverse analysis and topology optimization with focus on computational materials design of piezoelectric/flexoelectric nanostructures and topological insulators. In the first application of piezo/flexoelectricity, we use isogeometric basis functions (NURBS or RHT-splines) in combination with level sets since C1 continuity is required for the numerical solution of the flexoelectric problem. Hence, only the electric potential and the displacement field is discretized avoiding the need of a complex mixed formulation. The level set method will be used to implicitly describe the topology of the structure. In order to update the level set function, a stabilized Hamilton-Jacobi equation is solved and an adjoint method is employed in order to determine the velocity normal to the interface of the voids/inclusions, which is related to the sensitivity of the objective function to variations in the material properties over the domain. The formulation will be presented for continua though results will also be shown for thin plates. The method will be extended to composites consisting of flexible inclusions with poor flexoelectric constants. Nonetheless, it will be shown that adding these flexible inclusions will result in a drastic increase in the energy conversion factor of the optimized flexoelectric nanostructures. In the second application, we propose a computational methodology to perform inverse design of quantum spin hall effect (QSHE)-based phononic topological insulators. We first obtain two-fold degeneracy, or a Dirac cone, in the bandstructure using a level set- based topology optimization approach. Subsequently, four-fold degeneracy, or a double Dirac cone, is obtained by using zone folding, after breaking of translational symmetry, which mimics the effect of strong spin-orbit coupling and which breaks the four-fold degeneracy resulting in a bandgap, is applied. We use the approach to perform inverse design of hexagonal unit cells of C6 and C3 symmetry. The numerical examples show that a topological domain wall with two variations of the designed metamaterials exhibit topologically protected interfacial wave propagation, and also demonstrate that larger topologically- protected bandgaps may be obtained with unit cells based on C3 symmetry.