Two-scale finite element approximation of a homogenized plate model
Dienstag, 30.4.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We study the discretization of a homogenized and dimension reduced model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Velčić in 2014. Thereby, a nonlinear bending energy is based on a homogenized quadratic form which acts on the second fundamental form associated with the elastic deformation. Convergence is proven for a multi-affine finite element discretization of the involved three-dimensional microscopic cell problems and a discrete Kirchhoff triangle discretization of the two-dimensional isometry-constrained macroscopic problem. Finally, the convergence properties are numerically verified in selected test cases and qualitatively compared with deformation experiments for microstructured sheets of paper.
Stress-mediated growth determines division site morphology of E. Coli
Dienstag, 7.5.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Bacteria are enveloped by a rigid cell wall and replicate by cell division. During the division, the cell wall needs to be drastically reshaped. It is hypothesized that the remodeling process is stress-mediated and driven by the constrictive force of a protein assembly, the Z-ring. We found that a simple large-strain morpho-elastic model can reproduce the experimentally observed shape of the division site during the constriction and septation phases of E. Coli. Our model encapsulates the multiple enzyme-dependent wall restructuring processes into a single modulus. Depending on this parameter, different experimentally known morphologies can be recovered, corresponding either to mutated or wild type cells. In addition, a plausible range\nfor the cell stiffness and turgor pressure was determined by comparing numerical simulations with experimental data on cell lysis and reported cell sacculus deformation experiments.
Physical Control of Soft Robots
Montag, 27.5.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
In this lecture I show that when multiple nonlinear soft actuators are interconnected they can also embody the control function, by leveraging the local negative stiffness of the actuators to drive their motion out of phase. This allows soft robots to move in pre-programmed sequence using only a single input.
Phase separation on varying surfaces and convergence of diffuse interface approximations
Dienstag, 11.6.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
This talk's topic are phase separations on varying generalized hypersurfaces in\nEuclidian space. We consider a diffuse surface area (line tension) energy of Modica–\nMortola on surfaces and prove a compactness and lower bound estimate in the sharp interface\nlimit. We also consider an application to phase separated biomembranes where a Willmore energy\nfor the membranes is combined with a generalized line tension energy. For a diffuse\ndescription of such energies we give a lower bound estimate in the sharp interface limit. Time permitting I will present recent results about simultaneous phase field approximations of both the biomembrane and the indicator function for one of the two phases defined on the membrane.\n
Existence of optimal flat ribbons
Dienstag, 18.6.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We revisit the classical problem of constructing a developable surface along a given Frenet curve \(\bgamma\) in space. First, we generalize a well-known formula, introduced in the literature by Sadowsky in 1930, for the Willmore energy of the rectifying developable of \(\bgamma\) to any (infinitely narrow) flat ribbon along the same curve. Then we apply the direct method of the calculus of variations to show the existence of a flat ribbon along \(\bgamma\) having minimal bending energy. Joint work with Simon Blatt.
Optimal control of rate-independent systems with non-convex energies
Dienstag, 2.7.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Rate-independent systems arise in multiple applications, in particular in computational mechanics. They model processes, which are invariant w.r.t. time transformations of external loads. In some applications such as perfect plasticity or brittle damage, the stored energy functional is not uniformly convex. In this case one cannot expect uniqueness and continuity (in time) of solutions. In particular due to the lack of continuity, a variety of solutions concepts has been developed in the recent past, among them global energetic solutions and parametrized balanced viscosity solutions. In the talk, we will consider optimal control problems governed by rate-independent systems with energy functionals that are not uniformly convex. The external loads will serve as control variables. Due to the lack of uniqueness of solutions, we regularize the state equation by adding viscosity. The main part of the talk will then be concerned with the viscosity limit, i.e., we will discuss, if, and under which conditions, solutions of the optimal control problems under consideration can be approximated via viscous regularization.
Generative Models for the Design of Mechanical Metamaterials
Dienstag, 16.7.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10