Young Researchers' Minisymposia 2018

Computational science is quickly gaining traction among application engineers, and establishing itself as a fundamental investigation tool among practitioners. An immediate consequence was a paradigm shift in engineering design: Experimental trials are increasingly replaced by numerical simulations. Although the world of design and the world of analysis have traditionally been distinct, this dichotomy has recently been reconciled by CAD-conforming analysis methods, most prominently Isogeometric Analysis (IGA). IGA builds on the observation that by operating on the exact geometry, the geometry error component is automatically removed from the overall numerical error. Further advantages can be gained in terms of shape-optimization, adaptive refinement and others. A non-trivial consequence of this approach, which was realized only in recent times, is that isogeometric finite elements also feature superior approximation properties. In this spirit, this minisymposium aims at providing a forum for questions concerning both the mathematics behind and the application of isogeometric methods. It spans the bridge between different fields, such as structural or fluid mechanics as well as electromagnetics, by focusing on the common modelling and numerical problems.

Organizers: Wolfgang Dornisch (Kaiserslautern), Stefanie Elgeti (Aachen)
Speakers:

• Bastian Oesterle (U Stuttgart, Germany): “Intrinsically locking-free formulations for isogeometric shell analysis”
• Simone Morganti (University of Pavia, Italy): “Mixed formulations: an isogeometric collocation approach”
• Felix Wolf (TU Darmstadt, Germany): “Boundary Element Methods in the Isogeometric Framework”
• Benjamin Marussig (TU Graz, Austria): “Isogeometric Analysis with Trimmed CAD Models”
• Alexander Seitz (TU München, Germany): “Nitsche’s method for isogeometric thermo-mechanical contact problems”
• Andreas Apostolatos (TU München, Germany): “Weak imposition of constraints for geometrically nonlinear membranes in transient isogeometric analysis”

Porous cellular materials form a large class of materials found in nature like wood, cork, sponge, and coral. More recently, man has made cellular solids (foams) for applications as lightweight structural components. Techniques for foaming now exist for polymers, metals, ceramics, and glasses. These materials are increasingly being used structurally for insulation, as cushioning, and in systems for absorbing the kinetic energy from impact. Novel materials that are characterized by open cell porous morphology, e.g. aerogels, are also being invented and developed. In this Young Researcher’s Mini-Symposium we intend to discuss the mechanics of such porous cellular materials, both with open pores and filled ones, within the framework of experimental characterization and modeling. Different cellular materials like aerogels, metal foams and bioinspired materials will be discussed. Also, discussed will be topics on magneto-elastic properties of these cellular materials. Novel experimental techniques focusing on characterization of single struts (cell walls) within the micro-structure will be discussed. The use of atomistic simulations to describe the mechanical properties of such single struts will also be examined. Such nano-structural investigations, either via experimental techniques or via atomistic models that determine the nano-scale properties are then shown to strongly influence the multi-scale models that describe the response of such porous cellular materials up to the macro-scale. Composite cellular materials will also be reviewed. Characterization tools like X-ray tomography are also being used to obtain the micro-structural morphology of such materials that is then used within finite element programs to mesh and discretize the structure. Such interesting procedures will also be addressed within the framework of the mini-symposium. Different modeling techniques will be contended. Atomistic models, and continuum mechanical models, in particular inelastic models, plasticity based models and homogenization based models will be considered. The pros and challenges faced in each of these different approaches used for modeling cellular materials will be debated. The goal of organizing this Young Researcher’s Mini-Symposium is to discuss the state of art and outlook of characterizing and modeling highly porous cellular materials.

Organizers: Anne Jung (Saarland), Ameya Rege (Aachen)
Speakers:

• Anne Jung (Saarland University): “In-situ and ex-situ micromechanical testing of open-cell metal foams”
• Thomas Bleistein (Saarland University): “Multiscale characterisation and simulation of open cell metal foams”
• Christine Grill (Universität des Saalandes): “Modeling and Simulation of the Coating Process on Open Porous Metal Foams”
• Ameya Rege (RWTH Aachen University): “Multi-scale modeling of polysaccharide and protein based aerogels”
• Raghvendra Singh (University of Groningen): “Homogenization of cellular solids for magneto-elastic properties”
• Abdel Hassan Sweidan (RWTH Aachen University ): “Simulation of PCM-Saturated Porous Solid Matrix for Thermal Energy Storage using the Phase-Field Method”

The usual way to perform computations in solid mechanics is based on the representation of a primal variable, commonly the displacement or the pressure, by suitable finite element spaces. From such a finite element approximation, other variables like stresses can be reconstructed in a post-processing step. This primal formulation had great success in practical computational engineering for advanced problems in solid mechanics. However, the loss of accuracy due to the reconstruction step can lead to non-physical solutions, in particular for the simulation of challenging problems like in fracture mechanics or coupled problems, or for complex boundary value problems with discontinuities, strong anisotropy, heterogenity, or incompressibility. Further, accurate computations of the stress are also critical for two phase flow simulation to properly account for the coupling between the two phase behavior in applications such as porous medium in solid mechanics or bubble suspension in rheology. In order to master these challenges and develop robust numerical schemes, an accurate representation of the stress-field is needed. To this end, the associated first-order system can be considered, such that the stress-field and the primal variable are both part of the model. To obtain a model for complex problems like crack and contact problems, recent advances in engineering like the resolution of the local discontinuities as well as their evolution are needed, leading to innovative mixed models, e.g. the phase field model for fracture mechanics. In this model, the crack is approximated as a diffuse interface such that no explicit discontinuities are present. Furthermore, crack initiation, propagation and branching can be modeled without additional criteria but directly from the phase-field evolution equation. The computed stresses are degraded using the phase-field variable. The standard mixed finite element approach leads to a saddle-point problem, in which the momentum balance is approximated in an optimal way, if appropriate finite element combinations are used. However, since a stability condition between the mixed spaces has to be established, the construction of those finite element spaces is challenging. In order to avoid the complexity of proving a stability condition, a positive definite system can be obtained by minimizing the residuals in the partial differential equations. The use of the L2-norm leads to the Least-Squares method, which provides the advantage of an inherent a posteriori error estimator. However, there is a strong connection of this stress approximation to that obtained from a mixed formulation and the error associated with the momentum balance can be proved to be of higher order than the overall error of the least-squares approach. This implies that the favorable conservation properties of the dual-based mixed methods and the error control of the least squares method can be combined. Through the use of a non-standard localized dual norm in the minimization of the residual, the Least-Squares finite element method extends to the discontinuous Petrov-Galerkin method. By breaking the test spaces and using variables living only on the skeleton of the finite element mesh, finite elements can be chosen less restrictively. This provides convenient advantages in solid mechanics since additional physical conservation properties like the pointwise symmetry of the stress tensor can be incorporated easily, retaining the accurate approximation of the momentum balance and the built-in error estimate from the previous methods. At the annual meetings of GAMM, a young researcher’s Minisymposium on Non-Standard Mixed Finite Element Schemes for Solid Mechanics would allow to concentrate on the interacting relations between the aforementioned schemes, such as supercloseness results or comparison theorems. As a consequence, the fostered collaboration between the applicants supports the development and analysis of new numerical simulation techniques and the promotion of deeper understanding of mixed schemes. Further, a topic-based session and the possibility of a common presentation would endorse the exchange of ideas between the engineering and mathematical groups on this challenging topic and connect the huge field of applications of these mixed schemes. In conclusion, such a Minisymposium aims to visualize the advances and interactions, to bring recent development to broader attention and to create the highly valuable synergies between the involved researchers.

Organizers: Fleurianne Bertrand (Duisburg-Essen), Friederike Hellwig (Berlin)
Speakers:

• Fleurianne Bertrand (Universität Duisburg-Essen): “Supercloseness of a Least-Squares Finite Element Method for Elasticity”
• Mira Schedensack (Universität Münster): “A Mixed Finite Element Discretization for Plate Problems”
• Tuanny Cajuhi (Technische Universität Braunschweig): “Phase-Field Modeling of Fracture in Partially Saturated Porous Media”
• Carola Bilgen (Universität Siegen): “Numerical Simulation of Pressure-Driven Crack Propagation”
• Carola Bilgen (Universität Siegen): “Numerical Simulation of Crack Propagation in an anisotropic medium”
• Karol Cascavita (Ecole Nationale de Ponts et Chaussées): “Discontinuous Skeletal Methods for Yield Fluids”
• Friederike Hellwig (Humboldt-Universität zu Berlin): “Optimal Convergence Rates in dPG for Elasticity”

The method of multibody systems is a well-established approach for the analysis of dynamic mechanisms in a wide range of applications such as in robotics, for machine tools, in vehicle and railway dynamics, or in biodynamics. In many of these applications, the deformations of the components are negligibly small and do not influence the dynamics of the system. Thus, the traditional method of rigid multibody systems can be employed. In contrast, the method of flexible multibody systems should be used if there are bodies in the system that undergo both large rigid body motions and deformations. Two important approaches to incorporate flexible bodies are the floating frame of reference formulation and nonlinear finite element methods. While significant progress has been made in the modeling and simulation of multibody systems, the focus in research has recently shifted to the optimization of dynamic systems. The aim of this minisymposium is bringing together young researchers who deal with various aspects of the analysis, optimization, and control of rigid and flexible multibody systems and other closely related fields. This interdisciplinary nature of the minisymposium should enable an exchange of valuable information and also lead to significant dis¬cussions about optimal structural design and control design.

Organizers: Karin Nachbagauer (Wels, Austria), Alexander Held (Hamburg)
Speakers:

• Alexander Humer(Johannes Kepler University Linz): “Design and Optimization of Large-Deformation Compliant Mechanisms”
• Ali Moghadasi (Hamburg University of Technology (TUHH)): “Large-Scale Gradient Computation in Flexible Multibody Systems”
• Alexander Held (Hamburg University of Technology (TUHH)): “Constrained Structural Optimization of Dynamic Mechanical Systems”
• Johann Penner (University of Erlangen-Nuremberg): “Optimization based muscle wrapping in biomechanical multibody simulations”
• Karin Nachbagauer (University of Applied Sciences Upper Austria): “Parameter Identification in Multibody Systems in Frequency Domain using Adjoint Fourier Coeffcients”
• Thomas Lauß (University of Applied Sciences Upper Austria): “Identification of a nonlinear spring and damper characteristics of a motorcycle suspension using test ride data”

A great amount of materials exhibit interesting behaviours, being the result of the interplay of complex microstructures, the outcome of involved in-time evolutions, the effect of the action of internal variables, or the macroscopic counterpart of atomistic interactions. Understanding the interplay of such different material scales is a key problem in materials science. Indeed, it is crucial for the description of the physics behind phenomena, which are not yet fully understood, for the development of innovative metamaterials and the exploration of their industrial applications. Providing a characterization of multiscale phenomena is therefore currently one of the biggest scientific challenges lying at the interface between mathematics, physics, and materials science. In the last decade a combined effort from the mathematical community has allowed to tackle a variety of problems, spanning from periodic and stochastic homogenization, mathematical modelling of spin systems, passage from discrete to continuum, to the derivation of effective models for media with microstructures, and the modelling of failure phenomena, such as elastoplasticity, damage, and fracture. The techniques employed are often the outcome of the combination of ideas from various fields, ranging from geometric measure theory, to PDEs, and to the Calculus of Variations. The aim of the minisymposium is to promote and foster new connections and scientific cooperations between young researchers working in close areas of multiscale modelling, as well as to give them the opportunity of showcasing their results and of interacting with an expert public. The range of expertise of our speakers is quite broad and covers a selection of problems having the common feature of involving multiscale phenomena.

Organizers: Elisa Davoli (Wien), Manuel Friedrich (Wien)
Speakers:

• Leonard Kreutz (PostDoc, Universitat Wien): “Optimal Design for mixtures of ferromagnetic interactions”
• Matthias Ruf (PostDoc, ULB Bruxelles): “Free energies on stochastic lattices”
• Julian Braun (PostDoc, University of Warwick): “Long-range elastic elds induced by crystal defects”
• Mathias Schäffner (PostDoc, TU Dresden): “Gradient estimates for homogenization of nonlinear elasticity under
  small loads”
• Fabian Christowiak (PhD student, Universitat Regensburg): “Asymptotic rigidity for layered materials and its applications in elasto-plasticity”
• Vito Crismale (PostDoc, Ecole Polytechnique): “A density result in GSBDp with applications to the approximation of brittle fracture energies”