List of Mini-Symposia

• Bilen Emek Abali, Institute of Mechanics MS 2, Technische Universität Berlin, Germany

Miniaturization decreases the length scale of geometry. As this length scale approaches to molecular length scale, the continuum mechanics homogenization procedure is in danger and the molecular structure starts affecting the deformation behavior by introducing a polar nature to the material. Metamaterial is mostly used as name for emphasizing the structural dependence. Experimentally, this phenomenon is known as "size effect", and its computational modeling is established by using the so-called strain gradient theory. Simply stated, this theory incorporates not only the first gradients but also the second gradients of the displacement in elasticity. A generalized continuum mechanics includes theories introduced under different names, for example, strain gradient, micropolar, micromorphic theory. This generalized continuum mechanics, characterization of metamaterials, and a general computational implementation belong to a growing interest among several groups. Mainly there are three challenges in this topic:

• First, a proposed numerical method needs to be validated in its accuracy; however, this verification is difficult because of the lack of experimental data.
• Secondly, the structural dependence generates additional parameters to be determined experimentally or computationally.
• Thirdly, the sought after generalization to Multiphysics - for example including damage, thermodynamics, electromagnetism - is difficult from theoretical as well as computational perspectives.

The research has yielded up clear evidence that a generalized continuum mechanics is useful for a more accurate modeling in engineering design, especially in parts with relatively small geometric dimensions with respect to their molecular structure. This minisymposium attracts attention from various groups working in material modeling, parameter identification, and computational implementations in metamaterials. 

• Erdogan Madenci, Department of Aerospace and Mechanical Engineering, University of Arizona, USA
• Adi Adumitroaie, Faculty of Mechanical Engineering and Design, Kaunus University of Technology, Lithuania and Analysis and Advanced Materials for Structural Design (AMADE), University of Girona, Spain

Classical continuum mechanics models and their computational methods (e.g., FEM) are based on local stress-strain theories, and cast into systems of Partial Differential Equations (PDE).  However, PDE-based local methods suffer to properly include certain mechanical phenomena such as the influence of gradients, microscale size effects, discontinuities generated by fracture paths and strain localization due to softening. Therefore, they require special treatment to address the limitation of the specific method. Alternatively, nonlocal continuum theories (e.g., peridynamics, strain-gradient elasticity, etc) remove such shortcomings, and enable the solution of multiscale and multiphysics problems including damage and fracture. This symposium is intended to provide a forum for researchers to discuss the latest developments in the field of peridynamics and other nonlocal theories for mechanics related applications.  Possible contribution topics of interest includes, among others:

• theoretical approaches and numerical implementation
• nonlocal elasticity and plasticity
• nonlocal damage and fracture
• nonlocal multi-scale methods (e.g., for heterogeneous composite materials)
• nonlocal multi-physics methods
• local/nonlocal coupling methods
• practical engineering applications

• Fadi Aldakheel, Institute of Continuum Mechanics, Leibniz Universität Hannover, Germany
• Thomas Wick, Institut für Angewandte Mathematik (IfAM), Leibniz Universität Hannover, Germany
• Yousef Heider, Department of Civil Engineering and Engineering Mechanics, Columbia University in the City of New York, USA
• Resam Makvandi, Institute of Mechanics, Otto von Guericke University Magdeburg, Germany

This minisymposium provides a forum for the discussion of latest developments in the simulation of fracture mechanics. Of particular interest are problems related to crack initiation and propagation in inelastic solids, phase-field modeling of brittle and ductile fracture PFM,  extended finite elements XFEM, cohesive zone model CZM and failure in multi-physical environments all based on virtual/finite element methods (VEM/FEM).

Presentations addressing open problems in modeling as well as numerical treatment are particularly encouraged.

• Felix Boy, Institute of Mechanics - Engineering Dynamics, University of Kassel, Germany
• Simon Bäuerle, Institute of Mechanics - Engineering Dynamics, University of Kassel, Germany
• Robert Fiedler, Institute of Mechanics - Engineering Dynamics, University of Kassel, Germany

In modern technological application, the accurate prediction and understanding of stationary solutions has become an important task for scientists and engineers. In the majority of cases, the computation of a single solution is not sufficient but rather the change in a solution under parameter variation. An efficient way to predict such solution branches are continuation methods, whereby these involve the investigation of both statical and dynamical problems with application in mechanics and mathematics.

Although there has been tremendous research on the subject, there are still a lot of open questions to answer. These range from methodological aspects like improved algorithms for finding and continuing solutions, finding initial solutions, detecting detached branches, or handling high dimensional problems to their application in structural mechanics and machine dynamics, in chemical and biological processes, aerodynamics, electromagnetics and much more. Certainly methodological questions and applied problems are closely linked, whereby an interdisciplinary exchange is of great importance when working in this field.

This minisymposium aims at providing a platform to present and discuss questions about methodological and applied problems in the context of numerical continuation. Authors from all fields are invited and encouraged to contribute to this minisymposium, offering them and all other participants the possibility to get a throughout and diverse inside to the subject.

• Tuanny Cajuhi, Institute of Applied Mechanics, Braunschweig University of Technology, Germany
• Yousef Heider, Institute of General Mechanics, RWTH Aachen University, Germany
• Carola Bilgen, Institute of Solid Mechanics, Siegen University, Germany

Porous materials present a multi-phase nature associated with multi-physics coupled phenomena. These found several applications in engineering such as hydraulic fracturing (fracking), soil desiccation, shrinkage in cement-based materials, drying of biological materials, among many others. The mathematical modeling of such materials often results in complex systems of coupled partial differential equations in space and time. The Biot's theory and the Theory of Porous Media are well known in the context of continuum mechanical modeling of fully or partially saturated porous materials. These theories can be extended to account for the fracture behavior, e.g. by the phase-field method, which establishes a way to tackle the challenges of modeling cracks.

This mini-symposium aims at providing an opportunity to present recent advances and exchange ideas about the continuum-mechanical modeling and numerical treatment of multi-field problems in porous-media.

• Pietro Carrara, Institute of Applied Mechanics, TU Braunschweig, Germany
• Markus Kästner, Chair of Computational and Experimental Solid Mechanics, TU Dresden, Germany
• Marreddy Ambati, Institute of Applied Mechanics, TU Braunschweig, Germany

Failure of mechanical or structural components due to fatigue-induced cracks can strongly affect human life and economy, being responsible for about 80% of failures under service conditions.  

To date, fatigue life prediction is still dominated by empirical approaches that must be component-wise calibrated and that need extensive, costly experimental campaigns, e.g. the Wöhler or S-N curves relating the maximum number of cycles that a component can undergo before failure at the applied load amplitude. Despite their popularity, these approaches can be hardly generalized to conditions or geometries different than the specific situation tested. The advent of fracture mechanics led to several models starting from the pioneering work of Paris. Nowadays, many computational approaches are available but still need improvement. In particular, a suitable way to represent the crack along with a proper description of its formation and propagation as a result of repeated load cycles below the monotonic strength is needed. Furthermore, the study of the crack propagation based on the explicit cycle-by-cycle approach becomes unfeasible when dealing with large numbers of load cycles calling thus for temporal multiscale methods. Finally, the design of specific tests for the calibration and the validation of such models is also needed. 

The aim of this mini-symposium is to present novel analytical and numerical approaches to model fatigue crack formation and growth in brittle and ductile materials as well as experimental studies specifically oriented to their development and/or validation.

The topics include, but are not limited to, the following:

• Numerical and analytical modeling of fatigue crack growth;
• Constitutive models for cylcic inelastic material behavior;
• Modeling of small- and large-scale plasticity effects on fatigue;
• Experimental validation or calibration of fatigue crack growth models;
• Multiscale modeling of fatigue in space and time.

• Matthias Grafenhorst, Institute of Applied Mechanics, Clausthal University of Technology, Germany
• Bettina Schröder, Institute of Mechanics and Dynamics, University of Kassel, Germany

In many areas of engineering, numerical computations have become indispensable owing to the higher requirements on the description of complex problems. Hence, it is imperative to use numerical methods with high accuracy for solving the elliptic, parabolic- or hyperbolic-type of PDEs. The problems can be of spatial or temporal nature. For spatial problems, various extended formulations are developed and examined. For problems requiring high degree of continuity, the use of higher-order shape function must also be considered. Methods which ensure an error-free mapping of the geometry have also gained prominence in recent times. On the other hand, the ODEs and DAEs emanating from modern spatial discretization schemes require accurate and stable time integration methods. In order to achieve additional stabilization, numerical methods which preserve the structure of the underlying problem (energy, linear momentum, angular momentum, entropy, incompressibility, ...)  are increasingly being used. Other important aspects that come into play in the domain of high-frequency physics are numerical dissipation and dispersion.

This minisymposium is intended to appeal to speakers whose problems require more precise procedures in space and/or time. It is envisaged that this mini-symposium provides a forum for the exchange of experiences and ideas on numerical techniques, formulations and applications covering various aspects of higher accuracy.

• Sergii Kozinov, Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Germany
• Mokarram Hossain, Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, United Kingdom
• Ralf Landgraf, Chair of Solid Mechanics, Faculty of Mechanical Engineering, Chemnitz University of Technology, Germany
• Michael Johlitz, Institute of Mechanics, Faculty of Aerospace Engineering, Bundeswehr University Munich, Germany

Smart, active and polymer materials are applied in many different fields, like aerospace, mechanical engineering, medical treatment, energy harvesting, etc. Typically, mechanical loads on the materials are accompanied by different environmental or technical influences, like temperature, chemical processes, electric or magnetic fields or surrounding media with chemical or physical impact on the materials.

This Mini-Symposium is focused on theoretical modeling and simulation approaches to capture coupled processes of smart, active and polymer materials under environmental and technical influences. On the one hand, this includes thermo-, chemo-mechanical processes of polymers, like curing, recrystallization, ageing or degradation, among others. On the other hand, smart and active materials like ferroelectrics, multi-ferroic composites, dielectric elastomers, electro-active polymers or magneto-rheological elastomers are of interest. Research contributions related to constitutive modeling as well as strategies for the implementation and simulations within the finite element method are of special interests. Moreover, approaches regarding first-principles and molecular dynamics calculations, phase-field modeling, parameter identification and multi-scale approaches are highly welcomed alongside with the experimental studies.

The aim of the Mini-Symposium is to bring together and establish connections between scientists working on the different aspects of the smart, active and coupled-field materials, such as development, characterization, modeling and testing. This includes researchers from the materials science, micromechanics, physics and computational mechanics communities with common interests in coupled material properties and smart materials.

• Anne Jung, Applied Mechanics, Saarland University, Germany
• Stefan Diebels, Applied Mechanics, Saarland University, Germany

Modern materials science and experimental mechanics do not only focus on simple uniaxial tension and compression tests but also on multiaxial testing of materials. In such cases, the strain field can no longer be reliably determined from extensiometer measurements alone. Furthermore, microheterogeneous materials such as cellular materials or composites lead to strain localisations during deformation, which can hardly be tracked by conventional methods like extensometer measurements or the use of strain gauges.

During the last years, digital image correlation (DIC) became a powerful tool in material science for the visualisation of full-field displacements and full-field strains with a sub-pixel accuracy e.g. for failure investigation on the surface of specimens. By taking not only pictures from the surface but by doing computer tomography scans the concept of optical strain field measurements of DIC can be extended from the surface to the whole volume by digital volume correlation (DVC). All features occuring in a macroscopic stress-strain diagram can be traced back to a distinct deformation within the volume of a specimen. While DIC and DVC provide full-field strain information for a surface and a volume, respectively, infrared thermography (IRT) results in the determination of full-field temperature distributions of a specimen. IRT is a boundary technique, which means, that it does not only detect surface temperatures but also has the ability to gain information from a limited thickness of the specimen under the surface due to heat conduction. These temperature fields can be correlated to local strains or damage.

Full-field strain and full-field temperature measurement techniques as well as combinations of these techniques are a rising field of research in experimental mechanics and materials sciense. The minisymposium focusses on every kind of research related to the application, development or enhancement of these full-field measuring techniques in mechanics and materials science.

• Dominik Kern, Technische Mechanik/Dynamik, TU Chemnitz, Germany
• Ulrich Römer, Institute of Engineering Mechanics, Karlsruhe Institute of Technology, Germany

Dynamic systems with non-standard constraints and boundary conditions are a frequent subject of investigation in many areas of applied science and engineering, inter alia biomechanics, robotics, vehicle dynamics, gears, chain and belt drives. Non-standard constraints include, among others, rheonomic, non-holonomic, unilateral and coupled constraints. The numerical simulation of (flexible) multi-body systems and finite-element models for analysis and control purposes requires the inclusion of such constraints in accurate and fast time integration schemes.

This symposium reports about the state of the art and current developments for dynamic systems with non-standard constraints. The focus is on

• rheonomic constraints,
• non-holonomic constraints,
• unilateral constraints,
• coupled constraints

in the context of (higher-order) time integration schemes for ODEs and (high-index) DAEs, potentially with emphasis on structure-preservation. The considered spatial discretizations include, but are not limited to

• flexible multi-body systems,
• finite-element models,
• minimal models for demonstrations.

The Mini-Symposia 8 and 11 have merged together. For submitting an abstract for "Smart and Active Materials: Modeling and Experiments", please go to the Mini-Symposium MS08.

• Lisa Scheunemann, Institut für Mechanik, Bauwissenschaften, Universität Duisburg-Essen
• Matthias Labusch, Institut für Mechanik, Bauwissenschaften, Universität Duisburg-Essen

The minisymposium adresses topics from the field of multiscale modeling of microheterogeneous materials as well as multiphysics problems involving a coupling of electrical, magnetical and mechanical quantities. In many materials, heterogeneity is observed on small length scales, such as modern advanced high strength steels, composite materials, multiferroics and polycrystalline materials. These are known to have a strong influence on the material behavior observed at a larger scale.

 Contributions are welcome in the following topics of interest:

• Numerical homogenization methods for microheterogeneous materials
• Challenges and strategies for increased efficiency of multiscale methods and simulations
• Validation of multiscale techniques based on numerical and experimental investigations
• Simulation of multiphysical phenomena
• Numerical approaches for coupling induced product properties
• Generation of representative volume element models for real microstructures
• Multiscale simulation involving representative volume elements and realistic microstructures

• Michel Make, Chair for for Computational Analysis of Technical Systems, RWTH-Aachen, Germany
• Norbert Hosters, Chair for for Computational Analysis of Technical Systems, RWTH-Aachen, Germany
• Roland Wüchner, Lehrstuhl für Statik, Technische Universität München, Germany

The goal of this mini symposium is to discuss the recent developments on advanced numerical methods for fluid-structure interaction. The focus of the session will be on new methods that address the improvement of computational efficiency, software design, as well as the enhancement of numerical accuracy. Possible applications could be (although not limited to) aerospace, civil, biomechanical, and  production engineering. We especially encourage contributions in the field of spline base methods, spatial and temporal coupling schemes, multiscale models, reduced order models, but also software engineering for fluid- structure interaction problems.

 Keywords: Fluid-structure interaction, spatial and temporal coupling schemes, reduced order models, multiscale techniques

• Matthias Mayr, Institute for Mathematics & Computer-Based Simulation, University of the Bundeswehr Munich, Germany
• Anton Tkachuk, Institute for Structural Mechanics, University of Stuttgart, Germany
• Ajay Harish, Institute of Continuum Mechanics, Leibniz Universität Hannover, Germany
• Alexander Popp, Institute for Mathematics & Computer-Based Simulation, University of the Bundeswehr Munich, Germany

Computational contact and interface mechanics and related disciplines have received fast-growing attention in recent years. This mini-symposium addresses the most important and active research topics in computational contact and  interface mechanics, including

• robust discretization methods for large deformations,
• accurate constraint enforcement techniques,
• efficient solution algorithms,
• parallel and high-performance computing,
• interface mechanics (friction, wear, adhesion, lubrication, debonding, failure, etc.),
• multi-scale methods for contact,
• coupled multi-field problems,
• applications in biomechanics and bioengineering.

The aim of this mini-symposium is to provide a forum for young researchers to discuss promising developments and advances in computational contact and interface mechanics and to give new impulses towards future research in this area.

• Bastian Oesterle, Institute for Structural Mechanics, University of Stuttgart, Germany
• Wolfgang Dornisch, Institute of Applied Mechanics, Technische Universit\"at Kaiserslautern, Germany
• Oliver Weeger, Information Systems Technology and Design Pillar, Singapore University of Technology and Design, Singapore
• Josef Kiendl, Department of Marine Technology, Norwegian University of Science and Technology, Norway

In recent years, an increased activity in the scientific field of formulations and discretization methods for plate and shell structures can be observed. The topic has received a major boost due to the popularity of the isogeometric concept along with finite element methods using NURBS or B-Splines as shape functions. Here, one of the decisive features is a relatively easy control of continuity of shape functions, facilitating discretization of problems for which the weak form has a variational index of 2 or larger. This applies, for instance, to the classical Kirchhoff-Love thin shell model, which currently experiences a renaissance.

The proposed mini-symposium invites all contributions from the field of non-standard formulations and discretization methods for thin-walled structures, both from method development and application.  Typical topics are expected to be, but not restricted to: spline-based discretizations, formulations based on subdivision surfaces, non-local (patch-based) or smoothed finite elements, meshless methods, finite cell methods, isogeometric analysis and integration of CAD and CAE, rotation-free formulations for plates and shells, non-linear analyses, treatment of boundary conditions or trimmed surfaces as well as multi-layer and solid shell elements.

• Sigrun Ortleb, Fachbereich Mathematik und Naturwissenschaften, Universität Kassel, Germany
• Veronika Straub, Fachbereich Mathematik und Naturwissenschaften, Universität Kassel, Germany

The simulation of fluid phenomena covers a wide range of numerical techniques. Space discretization schemes range from finite differences to finite volume methods and finite element type approaches such as the discontinuous Galerkin method. These methods are generally quite elaborate and specifically designed to guarantee qualitative properties such as local conservation of the primary fluid quantities. Further aims are high accuracy of the method and flexibility with respect to the computational grid and the possible application in parallel hardware environment.

Time discretization of the resulting semi-discrete equations demands a comparative sophistication of techniques. In realistic test cases of flow around solid structures, the computational grid is usually significantly refined at the boundary leading to stiff semi-discrete equations. In addition, the occurence of boundary layers may require local grid refinement specifically for high Reynolds numbers. Purely explicit time integration will usually result in a very severe time step restriction based on the smallest grid cell. Purely implicit time integration results in very large systems of nonlinear equations to be solved.

This minisymposium focuses on advanced techniques which may be used to improve time integration of the stiff semi-discrete equations resulting from the space discretized fluid equations. Examples of such techniques include exponential integrators to increase efficiency of fully implicit schemes, implicit-explicit approaches which aleviate the global time step restriction and reduce the size of the nonlinear systems to be solved or multirate schemes allowing for different time step sizes in different regions of the computational domain. Furthermore, fully implicit schemes may profit from the use of multigrid techniques to obtain a grid-independent convergence rate. Hence, investigating such accelerating methods seems promising as well.

• Lars Radtke, Numerical Structural Analysis with Application in Ship Technology, Hamburg University of Technology, Germany
• Jan Philipp Heners, Department of Aerodynamics, MTU Aero Engines AG

Numerical methods for the solution of partial differential equations are commonly used in engineering design and analysis. Typical applications include discretization approaches for structural and fluid mechanics as well as heat transfer. Today, computational resources have increased to a point, where coupled problems can be solved. Based on the above examples, fluid-structure interaction (FSI) and thermo-elasticity are typical multifield problems that require the solution of coupled subproblems. While FSI constitutes a surface coupled problem, those from thermo-elasticity are termed volumetrically coupled. In general, multifield problems can be solved monolithically, i.e. using a common numerical method for the participating subproblems. Alternatively, partitioned solution approaches are used, where the subproblems are solved individually, holding the fields of the other subproblems fixed.

Irrespectively of the underlying solution approach, special techniques are needed in order to arrive at an efficient computational method that can be used in the mentioned applications. The development of preconditioners for the possibly ill-conditioned systems that arise in monolithic approaches or the data transfer between non-matching discretizations as needed in partitioned solutions approaches are just two examples for the many active fields of research in this scope.

In this minisymposium, presentations about recent developments in research areas related to coupled problems are welcome.

• Johannes Scheel, Institute of Mechanics, University of Kassel, Germany
• Philipp Rosendahl, Institute of Structural Mechanics, Technische Universität Darmstadt, Germany
• Julian Felger, Institute of Structural Mechanics, Technische Universität Darmstadt, Germany

Modern products and designs contain a multiplicity of materials such as composites, hyperelastic media, laminates and many more. They must be designed and constructed safely in order to avoid catastrophic failure primarily caused by the initiation and propagation of cracks. Their loading is complex causing mixed-mode loading conditions. In brittle solids, the initiation of initial cracks in such media is of great interest in regard of the initiation position and length of the initiating crack. The then following loading of the crack needs to be calculated accurately, so that crack growth conditions can be evaluated. The crack deflection and therefore the path of growing cracks is of great importance, as it can determine whether failure is benign  or catastrophic. Ductile solids require sophisticated plasticity and damage models to allow for fail-safe design.

The aim of this mini-symposium is to present and discuss state of the art analytical and numerical approaches of crack initiation and growth and damage in diverse media. Damage mechanical approaches are as welcome as fracture mechanical approaches. This mini-symposium welcomes speakers who present academic analyses, practical approaches as well as applications and case studies.  

• Christian Steinke, Institute of Structural Analysis, Technische Universität Dresden, Germany
• Dennie Supriatna, Institute of Structural Analysis, Technische Universität Dresden, Germany
• Michael Drass, Institute of Structural Mechanics and Design, Technische Universität Darmstadt
• Navid Pourmoghaddam, Institute of Structural Mechanics and Design, Technische Universität Darmstadt

Brittle fracture is one of the most critical failure mechanisms in industrial materials and structural components since it leads to the total loss of structural integrity. From a structural point of view, this failure mechanism usually is manfested by a drop in reaction force, which is followed by an abrupt crack formation and propagation.

On the continuum level, a crack represents the separation of initially intact material, which is accompanied by a jump in the displacement field. On the structural level, a crack may have a strong influence on the global load bearing characteristics. Three main categories of fracture exist, i.e. brittle, ductile and cohesive, where brittle crack formation often is considered to be the most dangerous mechanism in structural engineering. In contrast to cohesive and ductile behaviour, brittle fracture usually occurs abruptly and suddenly due to rapid and unstable crack growth, often resulting in total structural failure without redundancy in the material or structure.  Brittle fracture can occur independently of the material at very small deformations, such as in glass under tensile load, or at very large deformations under any load scenarios, as is often the case for structural silicones. Other materials prone to brittle fracture are concretes (unreinforced) and a variety of rigid polymers (e.g. PMMA, PS, PLA, etc.). 

The reliable and realistic prediction of brittle fracture in the form of suitable failure hypotheses, as well as the prediction of crack formation and propagation using analytical and numerical methods, is a broad field of ongoing research, that faces several fundamental challenges. In order to be able to describe the brittle failure, first, complex, multi-axial experimental investigations under evaluation of local strains using e.g. Digital Image Correlation, are required. From the experimental investigations, failure hypotheses for any materials can be derived and statistically evaluated in order to predict the failure of any structures or to have an evaluation criterion for the analysis of crack formation and propagation. Based on the experimental findings, different  mechanisms of crack formation such as crack initiation, propagation, branching, buckling and adhesion, can be thoroughly investigated, understood and mathematically described. In addition to the main physical principles, secondary aspects, e.g. ageing, temperature and moisture, may have an impact, which should also be investigated experimentally, analytically and numerically. 

This mini-symposium is addressed to researches investigating brittle fracture with an experimental, analytical or numerical focus. Novel experimental testing techniques and findings to deepen the understanding of the relevant processes are as welcome as recent or powerful approaches to model the phenomenon in an analytical or numerical way. 

• Tillmann Wiegold, Institute of Mechanics, TU-Dortmund University, Germany
• Christian Bleiler, Institute of Applied Mechanics, University of Stuttgart, Germany

The aim of this mini-symposium is to elaborate current state-of-the-art research in the field of biomechanical modeling and simulation and to give deeper insights into the underlying theories and their applications. Common topics are, for example, the modeling of bone tissue, muscles, lung, heart and brain with a focus on novel numerical and experimental methods. Some typical methods are the multiscale FEM, phase field method, finite differences on the one hand, and computer tomography or ultrasound tests on the other. As a consequence of the diversity of the applied approaches, the mini-symposium addresses a broad spectrum from the cellular, the tissue and organ scale up to the organ system scale.

• Jana Wilmers, Chair of Solid Mechanics, School of Mechanical Engineering and Safety Engineering, University of Wuppertal, Germany
• Swantje Bargmann, Chair of Solid Mechanics, School of Mechanical Engineering and Safety Engineering, University of Wuppertal, Germany
• Benjamin Klusemann, Institute of Product and Process Innovation, Leuphana University, Lüneburg, Germany, Institute of Materials Research, Materials Mechanics, Helmholtz-Zentrum Geesthacht, Geesthacht, Germany

 The macroscopic (effective) properties of heterogeneous materials are mainly determined by their microstructural behavior at lower scales. To account for the microstructural behavior at the macroscale the concept of representative volume elements (RVEs), describing a small but representative part of the structure, is typically employed. Especially in the past analytical and semi-analytical schemes on basis of RVEs were developed. In computational micromechanics, the effective properties are often directly determined from several RVE calculations. The identification of the effective behavior can be obtained in a concurrent or sequential fashion. In the latter case, the RVE is investigated for different load cases, where these information can also be used to deduce constitutive laws to set up a multiscale approach. Key point is to solve a boundary value problem on a sample RVE via numerical methods, such as finite element or fast Fourier transform methods. Consequently an example of a concurrent approach would be the FE² approach.

One crucial aspect of all the mentioned approaches is the set-up of the RVE, including an efficient meshing. RVEs can be generated based on the reconstruction of experimentally determined microstructures, based on the simulation of a physical microstructure formation process as well as based on a purely geometrical approach. Which approach is most useful depends strongly on the specific application case. This minisymposium intends to present state of the art multiscale modeling approaches including homogenization approaches which rely on the computation of representative volume elements. Therefore, we invite in particular contributions, but not limited to, which deal with the generation, meshing and calculation of all different kinds of RVEs to determine the effective properties of heterogeneous materials, including experimental approaches as well as contributions concerning homogenization and multiscale modeling approaches which use RVEs. 

• Bai-Xiang Xu, Mechanics of Functional Materials, Institute of Materials Science, TU Darmstadt, Germany
• Marc-André Keip, Institute of Applied Mechanics, University of Stuttgart, Germany

Phase-field approaches have proven to be a powerful tool for the continuum modeling of microstructural behavior of materials in diverse fields of applications, ranging from phase transformation and separation over damage and fracture to topology optimization. This is not only due to a very general and intuitive theoretical structure, but also thanks to advantageous features including straightforward numerical implementation and flexible extension to multiphysical scenarios. Nowadays, phase-field approaches find increasing application in emergent fields of engineering and science such as in structural, functional and biological contexts. This minisymposium offers a forum to exchange experiences and ideas in model development, numerical techniques and applications spanning various aspects of phase-field modeling.

Topics include (but are not limited to):

• Damage, fracture and plasticity
• Motion of dislocations
• Domain evolution in ferroic materials
• Formation of grain boundaries
• Solidification and grain coalescence
• Phase transformation and phase separation
• Topology optimization
• Variational formulations
• Numerics and algorithms

• Stefan Descher, Institute of Mechanics - Fluid Dynamics, University of Kassel, Germany
• Olaf Wünsch, Institute of Mechanics - Fluid Dynamics, University of Kassel, Germany  

In many fields of engineering the consideration of non-Newtonian fluid flow behavior is finding its way in. The main reason for this is that advanced implementations of rheological models have become more common. This process was driven by the ongoing development of techniques in reformulation, discretization, stabilization and algorithmic realizations. Thus researchers are nowadays able to enable a great insight into process engineering applications like polymer processing and are able to perform studies over a wide range of parameters helping to understand dependencies.

To perform a reliable simulation of a process, many fields come together. The foundation are experimental investigations of the fluids flow behavior with rheometric devices. Mainly with the focus on shear behavior, but also for extensional behavior and normal stress differences, steady state and transient experiments are carried out. Depending on the results, the material functions are modeled by an adequate rheological model. Examples are the generalized Newtonian fluid, a generalized Maxwell type equation for the stress tensor or a homogenization approach based on particles in the fluid. Modeling of the process w.r.t. the constitutive equation is the next step, since certain simplifications might not be applicable for some material models. Most material models can only be considered with an adequate numerical technique. This includes e.g. the discretization of fluxes, special boundary conditions, pressure-stress-velocity coupling or a reformulation of the constitutive equation. The last step is the validation using experimental data, which is in general challenging to gather. As an example, most process engineering applications allow only limited access for measurement equipment.

Every step in this chain concerns this symposium. It intends to bring together researchers that work in the field of non-Newtonian fluids, independent on if their background is experimental, material modeling, numerical simulations or mathematics.