Seminar "Material Modeling"

• Place: Weierstrass-Institute for Applied Analysis and Stochastics
  Place: Mohrenstraße 39, 10117 Berlin
  Place: Weierstrass Lecture Room (WIAS-406)
• Time: Tuesdays (monthly), 1:30PM - 3:00PM
• Organizers: Martin Heida, Wolfgang König, Dirk Peschka, Marita Thomas, Barbara Wagner

Title: Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations within GENERIC

Abstract: tba

25.07.2019, 10:00

Title: Arresting phase separation with polymer networks

Abstract: Some of the most beautiful colours in nature are seen in birds that have developed materials with extremely monodisperse, colloidal microstructures (these yield vivid structural colours). Previously it has been suggested that these can be grown by a process of arrested phase separation. Here, we take inspiration from such natural materials to grow composites with a uniform microstructure via a process of phase separation in an elastic gel network. These composites consist of uniform liquid droplets embedded in an elastic gel. The size of the droplets can be easily tuned with a number of different parameters, and presents an interesting challenge for modelling. I will also discuss how this process has applications in colloidal synthesis and phase-separation processes in living cells.

Title: Truncated nonsmooth Newton multigrid for nonsmooth minimization problems

Abstract: Many problems originating from continuum mechanics and material sciencelead to large scale nonsmooth optimization problems after discretization in time and space. Examples are classical binary or multi-component phase field models for phase transition and separation, frictional contact problems, plasticity, and phase field-like approaches for brittle and ductile fracture. Since standard numerical methods like, e.g., multigrid are not directly applicable due to the nonsmoothness, generic nonsmooth optimization methods are frequently used for such problems which often comes at the price of reduced efficiency. In the talk we present the Truncated Nonsmooth Newton Multigrid (TNNMG)method which combines techniques from nonsmooth optimization with multigrid and domain decomposition ideas. Instead of a black box approach this is done in a structure aware fashion leading to iterative methods whose efficiency is comparable to state of the art methods for smooth problems while being robust with respect nonsmoothness. In the talk we will introduce the algorithm, discuss convergence, and present numerical examples for various applications illustrating the efficiency of the presented approach.

Title: Unconventional frameworks for the simulation of coupled bulk-interface problems

Abstract: Partial differential equations with interfaces, holes, cracks, or defects often require the numerical solution of coupled bulk-interface problems. In this talk, I will discuss and analyse some techniques that can be used to tackle this class of problems, using non-matching discretisations that combine Finite Element Methods, regularization techniques, weighted Sobolev spaces, and reduced order models.

Title: Line Defect dynamics and solid mechanics

Abstract: Continuum mechanics has been a successful model for studying macroscopic deformations and the forces causing them. The usual framework allows the study of continuous deformations giving way to surfaces of discontinuity, but does not provide an adequate framework for considering the dynamics of the terminating lines of surfaces of discontinuity, were such to occur. It turns out that such terminating lines of surfaces of discontinuity serve as a model of common line defects that arise in a host of materials; dislocations and grain/phase boundary junctions in crystalline and soft matter. I will describe a framework for considering line defect dynamics within continuum mechanics. I will show how the kinematics of line defect dynamics provides a unifying theme for describing the defects mentioned above, resulting in an augmentation of the classical balance laws of continuum mechanics with a microscopic conservation law for topological charge carried by these defect lines. The theory will be illustrated with examples related to dislocation dynamics with inertia, the computation of fields of interfacial defects like the star disclination and grain boundary disconnections.

Title: On the convergence of viscous approximation for rate-independent processes with regulated inputs

Abstract: The vanishing viscosity method is a popular tool for describing rate-independent evolution. It consists in the analysis of the limiting behavior of a regularized problem obtained by introducing a viscous dissipation mechanism which stabilizes the process. In this talk, we discuss some issues related to viscous approximations to rate-independent processes when different choices of the viscosity operator are considered. We show that the viscous limit exists, and the associated input-output operator is continuous in the space of regulated functions. Notably, we observe that the vanishing viscosity limit may exhibit some unexpected behavior when the input has some jump discontinuities.

Title: Reliable, efficient and robust a posteriori estimators for the variational inequality in fracture phase-field models

Abstract: tba

Title: Aspects on the modelling of material degradation

Abstract: Material degradation describes the loss of nominal strength. The physical causes as well as the consequences are often manifold: Mechanical loads exceeding a threshold value or temperature/species-induced effects are possible and can lead e.g. to a reduced load-bearing capacity in general or to crack initiation and propagation in a local sense. The formulation and solution of this initial boundary value problem must therefore cover some crucial aspects: e.g. the fulfillment of the second law of thermodynamics by the constitutive as well as the degradation model or the consideration of the PDE system's stability loss when dealing with strict local models. Well-established models that will be discussed in the finite-element framework are the fracture-mechanics based cohesive zone model, the damage-mechanics based phase-field model and the micromechanics-based Gurson-model. Furthermore, an extension will be presented that allows for the simulation of corrosion processes.

Title: The alternating direction method of multipliers with variable step sizes for the iterative solution of nonsmooth minimization problems and application to BV-damage evolution

Abstract: The alternating direction method of multipliers (ADMM) is a flexible numerical method to solve a large class of convex minimization problems. Its most significant properties are the unconditional convergence with respect to the involved step size and the direct applicability. However, the performance critically depends on the choice of the step size. We propose an automated step size adjustment that relies on the monotonicity of the residual to accelerate the ADMM. Numerical experiments show a remarkable improvement over the standard ADMM with fixed step sizes. The ADMM with variable step sizes is then applied to a model for rate-independent, total variation regularized damage processes. The total variation regularization of the damage variable leads to sharp transitions of damaged to undamaged areas in the material. The results are compared to an H¹ regularization of the damage and the simulations reveal that, indeed, for the total variation regularization sharp transitions can be observed whereas for the H¹-regularization the interface is smeared out.

Thursday 28.02. 10am in Room 406 !!!

Title: Gradient dynamics models for films of complex fluids and beyond - dewetting, line deposition and biofilms

Abstract: After briefly reviewing a number of experiments on dewetting and evaporating thin films/drops of simple and complex liquids, I introduce the concept of a gradient dynamics description of the evolution of interface-dominated films and drops on solid substrates. First, the case of films/drops of simple non-volatile liquid is discussed, and illustrated with results on droplet patterns and sliding droplets. As a further example, the diffusion equation is formulated as a gradient dynamics. The obtained elements are combined into a thermodynamically consistent gradient dynamics formulation for films of mixtures and surfactant suspensions.
Next, such models are employed to investigate the out-of-equilibrium process of the deposition of line patterns at receding contact lines for evaporatively dewetting solutions/suspensions and in Langmuir Blodgett transfer. Finally, I discuss how to combine the presented thin-film dynamics with bioactive elements to obtain models for the osmotic spreading of biofilms growing on moist agars. I conclude with a summary and outlook.

Title: Charge and phonon transport in graphene

Abstract: ( pdf) The last years have witnessed a great interest for 2D-materials due to their promising applications. The most investigated one is graphene which is considered as a potential new material to exploit in nano-electronic and optoelectronic devices.
Charge transport in graphene can be described with several degrees of physical complexity. At quantum level an accurate model is represented by the Wigner equation but in several cases its semiclassical limit, the Boltzmann equation, constitutes a fully acceptable model. However, the numerical difficulties encountered in the direct solution of both the Wigner and the semiclassical Boltzmann equation has prompted the development of hydrodynamical, energy transport and drift diffusion models, in view of the design of a future generation of electron devices where graphene replaces standard semiconductors like silicon and gallium arsenide. Moreover, thermal effects in low dimensional structures play a relevant role and, therefore, also phonon transport must be included.
Interesting new mathematical issues related to the peculiar features of graphene arise. The main aspects will be discussed and recent results illustrated in the perspective of future developments, in particular the optimization of graphene field effect transistors.

Title: Representing crystals for kernel-based learning of their properties

Abstract: Accurate modeling of many-body systems like crystals requires to capture their quantum-mechanical nature at the atomic scale. The solution of the associated electronic structure problem is however illusional due to the number of variables, but we obtain certain properties by computational-demanding methods like density-functional theory. In this talk, I will discuss the potential of kernel-based machine learning to circumvent this computational bottleneck and predict crystal properties. A crucial preliminary step is the representation of crystals, which has to satisfy different conditions for the learning to perform optimally.

Title: From solvent free to dilute electrolytes: A unified continuum approach

Abstract: tba

16.10.2018, 10:15

Title: Phase field modelling of fracture -- From a mechanics point of view

Abstract: tba

Title: From individual motion to collective cell migration

Abstract: The motion of living cells plays an important role in many important processes, like in wound healing, as part of the immune system, and in tissue development. Modeling the migration of cells thereby involves the study of the motion of a single cell and on collective behavior of many cells.
Various different mechanisms have been pro-posed and studied to describe motility of a singlecell in different situations. We study the motil-ity mechanisms of eukaryotic cells by polymer-ization and depolymerization of and contractile stresses between cytoskeletal actin filaments. A (hydrodynamic) active polar gel model is presented with the polarity as mean alignment of actin fibres in the cytoskeleton. Modeling the fibre network as a field of polar liquid crystals, i.e. rod-like particles with polar order, a spontaneous symmetry breaking in the alignment leads to cell motility. Shape changes and an internal flow flow of actin push the cell forward. The model combines a Helfrich-Navier-Stokes model with surface tension and an active polar gel theory in a diffuse-interface setting.
While the mechanics, dynamics and motility of individual cells have received considerable attention, the understanding of collective behavior of cells, the interaction and influence of their motion, remains challenging. We consider a continuum model for collective cell movement. Each cell is modeled by a phase field, driven by an active polar gel model and the cells interact via steric interactions. The collision dynamics of two cells is studied in detail and the collective behavior of about 1000 cells in a crowded environment is considered. This process is computational challenging due to the high number of individuals, their local resolution and individual motion driven by principles shown before. This leads to a highly parallelized multi-phase field model.

Title: Localized Instabilities in Phase-Changing Systems: The Effect of Elasticity

Abstract: tba

07.03.2018, 14:00

Erhard-Schmidt lecture room

Title: Modeling and simulation of charge transport in organic semiconductors via kinetic and drift-diffusion models

Abstract: The use of organic materials in electronic applications such as displays, photovoltaics, lighting, or transistors, has seen an substantial increase in the last decade. This is mainly due to the lower production cost, sustainability, and flexibility. Moreover, the toolbox of organic chemistry opens an enormous potential for new device concepts.
In contrast to classical semiconductors such as silicon or gallium-arsenide, charge-transport in organic materials happens via temperature activated hopping transport of electrons or holes between adjacent molecules. Here, the crucial feature is the random alignment of the molecule, which leads to a disordered system with Gaussian distributed energy levels.
A common approach to simulate the transport of charge carriers in organic materials is based on a master equation description of the hopping transport and kinetic Monte-Carlo methods. However, the computational costs of this approach are typically very high and the treatment of complicated multi-dimensional device structures is very challenging. Moreover, the inclusion of multi-physics effects such as heat flow is out of scope. The latter, in particular, is of high importance as organic devices show a strong interplay between electrical current and heat flow. Here, drift-diffusion models provide an immense advantage.
In this talk, we give an overview over the two modeling approaches and give an outlook to future challenges.

Title: Dimension reduction in the context of structured deformations

Abstract: The theory of structured deformations shows good potential to deal with mechanical problems where multiple scales and fractures are present. Math- ematically, it amounts to relaxing a given energy functional and to show also the relaxed one has an integral representation. In this seminar, I will focus on a problem for thin objects: the derivation of a 2D relaxed energy via dimension reduction from a 3D energy, incorporat- ing structured deformations in the relaxation procedure. I will discuss the two-step relaxation (first dimension reduction, then structured deformations and vice versa) and I will compare it with another result in which the two relaxation procedures are carried out simultaneously. An explicit example for purely interfacial initial energies will complete the presentation. These results have been obtained in collaboration with G. Carita, J. Matias, and D.R. Owen.

Title: Modelling error estimates and model adaptation in compressible flows

Abstract: Compressible fluid flows may be described by different models having different levels of complexity. One example are the compressible Euler equations which are the limit of the Navier-Stokes-Fourier (NSF) equations when heat conduction and viscosity vanish. Arguably the NSF system provides a more accurate description of the flow since viscous effects which are neglected in Euler's equation play a dominant role in certain flow regimes, e.g. thin regions near obstacles. However, viscous effects are negligible in large parts of the computational domain where convective effects dominate. Thus, it is desirable to avoid the effort of handling the viscous terms in these parts of the domain, that is, to use the NSF system only where needed and simpler models, on the rest of the computational domain. To this end we derive an a posteriori estimator for the modelling error which is based on the relative entropy stability framework and reconstructions of the numerical solution. This is a crucial step in the construction of numerical schemes handling model adaptation in an automated manner.

14.12.2017, 14:00

Erhard-Schmidt lecture room

Title: Macroscopic models for ion transport in nanoscale pores

Abstract: During this talk, we discuss ionic transport through confined geometries. Our problem concerns modeling ionic flow through nanopores and ion channels. We present different methods of engineering the pores together with its characteristics. Next, we comment on the challenges in simulating the flow efficiently.
In the second part, we present a derivation of 1D asymptotic reduction of the Poisson-Nernst-Planck model applied to long and narrow pores. We discuss numerical schema and compare the results the solution of the two-dimensional system of equations.

HVP 11a, room 4.01

Title: Asymptotic analysis of models involving surface diffusion

Abstract: We study the evolution of solid surfaces and pattern formation by surface diffusion. Phase field models with degenerate mobilities are frequently used to model such phenomena, and are validated by investigating their sharp interface limits. We demonstrate by a careful asymptotic analysis involving the matching of exponential terms that a certain combination of degenerate mobility and a double well potential leads to a combination of surface and nonlinear bulk diffusion to leading order. We also present a stability analysis for the sharp interface model of an evolving non-homogeneous base state and show how to correctly determine the dominant mode, which is not the one predicted by a frozen mode eigenvalue analysis.

starts at 1:45 PM

Title: Homogenization of the generalized Poisson-Nernst-Planck system with nonlinear interface conditions

Abstract: We consider the generalized system of nonlinear Poisson-Nernst-Planck equations, which describes concentrations of multiple charged particles with the overall electrostatic potential. It is modeled in terms of the Fickian multiphase diffusion law coupled with thermodynamic principles. The generalized model is supplied by volume and positivity constraints and quasi-Fermi electrochemical potentials depending on the pressure. The model describes a plenty of electrokinetic phenomena in physical and biological sciences. We examine nonlinear inhomogeneous transmission conditions describing electro-chemical reactions on the interface in a periodic two-phase medium. We aim at a proper variational modeling, well-posedness, and asymptotic analysis as well as homogenization of the model.

Title: Existence for dynamic Griffith fracture with a weak maximal dissipation condition

Abstract: The study of dynamic fracture is based on the dynamic energy-dissipation balance. This condition is always satisfied by a stationary crack together with a displacement satisfying the system of elastodynamics. Therefore to predict crack growth a further principle is needed. We introduce a weak maximal dissipation condition that, together with elastodynamics and energy balance, provides a model for dynamic fracture, at least within a certain class of possible crack evolutions. In particular, we prove the existence of dynamic fracture evolutions satisfying this condition, subject to smoothness constraints, and exhibit an explicit example to show that maximal dissipation can indeed rule out stationary cracks.
These results are obtained in collaboration with G. Dal Maso (SISSA) and C. Larsen (WPI).

HVP 11a, room 4.01

Title: The applicative challenges of Smart Materials: from Sensing to Harvesting

Abstract: The talk would provide a view on functional materials observed and employed at the macro-scale. Starting from the most known Multi-Functional materials, a common modeling approach, based on the definition of constitutive relationships, is discussed.
Examples on the effectiveness of the constitutive equations in the analysis and design problems in engineering is illustrated, along with the basic challenges arising when these materials are of concern.
Further, the statement of consistent constitutive relationships when rate-independent memory processes (hysteresis) are considered is also carried out, through the definition of models for multi-input/multi-output systems that formally satisfy the Duhem inequality. Practical examples and specific applications are also proposed.

starts at 3:15 PM
Erhard-Schmidt lecture room

Title: In Between Energetic and Balanced Viscosity solutions of rate-independent systems: the Visco-Energetic concept, with some applications to solid mechanics

Abstract: This talk focuses on weak solvability concepts for rate-independent systems. Visco-Energetic solutions have been recently obtained by passing to the time- continuous limit in a time-incremental scheme, akin to that for Energetic solutions, but perturbed by a "viscous" correction term, as in the case of Balanced Viscosity solutions. However, for Visco-Energetic solutions this viscous correction is tuned by a fixed parameter. The resulting solution notion is characterized by a stability condition and an energy balance analogous to those for Energetic solutions, but, in addition, it provides a fine description of the system behavior at jumps as Balanced Viscosity solutions do. Visco-Energetic evolution can be thus thought as "in-between" Energetic and Balanced Viscosity evolution.
We will explore these aspects in a general metric framework. We will then illustrate the application of the Visco-Energetic concept to models for damage and finite-strain plasticity.
Joint work with Giuseppe Savaré.

starts at 1:00 PM

Title: Random conductance model in a degenerate ergodic environment

Abstract: Consider a continuous time random walk on the Euclidean lattice ℤ in an environment of random conductances taking values in [0, ∞). The law of the environment is assumed to be ergodic with respect to space shifts and satisfies some moment conditions. In this talk, I will review old and discuss recent results on quenched invariance principles (an instance of stochastic homogenization in path space), local limit theorems as well as heat kernel estimates for this Markov process.
This is joint work with Sebastian Andres (Univ. Cambridge), Jean-Dominique Deuschel (TU Berlin) and Tuan Ahn Nguyen (TU Berlin).

Title: Stochastic homogenization of discrete energies with degenerate growth

Abstract: We present a discrete-to-continuum analysis for lattice systems with random interactions. In particular, we assume that the interaction potentials satisfy polynomial growth conditions which degenerate and are given in terms of certain weight functions. Under suitable moment conditions on the weight functions and stationarity/ergodicity assumptions for the interaction potentials, we prove that the discrete energy Gamma-converges almost surely to a deterministic, homogeneous and non-degenerate integral functional.
This is joint work with S. Neukamm (TU Dresden) and A. Schlömerkemper (U Würzburg)

Title: Modelling Device Charge Dynamics on the Microscopic Scale

Abstract: We attempt to predict the properties of organic semiconductor (OSC) materials using a microscopic ab initio approach. Charge transport through organic semiconductors (OSCs) is qualitatively different from metallic semiconductors, charges hop between molecules discretely. Marcus theory describes the microscopic hopping mechanism, quantum chemistry methods can calculate the parameters and kinetic Monte Carlo methods can be used to model charge motion. We also need to describe realistic configurations of a set of given molecules. To combine all of these approaches into a single multi-scale model is the goal of the EXTMOS project. We present simulations of charge carrier motion in a system of discotic molecules with high levels of shape anisotropy; using explicitly calculated parameters we are able to capture and quantify the effect on charge transport anisotropy. We also consider the use of network models to describe collective behaviour.

Title: A numerical framework for optimal locomotion at low Reynolds numbers

Abstract: Swimming (advancing in a fluid in the absence of external propulsive forces by performing cyclic shape changes) is particularly demanding at low Reynolds numbers. This is the regime of interest for microorganisms and micro- or nano-robots, where hydrodynamics is governed by Stokes equations, and swimming is complicated by the fact that viscosity dominates over all participating forces. We exploit a formulation of the swimming problem in the context of Control Theory, and we present a numerical approximation scheme based on Boundary Element Methods (BEM) and reduced space Successive Quadratic Programming (rSQP) that is capable of computing efficiently optimal strokes for a variety of micro swimmers, both biological and artificial. We apply this framework to the study of the locomotion of euglenids (one of the best-known groups of flagellates). These organisms exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). We identify previously unnoticed features of metaboly, and we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.