Prof. Dr. Paul Steinmann

Institute of Applied Mechanics

Based on the theory of nonlinear continuum mechanics we model and simulate the complex mechanical behaviour of materials as well as transient processes such as growth, diffusion, or damage, to tackle open challenges in biomedical applications.

Research projects

  • Biomechanics
  • Biopolymers
  • Hydrogels
  • Brain mechanics across scales: Linking microstructure, mechanics and pathology (BRAINIACS)
  • Novel Biopolymer Hydrogels for Understanding Complex Soft Tissue Biomechanics
  • Microscale characterization methods for the calibration of substance laws for biomaterials and plastics
  • Modelling and computation of growth in soft biological matter

  • Micro-resolved finite element modeling and simulation of nonwovens

    (Third Party Funds Single)

    Term: 1. June 2021 - 31. May 2023
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)

    The goal of this project is to develop a modelling and simulation technique enabling:
    (i) the generation of nonwoven unit cell models according to a given set of structure parameters (size, density/grammage, orientation distribution function, fiber properties, …) and relying on a sophisticated beam discretization and formulation extended to contact treatment
    (ii) the simulation of the relevant processing steps, i.e. the densification and bond point genera-tion, whereby, for simplicity, only isothermal processes are initially considered and the newly formed bond points are introduced via Dirichlet boundary conditions confining the nonwoven unit cell
    (iii) deformation simulations (uniaxial, biaxial, bending,…) under due consideration of fiber proper-ties and contact behavior, validation against experimental data

  • Methodenentwicklung zur Simulation von hyperelastischen Klebverbindungen unter Crashbelastung

    (Third Party Funds Single)

    Term: 1. April 2021 - 30. September 2023
    Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
  • Eine nahtlose VE-basierte Mehrskalen-Kopplungsmethode für Meso-Heterogene Materialien

    (Third Party Funds Single)

    Term: 15. March 2021 - 14. March 2024
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    The overarching objective of our proposal is to develop a revolutionary seamless horizontally coupled multiscale method for meso-heterogeneous materials. For capturing the macroscopic mechanical behaviour of meso-heterogeneous materials by modelling and simulation, which is of utmost importance from an engineering perspective, computational challenges arise from the overwhelming geometric complexity and detail of the meso-structure. This urgently asks for multiscale coupling methods that enable to reduce the computational cost of simulations at the engineering scale, however without sacrificing accuracy when capturing the influence of the meso-structure on the macroscopic mechanical response. Our approach will not rely on scale-separation in order to be suited for problems involving singularities, e.g. at crack tips, and it will use a sole and uniform description of the underlying mesoscopic material behaviour in terms of its material properties and meso-structure in macro- and mesoscopically resolved sub-domains. To achieve this goal, we take inspiration from the quasi continuum (QC) method for crystalline materials that seamlessly bridges fully resolved atomistic domains with quasi continuum domains in which the majority of the atoms are enslaved to follow the motion of only a few representative atoms (Rep-Atoms). We thus propose to substitute the notion of atoms and Rep-Atoms as used in the QC method for the case of crystalline materials by the notion of nodes and Rep-Nodes for the case of meso-heterogeneous materials. Then, the underlying material meso-structure is fully represented everywhere within a macroscopic engineering structure. However, only a much smaller sub-set of the total amount of nodes and corresponding dofs is retained for the simulation of the engineering structure. We will distinguish between the underlying sub-discretization build on all nodes to capture the meso-structure and the overlaying Sup-Discretization build on only the much lesser number of Rep-Nodes used for the simulation of the macroscopic engineering structure. The assignment of sub-discretization nodes to Sup-Discretization Rep-Nodes and the definition of the corresponding Sup-Discretization follows adaptively. A versatile approach to mesh complex domains that allows for arbitrary polygons/polyhedra is the virtual element (VE) approach based on VE Ansatz functions. Noteworthy, VE Ansatz functions are not restricted to interpolate nodal dofs merely linearly along element edges/faces. This freedom in arbitrarily choosing the polynomial degree of the Ansatz functions makes VE conceptually also amenable to p-adaptivity. Of particular interest for our current proposal is moreover that the vertexes of the arbitrary polygons/polyhedra representing a VE and carrying the nodal dofs may also lay on straight lines/planar surfaces. Thus, VE elegantly and straightforwardly enables transition between sub-domains with strongly varying discretization densities.
  • Untersuchung eigenspannungsrelevanter Elemantarvorgänge bei fließgepressten Bauteilen in der Herstellungs- und Betriebsphase

    (Third Party Funds Single)

    Term: 1. January 2021 - 31. December 2022
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Geometrisch nichtlinear elastische symplektische Kontinuumsmechanik

    (Third Party Funds Single)

    Term: 1. January 2021 - 31. December 2022
    Funding source: Deutscher Akademischer Austauschdienst (DAAD)

    Die Kontinuumsmechanik ist eine wichtige Grundlagenwissenschaft in den Ingenieur- und Naturwissenschaften, die den Zusammenhang zwischen Kräften und Deformationen (und Bewegungen) in Materialien und Strukturen modelliert. Ihre numerische Umsetzung z.B. in der Finiten Element Methode ist aus dem Alltag von Berechnungsabteilungen von technologieorientierten Unternehmen aufgrund ihrer hervorgehobenen Relevanz heutzutage nicht mehr wegzudenken. Das hier beantragte Vorhaben zielt, motiviert durch Konzepte der Hamiltonschen Dynamik auf die erstmalige Etablierung eines völlig neuartigen, sogenannten symplektischen Zugangs zur geometrisch nichtlinearen Kontinuumsmechanik mit zunächst speziellem Fokus auf die nichtlineare Elastizität. Die symplektische Formulierung der geometrisch nichtlinearen Kontinuumsmechanik verspricht neben ihrer Eleganz dabei insbesondere zahlreiche Vorteile im Rahmen ihrer numerischen Umsetzung. Die nichtlineare Elastizität hat vielfältige bedeutende Modellierungsanwendungen im Bereich weicher und weichster Materialien mit größter aktueller Bedeutung beispielweise für die Mechanik biologischer Gewebe, die Soft-Robotik sowie zahlreicher derzeit entwickelter high-tech Metamaterialien. In Summe wird hier sehr vielversprechendes aber auch riskantes thematisches Neuland betreten, wobei die Erfolgsaussichten des Vorhabens aufgrund der komplementären Expertise der Projektpartner als sehr hoch einzuschätzen sind.

  • Eine hybride Fuzzy-Stochastische-Finite-Element-Methode für polymorphe, mikrostrukturelle Unsicherheiten in heterogenen Materialien

    (Third Party Funds Single)

    Term: 1. December 2020 - 30. November 2023
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Eine hybride Fuzzy-Stochastische-Finite-Element-Methode für polymorphe, mikrostrukturelle Unsicherheiten in heterogenen Materialien

    (Third Party Funds Single)

    Term: 1. December 2020 - 30. November 2023
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Experimentelle und numerische Untersuchung des Einflusses variabler Betriebstemparaturen auf das Trag- und Versagensverhalten struktureller Klebverbindungen unter Crashbelastung

    (Third Party Funds Single)

    Term: 1. June 2020 - 30. November 2022
    Funding source: Bundesministerium für Wirtschaft und Technologie (BMWi)
  • Investigation of residual stress related elementary processes in cold forged components in the manufacturing and operating phase

    (Third Party Funds Single)

    Term: 1. January 2020 - 31. December 2021
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Multiskalen Modellierung und Simulation ferroelektrischer Materialien

    (Third Party Funds Single)

    Term: 1. December 2019 - 30. November 2022
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Mesoscopic modelling and simulation of properties of additively manufactured metallic parts (C5)

    (Third Party Funds Group – Sub project)

    Overall project: CRC 814 - Additive Manufacturing
    Term: 1. July 2019 - 30. June 2023
    Funding source: DFG - Sonderforschungsbereiche
    URL: https://www.crc814.research.fau.eu/projekte/c-bauteile/teilprojekt-c5/

    Based on the gained knowledge of projects B4 and C5,the aim of this project is to account for the influence of part borders on theresulting material/part-mesostructure for powder- and beam-based additivemanufacturing technologies of metals and to model the resulting meso- andmacroscopic mechanical properties. The mechanical behavior of thesemesostructures and the influence of the inevitable process-based geometricaluncertainties is modelled, verified, quantified and validated especially forcellular grid-based structures.

  • Kombinierte Form- und Topologieoptimierung für elektro-magnetisch gekoppelte intelligente Materialien

    (Third Party Funds Single)

    Term: 15. June 2019 - 14. June 2022
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
  • Novel Biopolymer Hydrogels for Understanding Complex Soft Tissue Biomechanics

    (FAU Funds)

    Term: 1. April 2019 - 31. March 2022
    URL: https://www.biohydrogels.forschung.fau.de/

    Biological tissues such as blood vessels, skin, cartilage or nervous tissue provide vital functionality
    to living organisms. Novel computational simulations of these tissues can provide insights
    into their biomechanics during injury and disease that go far beyond traditional approaches. This
    is of ever increasing importance in industrial and medical applications as numerical models will
    enable early diagnostics of diseases, detailed planning and optimization of surgical procedures,
    and not least will reduce the necessity of animal and human experimentation. However, the extreme
    compliance of these, from a mechanical perspective, particular soft tissues stretches conventional
    modeling and testing approaches to their limits. Furthermore, the diverse microstructure
    has, to date, hindered their systematic mechanical characterization. In this project, we will, as a
    novel perspective, categorize biological tissues according to their mechanical behavior and identify
    biofabricated proxy (substitute) materials with similar properties to reduce challenges related
    to experimental characterization of living tissues. We will further develop appropriate mathematical
    models that allow us to computationally predict the tissue response based on these proxy
    materials. Collectively, we will provide a catalogue of biopolymeric proxy materials for different
    soft tissues with corresponding modeling approaches. As a prospect, this will significantly facilitate
    the choice of appropriate materials for 3D biofabrication of artificial organs, as well as modeling
    approaches for predictive simulations. These form the cornerstone of advanced medical
    treatment strategies and engineering design processes, leveraging virtual prototyping.

  • Teilprojekt P10 - Configurational Fracture/Surface Mechanics

    (Third Party Funds Group – Sub project)

    Overall project: Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics (FRASCAL)
    Term: 2. January 2019 - 30. June 2023
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/home/research/p-10-configurational-fracture-surface-mechanics/

    In a continuum the tendency of pre-existing cracks to propagate through the ambient material is assessed based on the established concept of configurational forces. In practise crack propagation is however prominently affected by the presence and properties of either surfaces and/or interfaces in the material. Here materials exposed to various surface treatments are mentioned, whereby effects of surface tension and crack extension can compete. Likewise, surface tension in inclusion-matrix interfaces can often not be neglected. In a continuum setting the energetics of surfaces/interfaces is captured by separate thermodynamic potentials. Surface potentials in general result in noticeable additions to configurational mechanics. This is particularly true in the realm of fracture mechanics, however its comprehensive theoretical/computational analysis is still lacking.

    The project aims in a systematic account of the pertinent surface/interface thermodynamics within the framework of geometrically nonlinear configurational fracture mechanics. The focus is especially on a finite element treatment, i.e. the Material Force Method [6]. The computational consideration of thermodynamic potentials, such as the free energy, that are distributed within surfaces/interfaces is at the same time scientifically challenging and technologically relevant when cracks and their kinetics are studied.

  • Teilprojekt P5 - Compressive Failure in Porous Materials

    (Third Party Funds Group – Sub project)

    Overall project: Skalenübergreifende Bruchvorgänge: Integration von Mechanik, Materialwissenschaften, Mathematik, Chemie und Physik (FRASCAL)
    Term: 2. January 2019 - 30. June 2023
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/home/research/p-5-compressive-failure-in-porous-materials/

    Materials such as solid foams, highly-porous cohesive granulates, for aerogels possess a mode of failure not available to other solids. cracks may form and propagate even under compressive loads (‘anticracks’, ‘compaction bands’). This can lead to counter-intuitive modes of failure – for instance, brittle solid foams under compressive loading may deform in a quasi-plastic manner by gradual accumulation of damage (uncorrelated cell wall failure), but fail catastrophically under the same loading conditions once stress concentrations trigger anticrack propagation which destroys cohesion along a continuous fracture plane. Even more complex failure patterns may be observed in cohesive granulates if cohesion is restored over time by thermodynamically driven processes (sintering, adhesive aging of newly formed contacts), leading to repeated formation and propagation of zones of localized damage and complex spatio-temporal patterns as observed in sandstone, cereal packs, or snow.

    We study failure processes associated with volumetric compaction in porous materials and develop micromechanical models of deformation and failure in the discrete, porous microstructures. We then make a scale transition to a continuum model which we parameterise using the discrete simulation results.

  • Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics (FRASCAL)

    (Third Party Funds Group – Overall project)

    Term: 1. January 2019 - 30. June 2023
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/

    The RTG aims to improve understanding of fracture in brittle heterogeneous materials by developing simulation methods able to capture the multiscale nature of failure. With i) its rooting in different scientific disciplines, ii) its focus on the influence of heterogeneities on fracture at different length and time scales as well as iii) its integration of highly specialised approaches into a “holistic” concept, the RTG addresses a truly challenging cross-sectional topic in mechanics of materials. Although various simulation approaches describing fracture exist for particular types of materials and specific time and length scales, an integrated and overarching approach that is able to capture fracture processes in different – and in particular heterogeneous – materials at various length and time resolutions is still lacking. Thus, we propose an RTG consisting of interdisciplinary experts from mechanics, materials science, mathematics, chemistry, and physics that will develop the necessary methodology to investigate the mechanisms underlying brittle fracture and how they are influenced by heterogeneities in various materials. The insights obtained together with the methodological framework will allow tailoring and optimising materials against fracture. The RTG will cover a representative spectrum of brittle materials and their composites, together with granular and porous materials. We will study these at length and time scales relevant to science and engineering, ranging from sub-atomic via atomic and molecular over mesoscale to macroscopic dimensions. Our modelling approaches and simulation tools are based on concepts from quantum mechanics, molecular mechanics, mesoscopic approaches, and continuum mechanics. These will be integrated into an overall framework which will represent an important step towards a virtual laboratory eventually complementing and minimising extensive and expensive experimental testing of materials and components. Within the RTG, young researchers under the supervision of experienced PAs will perform cutting-edge research on challenging scientific aspects of fracture. The RTG will foster synergies in research and advanced education and is intended to become a key element in FAU‘s interdisciplinary research areas “New Materials and Processes” and “Modelling–Simulation–Optimisation”.

  • Fractures across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics/ Skalenübergreifende Bruchvorgänge: Integration von Mechanik, Materialwissenschaften, Mathematik, Chemie und Physik

    (Third Party Funds Single)

    Term: 1. January 2019 - 30. June 2023
    Funding source: Deutsche Forschungsgemeinschaft (DFG)
    URL: https://www.frascal.research.fau.eu/
  • Investigation of residual stress related elementary processes in cold forged components in the manufacturing and operating phase

    (Third Party Funds Single)

    Term: 1. February 2018 - 31. December 2022
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)

    Due to the potential of forming induced residual stresses to influence component properties, a deeper understanding of the mechanisms of residual stress generation and stability is required. Therefore, the approach to the research project is structured into the phases of component manufacturing (generation of residual stresses), component operation (residual stress stability) and process design (exploitation of residual stresses). As reference process the forward rod extrusion is used, which is established as standard process in industrial use. Due to the trend towards component materials with higher strength and corrosion resistance, two stainless steels are used in the project. The investigations include parallel experimental and numerical analyses of the process and its synthesis.

    During the first phase, the necessary experimental equipment for component manufacture and testing was set up, material and friction parameters were identified, components were formed under consideration of different parameter variants and their residual stresses were determined by X-ray diffraction. In a complementary approach, macroscopic finite element models with subroutines for an extended post-processing of residual stresses were developed on the simulation side and applied in the context of numerical parameter variations. Furthermore, differential geometric and continuum mechanical relationships of residual stresses were investigated and the material modelling was extended to crystal plasticity. The predictivity of the numerical results was quantified on the basis of experimental results.

    The second phase concentrates on the residual stress stability in component use and the process robustness during component manufacture. The knowledge gained will be used at the end of the second and in the third phase to specifically influence the operating behaviour and to control the cyclic strength.

    The objective in the second phase is the experimental and numerical determination of the mechanical and thermal residual stress stability. As a requirement for the targeted influencing, relevant parameters will be identified. These cause-and-effect relationships are to be plausibilised by means of fundamental physical effects, whereby a recourse is made to effects described in the literature and numerical methods for the derivation of basic model ideas. Based on the experience gained so far, fluctuations of input variables and previously known disturbance variables are to be taken into account in all investigations. A further prerequisite for a systematic investigation of the fundamental mechanisms relevant to residual stresses is an increase in the numerical modeling and prediction accuracy of the deformation-induced residual stresses. In analogy to the generation phase, a constant comparison of simulation and experiment is therefore also carried out in the operating phase in the sense of an assessment of the prognosis quality of the numerical approaches and the plausibility of the experimental laboratory results.

    The Project is part of the DFG priority programm SPP2013 "Targeted Use of Forming Induced Internal Stresses in Metal Components". Within the priority program, the subproject takes part in the expert groups Production technology (thick-walled) and Mechanics and simulation.

  • Mikroskalige Charakterisierungsmethoden zur Kalibrierung von Stoffgesetzen für Biomaterialien und Kunststoffe

    (Own Funds)

    Term: 1. August 2014 - 31. December 2025

    Aussagefähige Bauteilsimulationen erfordern eine quantitativ exakte Kenntnis der Materialeigenschaften. Dabei sind klassische Charakterisierungsmethoden
    teilweise aufwendig, in der Variation und Kontrolle der Umgebungsbedingungen anspruchsvoll oder in der räumlichen Auflösung begrenzt. Das Projekt beschäftigt sich
    deshalb mit der Ertüchtigung hochauflösender Meßmethoden wie Nanoindentation oder Rastkraftmikroskopie und der komplementierenden Entwicklung numerischer
    Verfahren zur Kalibrierung (Parameteridentifikation) inelastischer Stoffgesetze aus den Meßdaten. Inhärent anspruchsvoll sind dabei die geeignete Gestaltung der
    Probekörper und ihrer Fixierung, die den gesuchten Eigenschaften angepaßte Versuchsführung und die hinreichend genaue Reproduktion derselben im Rahmen der zur
    Parameteridentifikation erforderlichen Finite-Elemente-Simulationen.
     

  • Kontinuumsmechanische Modellierung und Simulation der Aushärtung und Inelastizität von Polymeren sowie Interphasen in Klebverbunden

    (Own Funds)

    Term: 1. August 2008 - 31. December 2025

    Die mechanischen Eigenschaften von Polymerwerkstoffen hängen nicht nur von der chemischen Komposition und den Umgebungsbedingungen (Temperatur, Feuchte,...) ab,
    sondern sie variieren teilweise erheblich mit dem verwendeten Aushärteregime und der Temperaturhistorie. Sie sind darüber hinaus vor allem in Verbundsituationen
    u.U. sogar ortsabhängig von den Eigenschaften der Kontaktpartner beeinflußt, bilden also Eigenschaftgradienten (sog. Interphasen) aus.
    Um diese Effekte bei der Simulation von Bauteilen korrekt abbilden zu können werden im Rahmen des Projektes Modelle entwickelt und erweitert,
    die zeit-, orts- und umgebungsabhängige Materialeigenschaften wie Steifigkeitsevolutionen und -gradienten, Aushärteschrumpf und verschiedene Arten von
    Inelastizität (Viskoelastizität, Elastoplastizität, Viskoplastizität, Schädigung) berücksichtigen können.

2021

2020

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