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

  • Experimentelle und numerische Untersuchungen zur Alterung von Klebverbindungen unter zyklischer und hygrothermischer Beanspruchung im Stahl- und Anlagenbau

    (Third Party Funds Single)

    Term: 1. November 2023 - 30. April 2026
    Funding source: Bundesministerium für Wirtschaft und Klimaschutz (BMWK)

  • Configurational Mechanics of Soft Materials: Revolutionising Geometrically Nonlinear Fracture

    (Third Party Funds Single)

    Term: 1. January 2023 - 31. December 2027
    Funding source: Europäische Union (EU)
    Abstract
    SoftFrac will revolutionise geometrically nonlinear fracture mechanics of soft materials (in short soft fracture) by capitalising on configurational mechanics, an unconventional continuum formulation that I helped shaping over the past decades. Mastering soft fracture will result in disruptive progress in designing the failure resilience of soft devices, i.e. soft robotics, stretchable electronics and tissue engineering applications. Soft materials are challenging since they can display moduli as low as only a few kPa, thus allowing for extremely large deformations. Geometrically linear fracture mechanics is well established, nevertheless not applicable for soft fracture given the over-restrictive assumptions of infinitesimal deformations. The appropriate geometrically nonlinear, finite deformation counterpart is, however, still in its infancy. By combining innovative data-driven/data-adaptive constitutive modelling with novel configurational-force-driven fracture onset and crack propagation, I will overcome the fundamental obstacles to date preventing significant progress in soft fracture. I propose three interwoven research Threads jointly addressing challenging theoretical, computational and experimental problems in soft fracture. The theoretical Thread establishes a new constitutive modelling ansatz for soft in/elastic materials, and develops the transformational configurational fracture approach. The computational Thread provides the associated novel algorithmic setting and delivers high-fidelity discretisation schemes to numerically follow crack propagation driven by accurately determined configurational forces. The experimental Thread generates and analyses comprehensive experimental data of soft materials and their geometrically nonlinear fracture for properly calibrating and validating the theoretical and computational developments. Ultimately, SoftFrac, for the first time, opens up new horizons for holistically exploring the nascent field soft fracture.

  • Wissenschaftliche Koordination und Finanzverwaltung (Z)

    (Third Party Funds Group – Sub project)

    Overall project: SFB 1540: Erforschung der Mechanik des Gehirns (EBM): Verständnis, Engineering und Nutzung mechanischer Eigenschaften und Signale in der Entwicklung, Physiologie und Pathologie des zentralen Nervensystems
    Term: 1. January 2023 - 31. December 2026
    Funding source: DFG / Sonderforschungsbereich (SFB)

  • Modellbasierter Abgleich von ex vivo und in vivo Testdaten (X01)

    (Third Party Funds Group – Sub project)

    Overall project: SFB 1540: Erforschung der Mechanik des Gehirns (EBM): Verständnis, Engineering und Nutzung mechanischer Eigenschaften und Signale in der Entwicklung, Physiologie und Pathologie des zentralen Nervensystems
    Term: 1. January 2023 - 31. December 2026
    Funding source: DFG / Sonderforschungsbereich (SFB)
    Abstract
    X01 befasst sich mit dem Problem widersprüchlicher Ergebnisse mechanischer Eigenschaften von ultraweichen Materialien wie Hirngewebe, wenn unterschiedliche ex vivo und in vivo Testverfahren verwendet werden. Unsere Hypothese ist, dass es ein kontinuumsbasiertes Simulationsmodell ermöglichen wird, die verschiedenen experimentell beobachtbaren Regime in vivo und ex vivo zu vereinen. Damit können wir erstmals mechanische ex vivo Parameter verwenden, die aus verschiedenen Testmodalitäten gewonnen wurden, um das mechanische in vivo Verhalten des menschlichen Gehirns zu erklären.

  • Modellierung und Simulation der Mechanik von Zell-Matrix Interaktionen (C01)

    (Third Party Funds Group – Sub project)

    Overall project: SFB 1540: Erforschung der Mechanik des Gehirns (EBM): Verständnis, Engineering und Nutzung mechanischer Eigenschaften und Signale in der Entwicklung, Physiologie und Pathologie des zentralen Nervensystems
    Term: 1. January 2023 - 31. December 2026
    Funding source: DFG / Sonderforschungsbereich (SFB)
    Abstract
    C01 verbindet Modellierung und Simulation zur Aufdeckung der Rolle mechanischer Zell-Matrix-Wechselwirkungen im Gehirngewebe. Dabei berücksichtigen agentenbasierte und phänomenologische Kontinuumsmodelle die Zell-Matrix-Wechselwirkungen, die Zellmigration sowie die aktive Krafterzeugung. Mittels in silico Implementierungen werden wir analysieren, wie Zell-Zell- und Zell-Matrix-Wechselwirkungen die mechanischen Eigenschaften des Systems auf Kontinuumsebene bestimmen. Weiterhin werden wir die Dynamik der Bildung neuronaler Organoide in künstlichen Matrizen mittels nichtlinearer Kontinuumsmodellierung und -simulation untersuchen.

  • Modellierung und Simulation der Regeneration von Rückenmarksgewebe (B01)

    (Third Party Funds Group – Sub project)

    Overall project: SFB 1540: Erforschung der Mechanik des Gehirns (EBM): Verständnis, Engineering und Nutzung mechanischer Eigenschaften und Signale in der Entwicklung, Physiologie und Pathologie des zentralen Nervensystems
    Term: 1. January 2023 - 31. December 2026
    Funding source: DFG / Sonderforschungsbereich (SFB)
    Abstract
    B01 zielt auf die kontinuumsbasierte Simulation der Regeneration von Rückenmarksgewebe nach Verletzungen oder Krankheiten ab. Die Modellierung und Simulation wird die zeitliche und räumliche Entwicklung von Wachstums-, Umbau- und Heilungsprozessen erfassen. Wir werden uns insbesondere auf mechanisch bedingte Prozesse konzentrieren, die an der Regeneration des Rückenmarks nach traumatischen Verletzungen und bei Multipler Sklerose beteiligt sind. Um die konstitutiven Modelle zu kalibrieren, werden wir mechanische Tests an menschlichem und tierischem Rückenmarksgewebe nutzen.

  • Exploring Brain Mechanics (EBM): Understanding, engineering and exploiting mechanical properties and signals in central nervous system development, physiology and pathology

    (Third Party Funds Group – Overall project)

    Term: 1. January 2023 - 31. December 2026
    Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
    URL: https://www.crc1540-ebm.research.fau.eu/
    Abstract
    Thecentral nervous system (CNS) is our most complex organ system. Despite tremendousprogress in our understanding of the biochemical, electrical, and geneticregulation of CNS functioning and malfunctioning, many fundamental processesand diseases are still not fully understood. For example, axon growth patterns inthe developing brain can currently not be well-predicted based solely on thechemical landscape that neurons encounter, several CNS-related diseases cannotbe precisely diagnosed in living patients, and neuronal regeneration can stillnot be promoted after spinal cord injuries.Duringmany developmental and pathological processes, neurons and glial cells aremotile. Fundamentally, motion is drivenby forces. Hence, CNS cells mechanicallyinteract with their surrounding tissue. They adhere to neighbouring cells and extracellular matrix using celladhesion molecules, which provide friction, and generate forces usingcytoskeletal proteins.  These forces aretransmitted to the outside world not only to locomote but also to probe themechanical properties of the environment, which has a long overseen huge impacton cell function.Onlyrecently, groups of several project leaders in this consortium, and a few other groupsworldwide, have discovered an important contribution of mechanical signalsto regulating CNS cell function. For example, they showed that brain tissuemechanics instructs axon growth and pathfinding in vivo, that mechanicalforces play an important role for cortical folding in the developing humanbrain, that the lack of remyelination in the aged brain is due to an increasein brain stiffness in vivo, and that many neurodegenerative diseases areaccompanied by changes in brain and spinal cord mechanics. These first insights strongly suggest thatmechanics contributes to many other aspects of CNS functioning, and it islikely that chemical and mechanical signals intensely interact at the cellularand tissue levels to regulate many diverse cellular processes.The CRC 1540 EBM synergises the expertise of engineers, physicists,biologists, medical researchers, and clinicians in Erlangen to explore mechanicsas an important yet missing puzzle stone in our understanding of CNSdevelopment, homeostasis, and pathology. Our strongly multidisciplinary teamwith unique expertise in CNS mechanics integrates advanced invivo, in vitro, and in silico techniques across time(development, ageing, injury/disease) and length (cell, tissue, organ) scalesto uncover how mechanical forces and mechanical cell and tissue properties,such as stiffness and viscosity, affect CNS function. We especially focus on(A) cerebral, (B) spinal, and (C) cellular mechanics. Invivo and in vitro studies provide a basic understanding ofmechanics-regulated biological and biomedical processes in different regions ofthe CNS. In addition, they help identify key mechano-chemical factors forinclusion in in silico models and provide data for model calibration andvalidation. In silico models, in turn, allow us to test hypotheses without the need of excessive or even inaccessibleexperiments. In addition, they enable the transfer and comparison of mechanics data and findingsacross species and scales. They also empower us to optimise processparameters for the development of in vitro brain tissue-like matricesand in vivo manipulation of mechanical signals, and, eventually, pavethe way for personalised clinical predictions. Insummary, we exploit mechanics-based approaches to advance ourunderstanding of CNS function and to provide the foundation for futureimprovement of diagnosis and treatment of neurological disorders.

  • Ein numerisches Model für den translatorischen und rotatorischen Impulstransfer von weichen deformierbaren Mikropartikeln in verdünnten Zweiphasenströmungen

    (Third Party Funds Single)

    Term: 1. January 2023 - 31. December 2025
    Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
    Abstract
    Das Hauptziel dieses Projekts ist die Erweiterung des in dem Vorgängerprojekt entwickelten numerischen Modells (starre Mikropartikel in verdünnt dispergierter Zweiphasenströmung unter Verwendung des Lagrange-Euler-Ansatzes) auf ein numerisches Modell für die Translations- und Rotationsimpulsübertragung von weichen verformbaren Mikropartikeln. Der erste Teil ist der Entwicklung eines direkten numerischen Simulationswerkzeugs (DNS) gewidmet, das die strömungsinduzierten Spannungsvektoren und die daraus resultierenden Kräfte und Momente, die auf ein weiches verformbares Partikel endlicher Abmessung wirken, gemeinsam mit der Partikelverformung lokal bestimmt. Darüber hinaus wird die Kopplung zwischen einem CFD-Löser für die Strömung auf globaler Ebene und der Lagrangschen Partikelverfolgung auf der Grundlage des neuartigen Punktpartikelansatzes für weiche verformbare Partikel hergestellt. Diese Kombination wird sowohl durch einen Online-Ansatz unter Verwendung der DNS-Ergebnisse als auch durch einen Offline-Ansatz, d.h. durch ein maschinell erlerntes (ML) Surrogatmodell, erreicht. In dem ML Rahmen wird eine große Datenbank mit strömungsinduzierten Kräften und Momenten für verschiedene Partikelformen, Ausrichtungen und Strömungsbedingungen erstellt. Diese erlaubt die Anwendung auf numerisch anspruchsvolle Strömungsprobleme mit hunderttausenden von weichen verformbaren Partikeln. Schließlich wird das abgeleitete Modell auf ein technologisch relevantes Beispiel einer verdünnen Mehrphasenströmung mit linsenförmigen Vesikeln angewendet.

  • 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 - 31. December 2027
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/home/research/p-5-compressive-failure-in-porous-materials/
    Abstract
    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.

  • 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 - 31. December 2027
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/home/research/p-10-configurational-fracture-surface-mechanics/
    Abstract
    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.

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

    (Third Party Funds Group – Overall project)

    Term: 1. January 2019 - 31. December 2027
    Funding source: DFG / Graduiertenkolleg (GRK)
    URL: https://www.frascal.research.fau.eu/
    Abstract
    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”.

  • Mikroskalige Charakterisierungsmethoden zur Kalibrierung von Stoffgesetzen für Biomaterialien und Kunststoffe

    (Own Funds)

    Term: 1. August 2014 - 31. December 2025
    Abstract
    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
    Abstract
    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.

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