# Material Mechanics

The precise modeling of the material behavior is of crucial importance for the success of numerical simulations of the stress behavior of components or of processes. A research focus of the LTM is the development of constitutive models for the description of the elastic, plastic or viscoelastic behavior of different engineering materials. In addition to damage or fracture, physically coupled problems are also considered, for example the modeling of electro- or magnetoactive polymers.

### Projects:

## Bridging scales - from Quantum Mechanics to Continuum Mechanics. A Finite Element approach.

The concurrently coupled Quantum Mechanics (QM) - Continuum Mechanics (CM) approach for electro-elastic problems is considered in this proposal. Despite the fact that efforts have been made to bridge different description of matter, many questions are yet to be answered. First, an efficient Finite Element (FE)-based solution approach to the Kohn-Sham (KS) equations of Density Functional Theory (DFT) will be further developed. The h-adaptivity in the FE-based solution with non-local pseudo-potentials,…

## Modeling and computation of growth in soft biological matter

## NanoModel: Multi-scale modeling of nano-structured polymeric materials: from chemistry to materials performance

## Electronic electro-active polymers under electric loading: Experiment, modeling and simulation

The mechanical response of electronic electro-active polymers (EEAP) under electric loading is influenced both by mechanical and electric properties of the material. Understanding the behavior of EEAP is vital in the development and design of EEAP based actuators and artifical muscles. Despite the fact that applications of EEAP are very promising, until now only a handful of experimental works have been realized to characterize their material properties. Moreover, so far only one-sided coupled models were used to explain experimental data and there exist discrepancies between meausrement, modeling and simulation. In this proposal, first experimental work will be performed to determine the material characteristics of a typical EEAP material then the electro-mechanical coupling phenomenon exhibited by EEAP will be modeled within the frameof hyperelasticity and viscoelasticity. Finally, by using a variational approach, a formulation representing the fully coupled problem will be derived, discretized, linearized and solved by the Finite Element Method in order to simulate the behavior of EEAP. Benchmark simulations will be performed to validate the applicability of the coupled model. Efforts will also be directed to the study of defects of EEAP by the Material Force Method and with the help of some recent developments in the spatial and material setting of nonlinear electro-elasticity. Especially the Material Force Method will be applied in numerical studies of cracked structures made of EEAP.

## A coupled MD-FE simulation method accounting for interphases in nanoparticle filled thermoplastics.

This proposal aims at an extension of a recently developed, hybrid MD-FE simulation scheme towards its application to materials dominated by polymer-solid interphases. Only particle-based methods are able to intrinsically resolve microstructure and mechanical behavior of interphases. Therefore, we proceed with the following setup: A coarse-grained MD domain, which contains a single nanoparticle and as much polymer as necessary to ensure bulk behavior at the boundary, is included into a FE do-main. The FE boundary is used to apply various types of deformations and to record the overall stress responses of particle, surrounding interphase and bulk. With these data, the parameters of a purely continuous counterpart to the hybrid setup are iteratively adjusted until it behaves identically. As its main feature, the continuous ersatz-model substitutes the interphase between particle and polymer by an interface governed by a surface energy in the sense of Gibbs. This can be understood as a condensation of micro-scale property profiles within the 3-D interphase into a 2-D continuum mechanical model. Ultimately, after homogenizing the continuous ersatzmodel, macroscopic structure simulations allowing for a due consideration of interphase effects as occurring around nanoparticles are to be realized.

## MOCOPOLY: Multi-scale, Multi-physics Modelling and Computation of magneto-sensitive POLYmeric materials

MOCOPOLY is a careful revision of an AdG2010-proposal that was evaluated above the quality threshold in steps1&2. In the meantime the applicant has made further considerable progress related to the topics of MOCOPOLY. Magneto-sensitive polymers (elastomers) are novel smart materials composed of a rubber-like matrix filled with magneto-active particles. The non-linear elastic characteristics of the matrix combined with the magnetic properties of the particles allow these compounds to deform…

## Mehrskalenmodellierung und -simulation der Mechanik von Materialien mit Faserstruktur

Im Fokus dieses Vorhabens steht die mechanische Mehrskalenmodellierung und -simulation von Materialien mit heterogener Faserstruktur (z.B. schaumartige Filterstrukturen oder Dämmungs-materialien aus der Automobilindustrie) unter besonderer Berücksichtigung des Kontakts zwi-schen den einzelnen Fasern. Das Problem wird dabei durch die Berücksichtigung der verschie-denen geometrischen Längenskalen so komplex, dass eine direkte numerische Simulation nicht mehr möglich ist.…

## On the Modelling and Computation of Magneto-Sensitive-Elastomers

Magneto-sensitive-elastomers are smart materials which are composed of a rubber-like basis matrix filled with magneto-active particles. Due to the highly elastic properties of the rubberlike material, these compounds are able to deform significantly, i.e. geometrically non-linearly by the application of external magnetic fields. The rapid response, the high level of deformations that may be achieved, and the possibility of controlling these deformations by varying an external magnetic field, make…

## Mehrskalenmodellierung und -simulation der Mechanik von Materialien mit Faserstruktur

Im Fokus dieses Vorhabens steht die mechanische Mehrskalenmodellierung und -simulation von Materialien mit heterogener Faserstruktur (z.B. schaumartige Filterstrukturen oder Dämmungs-materialien aus der Automobilindustrie) unter besonderer Berücksichtigung des Kontakts zwi-schen den einzelnen Fasern. Das Problem wird dabei durch die Berücksichtigung der verschie-denen geometrischen Längenskalen so komplex, dass eine direkte numerische Simulation nicht mehr möglich ist.…

## A hybrid Sampling-Stochastic-Finite-Element-Method for polymorphic, microstructural uncertainties in heterogeneous materials

The overarching goal of the proposed project at the methodological side is to establish a computationally tractable numerical method that is suited to capture polymorphic uncertainties in large-scale problems (as arising from the numerical analysis of heterogeneous materials microstructures). On the one hand the method will allow for fuzzy probability distributions of the random parameters (describing a microstructures geometry) and on the other hand the method will be based on only a few reduced…

## Modeling and computation of solvent penetration in glassy polymers

The main goal of this proposal is the computational modeling of solvent penetration in glassy polymers. For most engineering applications, Fick s law accurately describes diffusive processes, but one of the applications where it miserably fails is in glassy polymers near the glass transition temperature. In the vicinity of the glass transition temperature, when a low molecular weight solvent diffuses into a glassy polymer, the latter is caused to undergo a rubber-glass phase transition. The diffsive…

## On the Formulation and the Micromechanical Origin of Non-Classical Models of Diffusion

Diffusionsprozesse, insbesondere deren Kopplung mit Verformungen, sind von großer wissenschaftlicher und technologischer Bedeutung in verschiedensten Feldern der Ingenieur-, Material- und Naturwissenschaften und deren Schnittmengen. Hervorstechende Beispiele sind etwa die Modellierung und Simulation von Lötverbindungen, die Entwicklung von Mikrostrukturen in modernen Materialien, wie sie z.B in hochentwickelten sowie zukünftigen einkristallinen Turbinenblättern verwendet werden,…

## Modelling and simulation of nonlinear electro-thermo-visco-elastic EAPs(Electronic Electro-Active Polymers)

The numerical modeling and simulation of the behavior of EEAPs (Electronic Electro-Active Polymers) under electric loading is considered in this proposal. Despite the fact that efforts have been made to simulate the behavior of EEAPs, work still needs to be done to model the electro-thermo-mechanical interaction in a body undergoing large deformation and being subjected to the influence of the free space surrounding the material body. First of all, until now there exists no thermo-dynamically consistent…

## Discrete and Continuous Methods for Modelling and Simulation of Polymeric Materials

Classical continuum approaches do not explicitly consider the specific atomistic or molecular structure of materials. Thus, they are not well suited to describe properly highly multiscale phenomena as for instance crack propagation or interphase effects in polymer materials. To integrate the atomistic level of resolution, the “Capriccio” method has been developed as a novel multiscale technique and is employed to study e.g. the impact of nano-scaled filler particles on the mechanical properties of …

## Mikroskalige Charakterisierungsmethoden zur Kalibrierung von Stoffgesetzen für Biomaterialien und Kunststoffe

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…

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

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.

## Material modelling of sheet-layered lamination stacks

The numerical simulation of sheet-layered lamination stacks, which can be found in electric motors and transformers, is a challenging task in structural mechanics due to the layout of these components. Depending on the manufacturing process, these sheets are either in frictional contact to each other or are linked together with the help of a bonding varnish. Especially the interlayer between individual sheets and their interaction have a strong influence on the structure and may be responsible for a nonlinear deformation behavior. In the context of performance and computational effort, it is desirable to avoid a full Finite-Element simulation incorporating every layer such that homogenization techniques are used in this project to derive a sophisticated surrogate material model, which takes the special micro-structure of these lamination stacks into account.

## GRK2423 - P8: Teilprojekt P8 - Fracture in Polymer Composites: Meso to Macro

The mechanical properties and the fracture toughness of polymers can be increased by adding silica nanoparticles. This increase is mainly caused by the development of localized shear bands, initiated by the stress concentrations due to the silica particles. Other mechanisms responsible for the observed toughening are debonding of the particles and void growth in the matrix material. The particular mechanisms depend strongly on the structure and chemistry of the polymers and will be analysed for two classes of polymer-silica composites, with highly crosslinked thermosets or with biodegradable nestled fibres (cellulose, aramid) as matrix materials.

The aim of the project is to study the influence of different mesoscopic parameters, as particle volume fraction, on the macroscopic fracture properties of nanoparticle reinforced polymers.

## GRK2423 - P10: Teilprojekt P10 - 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.

## Identifikation von Interphaseneigenschaften in Nanokompositen

In engineering applications, plastics play an important role and offer new possibilities to achieve and to adjust a specific material behaviour. They consist of long-chained polymers and possess, together with additives, an enormous potential for tailored properties.

Recently, techniques have been established to produce and to disperse filler particles with typical dimensions in the range of nanometers. Even for low volume contents of filler particles, these so-called nanofillers may have significant impact on the properties of plastics. This can be most likely traced back to their very large volume-to-surface ratio. In this context, the polymer-particle interphase is of vital importance: as revealed by experiments, certain nanofillers may e.g. increase the fatigue lifetime of plastics by a factor of 15.

The effective design of such nanocomposites quite frequently requires elaborated mechanical testing, which might - if available - be substituted or supplemented by simulations. For this purpose, however, continuum mechanics together with the Finite Element Method (FE) as the usual tool for engineering applications is not well-suited since it is not able to capture processes at the molecular level. Therefore, particle-based techniques such as molecular dynamics (MD) have to be employed. However, these typically allow only for extremely small system sizes and simulation times. Thus, a multiscale technique that couples both approaches is required to enable the simulation of so-called representative volume elements (RVE) under consideration of atomistic effects.

The goal of this 4-year project is the development of a methodology which yields a continuum-based description of the material behaviour of the polymer-particle interphase of nanocomposites, whereby the required constitutive laws are derived from particle-based simulations. Due to their very small dimensions of some nanometers, the interphases cannot be accessed directly by experiments and particle-based simulations must substitute mechanical testing. The recently developed Capriccio method, designed as a simulation tool to couple MD and FE descriptions for amorphous systems, will be employed and refined accordingly in the course of the project.

In the first step, the mechanical properties of the polymer-particle interphase shall be determined by means of inverse parameter identification for small systems with one and two nanoparticles. In the second step, these properties shall be transferred to large RVEs. With this methodology at hand, various properties as e.g. the particles’ size and shape as well as grafting densities shall be mapped from pure particle-based considerations to continuum-based descriptions. Further consideration will then offer prospects to transfer the material description to applications relevant in engineering and eventually suited for the simulation of parts.

## GRK2423 - P6: Teilprojekt P6 - Fracture in Thermoplastics: Discrete-to-Continuum

Nanocomposites have great potential for various applications since their properties may be tailored to particular needs. One of the most challenging fields of research is the investigation of mechanisms in nanocomposites which improve for instance the fracture toughness even at very low filler contents. Several failure processes may occur like crack pinning, bi-furcation, deflections, and separations. Since the nanofiller size is comparable to the typical dimensions of the monomers of the polymer chains, processes at the level of atoms and molecules have to be considered to model the material behaviour properly. In contrast, a pure particle-based description becomes computationally prohibitive for system sizes relevant in engineering. To overcome this, only e.g. the crack tip shall be resolved to the level of atoms or superatoms in a coarse-graining (CG) approach.

Thus, this project aims to extend the recently developed multiscale Capriccio method to adaptive particle-based regions moving within the continuum. With such a tool at hand, only the vicinity of a crack tip propagating through the material has to be described at CG resolution, whereas the remaining parts may be treated continuously with significantly less computational effort.

## GRK2423 - P12: Teilprojekt P12 - Postdoctoral Project: Quantum-to-Continuum Model of Thermoset Fracture

Fracture is an inherently multiscale process in which processes at all length- and timescales can contribute to the dissipation of energy and thus determine the fracture toughness. While the individual processes can be studied by specifically adapted simulation methods, the interplay between these processes can only be studied by using concurrent multiscale modelling methods. While such methods already exist for inorganic materials as metals or ceramics, no similar methods have been established for polymers yet.

The ultimate goal of this postdoc project is to develop a concurrent multiscale modelling approach to study the interplay and coupling of process on different length scales (e.g. breaking of covalent bonds, chain relaxation processes, fibril formation and crazing at heterogeneities,…) during the fracture of an exemplary thermoset and its dependence on the (local) degree of cross-linking. In doing so, this project integrates results as well as the expertise developed in the other subprojects and complements their information-passing approach.

## GRK2423 - P5: Teilprojekt P5 - 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.

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

## GRK2423 - P11: Teilprojekt P11 - Fracture Control by Material Optimization

In previous works, the dependence of failure mechanisms in composite materials like debonding of the matrix-fibre interface or fibre breakage have been discussed. The underlying model was based on specific cohesive zone elements, whose macroscopic properties could be derived from DFT. It has been shown that the dissipated energy could be increased by appropriate choices of cohesive parameters of the interface as well as aspects of the fibre. However due to the numerical complexity of applied simulation methods the crack path had to be fixed a priori. Only recently models allow computing the full crack properties at macroscopic scale in a quasi-static scenario by the solution of a single nonlinear variational inequality for a given set of material parameters and thus model based optimization of the fracture properties can be approached.

The goal of the project is to develop an optimization method, in the framework of which crack properties (e.g. the crack path) can be optimized in a mathematically rigorous way. Thereby material properties of matrix, fibre and interfaces should serve as optimization variables.

## BRAINIACS: BRAIn mechaNIcs ACross Scales: Linking microstructure, mechanics and pathology

The current research project aims to develop microstructurallymotivated mechanical models for brain tissue that facilitate early diagnosticsof neurodevelopmental or neurodegenerative diseases and enable the developmentof novel treatment strategies. In a first step, we will experimentallycharacterize the behavior of brain tissue across scales by using versatiletesting techniques on the same sample. Through an accompanying microstructuralanalysis of both cellular and extra-cellular components,…

## Multiscale modeling of nervous tissue: comprehensively linking microstructure, pathology, and mechanics

## Novel Biopolymer Hydrogels for Understanding Complex Soft Tissue Biomechanics

This project involves manufacturing biopolymer hydrogels and cataloguing their mechanical properties. They serve as replacement materials in order to understand and model the highly-complex behaviour of soft biological tissue. The aim is to generate a catalogue of replacement materials for various soft tissue that links the specific characteristics of their mechanical responses with the relevant modelling approach. This catalogue could make the process of selecting suitable materials for 3D printing of artificial organs or generating suitable models for prognostic simulations considerably easier in the future.

### Participating Scientists:

### Publications:

**Determination of material parameters for a sheet‐layered lamination stack**

In:**Proceedings in Applied Mathematics and Mechanics**17 (2017), p. 393-394

ISSN: 1617-7061

DOI: 10.1002/pamm.201710166

URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/pamm.201710166 , :**Experimentelle und numerische Untersuchung des Einflusses variabler Betriebstemperaturen auf das Trag- und Versagensverhalten struktureller Klebverbindungen unter Crashbelastung**

22. Kolloquium: Gemeinsame Forschung in der Klebtechnik (Online-Tagung, 15. February 2022 - 16. February 2022) , , , , , :