# Bernhard Eidel

## Forschung

• Kontinuumsmechanische Modellierung der Inelastizität von metallischen und polymeren Werkstoﬀen

• Zeitintegrationsverfahren höherer Ordnung für Inelastizität

• Konsistente Raum-Zeit-Kopplung bei finiter Viskoelastizität

• Atomistik-Kontinuumskopplung (Molekularstatik, Molekulardynamik, Quasi-Continuum)

• Finite-Element-Methoden

• Kopplung von Phasentransformationen und Plastizität mit der Phasenfeldmethode

• Modellierung und Simulation von Oberﬂächen- und Interphase-phänomenen in nanokristallinen Materialien

• Simulationsanalyse von Schädigungs-, Lokalisierungs- und Versagensmechanismen sowie von Stabilitätsproblemen

• Indentierung in Simulation und Experiment

Für Kooperationen siehe Publikationen.

## Lehre

Vorlesungen und Übungen (V, Ü)

• WiSe 2012/13:  Computational Inelasticity, V+Ü, für Masterstudiengänge an der Universität Duisburg-Essen.
• SoSe 2012:  Introduction into Nanomechanics and Atomistic-based Finite Elements (in Englisch), V+Ü, für Masterstudiengänge an der Universität Duisburg-Essen.
• WiSe 2011/12:  Finite Elemente Methoden I, V+Ü, für Masterstudiengänge an der Universität Duisburg-Essen.
• SoSe 2011:  Introduction into Nanomechanics and Atomistic-based Finite Elements (in Englisch), V+Ü, für Masterstudiengänge an der Universität Duisburg-Essen.
• SoSe 2010:  Introduction to Crystal Plasticity Modelling (in Englisch), V+Ü: 440101, für Masterstudiengänge an der Ruhr-Universität Bochum, mit Dr. A. Ma.
• SoSe 2010:  ICAMS Seminar: Advanced Materials Simulation (in Englisch), V: 440001 , Ruhr-Universität Bochum.
• WiSe 2009/10:  Introduction into Micromechanics and Multiscale Materials Modelling (in Englisch), V+Ü: 440107, für Masterstudiengänge an der Ruhr-Universität Bochum.
• SoSe 2009:  Introduction to Crystal Plasticity Modelling (in Englisch), V+Ü: 440101, für Masterstudiengänge an der Ruhr-Universität Bochum, zusammen mit Dr. A. Ma.
• WiSe 2007/08:  Finite Element Methoden I, V/Ü: 13.1962.1/2, TU Darmstadt.
• SoSe 2007:  Finite Element Methoden II, V/Ü: 13.249.1/2, TU Darmstadt.
• WiSe 2006/07:  Finite Element Methoden I, V/Ü: 13.196.1/2, TU Darmstadt.
• SoSe 2006:  Finite Element Methoden II, V/Ü: 13.249.1/2, TU Darmstadt.
• WiSe 2005/06:  Finite Element Methoden I, V/Ü: 13.196.1/2, TU Darmstadt.
• SoSe 2005:  Finite Element Methoden II, V/Ü: 13.249.1/2, TU Darmstadt.
• WiSe 2004/05:  Finite Element Methoden I, V/Ü: 13.196.1/2, TU Darmstadt.
• WiSe 2000/01:  Ü: Finite Element Methoden I, TU Darmstadt.
• SoSe 1999:  Ü: Finite Element Methoden II, TU Darmstadt.
• 1999-2008:  Lehre: Statik I–IV, TU Darmstadt.
• 1992-1996:  Tutor für Technische Mechanik I–III, Uni Karlsruhe (TH).

Workshops & Sommerschulen

• 08.10.-12.10.2012  Stuttgart: Sommer-Schule "Computational Mechanics of Materials and Structures" (COMMAS), Dozent für "Atomistic-Continuum Coupling", Veranstalter: Universität Stuttgart, Prof. Ch. Miehe.
• 03.09.-07.09.2012  Bad Herrenalb: "Workshop Advanced Discussion on Multiscale Engineering", Dozent für "Atomistic-Continuum Coupling via the Quasi-Continuum Method", Veranstalter: Karlsruher Institut für Technologie (KIT) und Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), Prof. Böhlke, Prof. Diebels, Prof. Svendsen.
• 22.02.-05.03.2010  Bochum: Max-Planck-Research School for Surface and Interface Engineering in Advanced Materials (SURMAT), Vorlesungen über "Multiscale Modelling based on Atomistic Coarse-Graining", Veranstalter: MPI für Eisenforschung und Ruhr-Universität Bochum.
• 28.06.-01.07.2010  Stockholm: Sommer-Schule "Advanced Discussion on Multiscale Engineering", Leitung der Sektion "Hierarchical and Concurrent Multiscale Methods", Veranstalter: KTH Stockholm, HERO-M (Hierarchic Engineering of Industrial Materials) und ICAMS.
• 20.03.2009 ICMS-Advanced Discussions: Industrie-Seminar über "Computational Methods in Materials Science", Veranstalter: ICAMS, Ruhr-Universität Bochum.

## Werdegang

 04.2013- Vertretungsprofessur, Lehrstuhl Numerische Mechanik, Institut für Mechanik und Regelungstechnik - Mechatronik, Department Maschinenbau, Universität Siegen 02.2013- Heisenberg-Stipendium (DFG) 10.2011- Privatdozent, Universität Duisburg-Essen 21.09.2011 Habilitation und venia legendi im Fach Mechanik  Titel der Arbeit: Modeling and Numerical Analysis of Inelasticity On and Across Multiple Length Scales  Gutachter: Prof. Dr.-Ing. habil. J. Schröder, Prof. Dr.-Ing. habil. P. Steinmann, Prof. Dr. habil. P. Neff 01/2011- Institut für Mechanik, Universität Duisburg-Essen 10/2008-10/2010 Gruppenleiter "Multiscale Mechanics of Solids", Interdisciplinary Centre for Advanced Materials Simulation (ICAMS),  Ruhr-Universität Bochum 10/2004-05/2008 Oberingenieur mit Lehrauftrag für Finite-Element-Methoden, TU Darmstadt 30.09.2004 Promotion zum Dr.-Ing.im Fachbereich Bauingenieurwesen und Geodäsie, TU Darmstadt  Titel der Arbeit: Anisotropic Inelasticity - Modelling, Simulation, Validation  Gutachter: Prof. Dr.-Ing. habil. F. Gruttmann, Prof. Dr.-Ing. habil. Ch. Tsakmakis 02/1999-09/2004 Wissenschaftlicher Mitarbeiter am Institut für Statik und am SFB 298 "Deformation und Versagen bei metallischen und granularen Strukturen", TU Darmstadt

## Publikationen (peer-reviewed)

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 Eidel, B., Tempel-Stumpf, F. & Schröder, J. (2013), "Finite strain viscoelasticity: how to consistently couple discretizations in time and space on quadrature-point level for full order p>=2 and a considerable speed-up", Computational Mechanics. Vol. 52, pp. 463-483. Abstract: In computational viscoelasticity, the spatial finite element discretization for the global solution of the weak form of the balance of momentum is coupled to the temporal discretization for solving local initial value problems (IVP) of viscoelastic flow. In this contribution we show that this global-local or space-time coupling is consistent, if the total strain tensor as the coupling quantity exhibits the same approximation order p in time as the Runge-Kutta (RK) integration algorithm. To this end we construct interpolation polynomials, based on data at t_n+1, t_n, ... , t_n+2-p, p>=2, which provide consistent strain data at RK stages. This is a generalization of the idea proposed in (Eidel, Kuhn, Int. J. Numer. Methods Eng. 2011). For lower-order strain interpolation, time integration exhibits order reduction and therefore low efficiency. For consistent strain interpolation, the adapted RK methods up to p = 4 obtain full convergence order and thus approve the novel concept of consistency. High speed-up factors substantiate the improved efficiency compared with Backward-Euler. BibTeX: @article{EidelStumpfSchroeder2012, author = {B. Eidel and F. Tempel-Stumpf and J. Schröder}, title = {Finite strain viscoelasticity: how to consistently couple discretizations in time and space on quadrature-point level for full order p>=2 and a considerable speed-up}, journal = {Computational Mechanics}, year = {2013}, volume = {52}, pages = {463-483}, doi = {http://dx.doi.org/10.1007/s00466-012-0823-6} }  Spatschek, R. & Eidel, B. (2013), "Driving forces for interphase kinetics and phase field models", International Journal of Solids and Structures. Vol. 14-15, pp. 2424-2436. Abstract: Phase field models are typically written in variational form starting from a free energy functional, and sharp interface descriptions for moving boundary problems can be formulated similarly. Here we discuss why and under which circumstances this postulate for deriving the equations of motion is justified, and what are limitations. We discuss this in particular for alloys, systems with elastic, viscoelastic and plastic effects, mainly based on analytical and numerical investigations in one dimension. We find that the naturally guessed equations of motion, as derived via partial functional derivatives from a free energy, are usually reasonable, only for materials with plastic effects this assumption is more delicate due to the presence of internal variables. BibTeX: @article{SpatschekEidel2012, author = {R. Spatschek and B. Eidel}, title = {Driving forces for interphase kinetics and phase field models}, journal = {International Journal of Solids and Structures}, year = {2013}, volume = {14-15}, pages = {2424-2436}, doi = {http://dx.doi.org/10.1016/j.ijsolstr.2013.03.016} }  Neff, P., Eidel, B., Osterbrink, F. & Martin, R. (2013), "A Riemannian approach to strain measures in nonlinear elasticity", Comptes Rendues Mecanique, accepted for publication. BibTeX: @article{, author = {P. Neff and B. Eidel and F. Osterbrink and R. Martin}, title = {A Riemannian approach to strain measures in nonlinear elasticity}, journal = {Comptes Rendues Mecanique, accepted for publication}, year = {2013} }  Eidel, B. (2011), "Modeling and Numerical Analysis of Inelasticity On and Across Multiple Length Scales" Habilitation Thesis, University Duisburg-Essen. BibTeX: @book{Eidel-Habil, author = {Eidel, B.}, title = {Modeling and Numerical Analysis of Inelasticity On and Across Multiple Length Scales}, publisher = {Habilitation Thesis, University Duisburg-Essen}, year = {2011} }  Eidel, B. (2011), "Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (001) fcc single crystal", Acta Materialia. Vol. 59(4), pp. 1761-1771. Abstract: Pyramidal microindentation into the (001) surface of an face-centered cubic (fcc) single crystal made of a Ni-base superalloy is analyzed in experiment and crystal plasticity finite-element simulations. The resultant material pile-up at the surface reflects the materials symmetry and turns out to be insensitive to different loading scenarios as induced by (i) different azimuthal orientations of the pyramidal indenter, (ii) different indenter shapes (sphere or pyramid) and (iii) the elastic anisotropy. Experiments and simulations are in agreement and suggest that pile-up deformation patterns merely depend on the geometry of discrete slip systems but are invariant to different anisotropic stress distributions as induced by (i)-(iii). The local adaption of pile-up to the pyramidal indenter leads to convex or concave indent shapes corresponding to the indenter orientation. We contrast the present findings for curved indent shapes of fcc single crystals to similar, well-known observations for quasi-isotropic polycrystals. Although phenomenologically similar in kind, the driving mechanisms are different: for the single crystal it is the discrete and anisotropic nature of plastic glide in certain slip systems; for isotropic polycrystals it is the rate of strain-hardening caused by the cumulative response of dislocations. BibTeX: @article{Eidel2011, author = {B. Eidel}, title = {Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (001) fcc single crystal}, journal = {Acta Materialia}, year = {2011}, volume = {59}, number = {4}, pages = {1761-1771}, doi = {http://dx.doi.org/10.1016/j.actamat.2010.11.042} }  Eidel, B. & Kuhn, C. (2011), "Order reduction in computational inelasticity: why it happens and how to overcome it - the ODE-case of viscoelasticity", International Journal for Numerical Methods in Engineering. Vol. 87(11), pp. 1046-1073. Abstract: Time integration is the numerical kernel of inelastic finite element calculations,which largely determines their accuracy and efficiency. If higher order Runge-Kutta (RK) methods, p >=3, are used for integration in a standard manner, they do not achieve full convergence order but fall back to second-order convergence. This deficiency called order reduction is a longstanding problem in computational inelasticity.We analyze it for viscoelasticity, where the evolution equations follow ordinary differential equations.We focus on RK methods of third order. We prove that the reason for order reduction is the (standard) linear interpolation of strain to construct data at the RK-stages within the considered time interval. We prove that quadratic interpolation of strain based on t_n, t_n+1 and, additionally, t_n-1 data implies consistency order three for total strain, viscoelastic strain and stress. Simulations applying the novel interpolation technique are in perfect agreement with the theoretical predictions. The present methodology is advantageous, since it preserves the common, staggered structure of finite element codes for inelastic stress calculation. Furthermore, it is easy to implement, the overhead of additional history data is small and the computation time to obtain a defined accuracy is considerably reduced compared with backward Euler. BibTeX: @article{EidelKuhn2011, author = {B. Eidel and C. Kuhn}, title = {Order reduction in computational inelasticity: why it happens and how to overcome it - the ODE-case of viscoelasticity}, journal = {International Journal for Numerical Methods in Engineering}, year = {2011}, volume = {87}, number = {11}, pages = {1046-1073}, doi = {http://dx.doi.org/10.1002/nme.3144} }  Eidel, B., Hartmaier, A. & Gumbsch, P. (2010), "Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics" Vol. 522, pp. 1-58. Springer. Abstract: The present work on the molecular dynamics method covers the theoretical background of the method and gives practical examples to demonstrate its capabilities and limitations. The work focusses on topics which reveal fundamental mechanisms associated with fracture processes. Moreover, promising hybrid methods based on a concurrent atomistic/continuum coupling are reviewed since they combine accuracy and efficiency in a most favorable manner. BibTeX: @inbook{EidelHartmaierGumbsch2010, author = {B. Eidel and A. Hartmaier and P. Gumbsch}, title = {Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics}, publisher = {Springer}, year = {2010}, volume = {522}, pages = {1-58}, url = {http://link.springer.com/chapter/10.1007%2F978-3-7091-0283-1_1} }  Fleck, M., Brener, E., Spatschek, R. & Eidel, B. (2010), "Elastic and plastic effects on solid-state transformations: A phase field study", International Journal of Materials Research. Vol. 101(4), pp. 462-466. Abstract: We discuss a model of diffusion limited growth in solid-state transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase equilibrium conditions. We study the growth of a stable phase from a metastable solid in a channel geometry, and perform phase field simulations. Extensions to plastic models are discussed. BibTeX: @article{Fleck2010, author = {M. Fleck and E.A. Brener and R. Spatschek and B. Eidel}, title = {Elastic and plastic effects on solid-state transformations: A phase field study}, journal = {International Journal of Materials Research}, year = {2010}, volume = {101}, number = {4}, pages = {462-466}, doi = {http://dx.doi.org/10.3139/146.110295} }  Eidel, B. (2009), "Coupling atomistic accuracy with continuum effectivity for predictive simulations in materials research - the Quasicontinuum Method", International Journal of Materials Research. Vol. 100(11), pp. 1503-1512. Abstract: In this article we present a comparative analysis of different versions of the quasicontinuum method, which aim at a seamless transition from the atomistic to the continuum description of crystalline solids at zero temperature. All versions of this popular and powerful method exhibit the same building blocks, namely (i) a coarse-graining of fully atomistic resolution via kinematic constraints, (ii) an approximation of the energy/forces in coarse-grained regions via numerical quadrature and (iii) adaptive mesh refinement. The quasicontinuum versions are assessed in ail example where a Lomer dislocation dipole is subject to shear deformation. In a second example, the fully nonlocal quasicontinuum method is used to Simulate nanoindentation into an fcc single crystal. Compared with lattice statics good agreement is achieved with respect to significant details of the material behaviour for a small fraction of the computational costs. BibTeX: @article{Eidel2009, author = {B. Eidel}, title = {Coupling atomistic accuracy with continuum effectivity for predictive simulations in materials research - the Quasicontinuum Method}, journal = {International Journal of Materials Research}, year = {2009}, volume = {100}, number = {11}, pages = {1503-1512}, doi = {http://dx.doi.org/10.3139/146.110208} }  Eidel, B. & Stukowski, A. (2009), "A variational formulation of the quasicontinuum method based on energy sampling in clusters", Journal of the Mechanics and Physics of Solids. Vol. 57(1), pp. 87-108. Abstract: This contribution presents a novel quasicontinuum (QC) approach aiming at a seamless transition from the atomistic to the continuum description of crystalline solids at zero temperature, which heavily draws on the framework proposed by Knap and Ortiz [2001. An analysis of the quasicontinuum method. J. Mech. Phys. Solids 49, 1899-1923]. Opposed to Knap and Ortiz, the energy instead of forces is subject to a cluster-based sampling scheme with adaptive resolution. We show that only the present ansatz endows the QC theory with a variational structure leading to conservative forces and symmetric stiffnesses. Equally, we show the strict symmetry in atomic interactions. This approach allows for the direct application of standard minimization methods and guarantees the existence of an equilibrium state provided that the total potential exhibits a minimum. A special focus is on the numerical error in the cluster-based summation rule for energy sampling. We compare two strategies to improve the accuracy, which are also particularly useful to account for surface effects. The fully nonlocal methodology is assessed in nanoindentation into an fcc single crystal. Compared with lattice statics good agreement is achieved with respect to the force-displacement curve, the load level and locus of dislocation nucleation and the dislocation microstructure for a small fraction of the computational costs. (C) 2008 Elsevier Ltd. All rights reserved. BibTeX: @article{EidelStukowski2009, author = {B. Eidel and A. Stukowski}, title = {A variational formulation of the quasicontinuum method based on energy sampling in clusters}, journal = {Journal of the Mechanics and Physics of Solids}, year = {2009}, volume = {57}, number = {1}, pages = {87-108}, doi = {http://dx.doi.org/10.1016/j.jmps.2008.09.017} }  Eidel, B. & Gruttmann, F. (2007), "Squaring the circle - A curious phenomenon of fcc single crystals in spherical microindentation", Computational Materials Science. Vol. 39(1), pp. 172-178. Abstract: Spherical microindentation into the (001) surface of a FCC single crystal made of the Ni-base superalloy CMSX-4 has shown a remaining indent shape, that looks rather like a square than like a circle. In order to investigate this curious phenomenon, a digital surface model of the indentation crater is generated applying a backscatter electron detector along with digital image processing. The experimental measurings indicate a direction dependent pile-up accompanied by locally extended contact zones, which explains the squared shape of the spherical indent. Finite element simulations are conducted by means of a phenomenological orthotropic elasto-plasticity model within the framework of a multiplicative decomposition of the deformation gradient. The constitutive equations are formulated with respect to the isoclinic intermediate configuration. The simulation is in qualitative agreement with the experiment. Various rates of strain hardening in the simulation reveal the overlap of pile-up/sink-in with the direction dependent pile-up due to the crystal's anisotropy. The simulations predict that it is mainly the rate of strain hardening which shapes the anisotropy of the indentation topography. (c) 2006 Elsevier B.V. All rights reserved. BibTeX: @article{EidelGruttmann2007, author = {B. Eidel and F. Gruttmann}, title = {Squaring the circle - A curious phenomenon of fcc single crystals in spherical microindentation}, journal = {Computational Materials Science}, year = {2007}, volume = {39}, number = {1}, pages = {172-178}, doi = {http://dx.doi.org/10.1016/j.commatsci.2006.03.026} }  Eidel, B. (2004), "Anisotropic Inelasticity - Modelling, Simulation, Validation" , pp. 230pp. PhD Thesis, TU-Darmstadt, Shaker-Verlag. BibTeX: @book{Eidel2004, author = {B. Eidel}, title = {Anisotropic Inelasticity - Modelling, Simulation, Validation}, publisher = {PhD Thesis, TU-Darmstadt, Shaker-Verlag}, year = {2004}, pages = {230pp}, url = {http://www.shaker.de/de/content/catalogue/index.asp?ID=8&ISBN=978-3-8322-4473-6} }  Eidel, B. & Gruttmann, F. (2003), "Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation", Computational Materials Science. Vol. 28(3-4), pp. 732-742. Abstract: A constitutive model for orthotropic elastoplasticity at finite plastic strains is discussed and basic concepts of its numerical implementation are presented. The essential features are the multiplicative decomposition of the deformation gradient in elastic and inelastic parts, the definition of a convex elastic domain in stress space and a representation of the constitutive equations related to the intermediate configuration. The elastic free energy function and the yield function are formulated in an invariant setting by means of the introduction of structural tensors reflecting the privileged directions of the material. The model accounts for kinematic and isotropic hardening. The associated flow rule is integrated using the so-called exponential map which preserves exactly the plastic incompressibility condition. The constitutive equations are implemented in a brick-type shell element. Representative numerical simulations demonstrate the suitability of the proposed formulations. (C) 2003 Elsevier B.V. All rights reserved. BibTeX: @article{EidelGruttmann2003, author = {B. Eidel and F. Gruttmann}, title = {Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation}, journal = {Computational Materials Science}, year = {2003}, volume = {28}, number = {3-4}, pages = {732-742}, doi = {http://dx.doi.org/10.1016/j.commatsci.2003.08.027} }  Eidel, B. & Gruttmann, F. (2003), "Deformation and Failure in Metallic Materials" , pp. 51-78. Springer. Abstract: A constitutive model for orthotropic elastoplasticity at finite plastic strains is discussed and basic concepts of its numerical implementation are presented. The essential features are the multiplicative decomposition of the deformation gradient in elastic and inelastic parts, the definition of a convex elastic domain in stress space and a representation of the constitutive equations related to the intermediate configuration. The elastic free energy function and the yield function are formulated in an invariant setting by means of the introduction of structural tensors reflecting the privileged directions of the material. The model accounts for kinematic and isotropic hardening. The associative flow rule is integrated using the socalled exponential map which preserves exactly the plastic incompressibility condition. The constitutive equations are implemented in a brick type shell element. Due to special interpolation techniques based on mixed variational principles, the element is able to predict a locking-free deformation behaviour even for very thin structures. Representative numerical simulations demonstrate the suitability of the proposed formulations. BibTeX: @inbook{EidelGruttmann2003b, author = {B. Eidel and F. Gruttmann}, title = {Deformation and Failure in Metallic Materials}, publisher = {Springer}, year = {2003}, pages = {51-78}, doi = {http://www.springer.com/materials/mechanics/book/978-3-540-00848-4} } 

Stand: 27.08.2013

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 Eidel, B., Stumpf, F. & Schröder, J. (2013), "Algorithmic consistency in computational inelasticity - a conceptual completion", Proceedings of Applied Mathematics and Mechanics, submitted for publication. BibTeX: @article{, author = {B. Eidel and F. Stumpf and J. Schröder}, title = {Algorithmic consistency in computational inelasticity - a conceptual completion}, journal = {Proceedings of Applied Mathematics and Mechanics, submitted for publication}, year = {2013} }  Schröder, J., Eidel, B., Brands, D. & Balzani, D. (2012), "Nano to Micro - Perspectives for Homogenization in Crystalline Solids", Proceedings of Applied Mathematics and Mechanics. Vol. 12, pp. 19-22. BibTeX: @article{JS-BE-etal2012, author = {J. Schröder and B. Eidel and D. Brands and D. Balzani}, title = {Nano to Micro - Perspectives for Homogenization in Crystalline Solids}, journal = {Proceedings of Applied Mathematics and Mechanics}, year = {2012}, volume = {12}, pages = {19-22} }  Eidel, B. & Kuhn, C. (2012), "Runge-Kutta methods for time integration in computational inelasticity - how to go beyond order 2", In CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 10-14, 2012, Vienna, Austria. Publisher: Vienna University of Technology, Austria, ISBN: 978-3-9502481-9-7. BibTeX: @inproceedings{, author = {B. Eidel and C. Kuhn}, title = {Runge-Kutta methods for time integration in computational inelasticity - how to go beyond order 2}, booktitle = {CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 10-14, 2012, Vienna, Austria}, publisher = {Publisher: Vienna University of Technology, Austria, ISBN: 978-3-9502481-9-7}, year = {2012} }  Eidel, B., Stumpf, F. & Schröder, J. (2012), "Effective, higher-order Runge-Kutta methods for time integration of viscoelastic constitutive models at finite strains", In 10th World Congress on Computational Mechanics (WCCM2012), July 8-13, 2012, Sao Paulo, Brazil. Minisymposium in honor of the 75th birthday of Prof. J. Tinsley Oden: Innovative Higher Order Discretization Methods. BibTeX: @conference{, author = {B. Eidel and F. Stumpf and J. Schröder}, title = {Effective, higher-order Runge-Kutta methods for time integration of viscoelastic constitutive models at finite strains}, booktitle = {10th World Congress on Computational Mechanics (WCCM2012), July 8-13, 2012, Sao Paulo, Brazil. Minisymposium in honor of the 75th birthday of Prof. J. Tinsley Oden: Innovative Higher Order Discretization Methods}, year = {2012} }  Eidel, B., Stukowski, A. & Schröder, J. (2011), "Accelerated energy-minimization in the quasicontinuum method with application to nanopillar compression", In Proceedings of the XI International Conference on Computational Plasticity (COMPLAS XI)., pp. 360-367. BibTeX: @inproceedings{, author = {B. Eidel and A. Stukowski and J. Schröder}, title = {Accelerated energy-minimization in the quasicontinuum method with application to nanopillar compression}, booktitle = {Proceedings of the XI International Conference on Computational Plasticity (COMPLAS XI)}, year = {2011}, pages = {360-367} }  Eidel, B., Stukowski, A. & Schröder, J. (2011), "Energy-Minimization in Atomic-to-Continuum Scale-Bridging Methods", Proceedings in Applied Mathematics and Mechanics. Vol. 11, pp. 509-510. BibTeX: @article{, author = {B. Eidel and A. Stukowski and J. Schröder}, title = {Energy-Minimization in Atomic-to-Continuum Scale-Bridging Methods}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2011}, volume = {11}, pages = {509-510}, doi = {http://dx.doi.org/10.1002/pamm.201110246} }  Eidel, B. & Schürg, M. (2008), "Pyramidal indentation into fcc single crystals and quasi-isotropic polycrystals: similar phenomena, different driving mechanisms", Proceedings in Applied Mathematics and Mechanics. Vol. 8, pp. 10543-10544. BibTeX: @article{EidelSchurg2008, author = {B. Eidel and M. Schürg}, title = {Pyramidal indentation into fcc single crystals and quasi-isotropic polycrystals: similar phenomena, different driving mechanisms}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2008}, volume = {8}, pages = {10543-10544}, doi = {http://dx.doi.org/10.1002/pamm.200810543} }  Eidel, B. & Stukowski, A. (2007), "A novel quasicontinuum method for the seamless transition for atomistic to continuum length scales and its applications to nanoindentation of single-crystalline materials", Proceedings in Applied Mathematics and Mechanics. Vol. 7, pp. 4080007-4080008. BibTeX: @article{EidelStukowski2007A, author = {B. Eidel and A. Stukowski}, title = {A novel quasicontinuum method for the seamless transition for atomistic to continuum length scales and its applications to nanoindentation of single-crystalline materials}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2007}, volume = {7}, pages = {4080007-4080008}, doi = {http://dx.doi.org/10.1002/pamm.200700334} }  Eidel, B. & Stukowski, A. (2007), "Dislocation nucleation and defect structure during nanoindentation: an analysis by means of a novel quasicontinuum method", In Proceedings of the IX International Conference on Computational Plasticity (COMPLAS IX)., pp. 425-428. BibTeX: @inproceedings{EidelStukowski2007b, author = {B. Eidel and A. Stukowski}, title = {Dislocation nucleation and defect structure during nanoindentation: an analysis by means of a novel quasicontinuum method}, booktitle = {Proceedings of the IX International Conference on Computational Plasticity (COMPLAS IX)}, year = {2007}, pages = {425-428} }  Fell, C. & Eidel, B. (2007), "A novel class of thermodynamically consistent isotropic hardening rules for some damage models at finite strains", Proceedings of Applied Mathematics and Mechanics. Vol. 7, pp. 4060025-4060026. BibTeX: @article{FellEidel2007, author = {C. Fell and B. Eidel}, title = {A novel class of thermodynamically consistent isotropic hardening rules for some damage models at finite strains}, journal = {Proceedings of Applied Mathematics and Mechanics}, year = {2007}, volume = {7}, pages = {4060025-4060026}, doi = {http://dx.doi.org/10.1002/pamm.200700406} }  Kuhn, C. & Eidel, B. (2007), "Time integration of inelastic material models exhibits an order reduction for higher-order methods  can this be avoided?", Proceedings of Applied Mathematics and Mechanics. Vol. 7, pp. 20900192090020. BibTeX: @article{KuhnEidel2007, author = {C. Kuhn and B. Eidel}, title = {Time integration of inelastic material models exhibits an order reduction for higher-order methods  can this be avoided?}, journal = {Proceedings of Applied Mathematics and Mechanics}, year = {2007}, volume = {7}, pages = {20900192090020}, doi = {http://dx.doi.org/10.1002/pamm.200700662} }  Stukowski, A. & Eidel, B. (2006), "Atomistic to continuum scale transition for crystalline materials  a comparative study of quasicontinuum approaches", In Proceedings of the Third International Conference for Multiscale Materials Modelling (MMM), September 18-22., pp. 167-169. BibTeX: @inproceedings{StukowskiEidel2007, author = {A. Stukowski and B. Eidel}, title = {Atomistic to continuum scale transition for crystalline materials  a comparative study of quasicontinuum approaches}, booktitle = {Proceedings of the Third International Conference for Multiscale Materials Modelling (MMM), September 18-22}, year = {2006}, pages = {167-169} }  Eidel, B. & Gruttmann, F. (2005), "Spherical indentation into a fcc single crystal - the squaring of the circle?", Proceedings in Applied Mathematics and Mechanics. Vol. 5, pp. 265-266. BibTeX: @article{EidelGruttmann2005, author = {B. Eidel and F. Gruttmann}, title = {Spherical indentation into a fcc single crystal - the squaring of the circle?}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2005}, volume = {5}, pages = {265-266}, doi = {http://dx.doi.org/10.1002/pamm.200510109} }  Eidel, B. & Gruttmann, F. (2005), "Anisotropic pile-up pattern at spherical indentation in a CMSX-4 single crystal  finite element simulation versus experimental results", In Proceedings of the Third M.I.T. Conference on Computational Fluid and Solid Mechanics., pp. 246-248. Elsevier. BibTeX: @inproceedings{EidelGruttmann2005a, author = {B. Eidel and F. Gruttmann}, title = {Anisotropic pile-up pattern at spherical indentation in a CMSX-4 single crystal  finite element simulation versus experimental results}, booktitle = {Proceedings of the Third M.I.T. Conference on Computational Fluid and Solid Mechanics}, publisher = {Elsevier}, year = {2005}, pages = {246-248} }  Eidel, B. & Gruttmann, F. (2003), "On the formulation and finite element implementation of anisotropic multiplicative finite strain elastoplasticity", Proceedings in Applied Mathematics and Mechanics. Vol. 2, pp. 186-187. BibTeX: @article{EidelGruttmann2003a, author = {B. Eidel and F. Gruttmann}, title = {On the formulation and finite element implementation of anisotropic multiplicative finite strain elastoplasticity}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2003}, volume = {2}, pages = {186-187}, doi = {http://dx.doi.org/10.1002/pamm.200310078} }  Eidel, B. & Gruttmann, F. (2003), "On the theory and numerics of orthotropic elastoplasticity at finite plastic strains", In Proceedings of the Second M.I.T. Conference on Computational Fluid and Solid Mechanics. BibTeX: @inproceedings{EidelGruttmann2003c, author = {B. Eidel and F. Gruttmann}, title = {On the theory and numerics of orthotropic elastoplasticity at finite plastic strains}, booktitle = {Proceedings of the Second M.I.T. Conference on Computational Fluid and Solid Mechanics}, year = {2003} }  Eidel, B. & Gruttmann, F. (2002), "Finite strain inelasticity for isotropy, a simple and efficient finite element formulation", Proceedings in Applied Mathematics and Mechanics. Vol. 1, pp. 185-186. BibTeX: @article{EidelGruttmann2002, author = {B. Eidel and F. Gruttmann}, title = {Finite strain inelasticity for isotropy, a simple and efficient finite element formulation}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2002}, volume = {1}, pages = {185-186}, doi = {http://dx.doi.org/10.1002/1617-7061} }  Gruttmann, F. & Eidel, B. (2002), "On the implementation of anisotropic finite strain plasticity", In Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), July 7-12, 2002, Vienna, Austria. BibTeX: @inproceedings{GruttmannEidel2002, author = {F. Gruttmann and B. Eidel}, title = {On the implementation of anisotropic finite strain plasticity}, booktitle = {Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), July 7-12, 2002, Vienna, Austria}, year = {2002} } 

Stand: 27.08.2013

## PD Dr.-Ing. habil. Bernhard Eidel

Tel. +49(0)201/183-2484
Fax +49(0)201/183-2680
Raum V15 S05 D81
bernhard.eidel@uni-due.de