Bernhard Eidel
Priv.Doz. Dr.Ing. habil. Bernhard Eidel
Research

Continuum mechanics and materials modeling of inelasticity

Atomisticcontinuum coupling, QuasiContinuum (QC) method

Highorder timeintegration algorithms for viscoelasticity and elastoplasticity
 Consistent spacetime coupling for finite viscoelasticity

Coupling phasetransformations and plasticity

Modeling and simulation of surface/interfacerelated phenomena in crystalline nanostructures

Indentation in simulation and experiment
 Analyses of damage, localization and failure mechanisms and of structural/material instabilities on different length scales
For cooperations see publications.
Teaching
Lectures & Exercises (L & Ex)
 WiSe 2012/13: Computational Inelasticity, L+Ex, for Master students at Universität DuisburgEssen.
 SoSe 2012: Introduction into Nanomechanics and Atomisticbased Finite Elements, L+Ex, for Master students at Universität DuisburgEssen.
 WiSe 2011/12: Finite Elemente Methoden I (in german), L+Ex, for Master students at Universität DuisburgEssen.
 SoSe 2011: Introduction into Nanomechanics and Atomisticbased Finite Elements, L+Ex, for Master students at Universität DuisburgEssen.
 SoSe 2010: Introduction to Crystal Plasticity Modelling, L+Ex: 440101, for Master students at the RuhrUniversität Bochum, with Dr. Ma Anxin.
 SoSe 2010: ICAMS Seminar: Advanced Materials Simulation, L: 440001 , RuhrUniversität Bochum.
 WiSe 2009/10: Introduction into Micromechanics and Multiscale Materials Modelling, L+Ex: 440107, for Master students at the RuhrUniversität Bochum.
 SoSe 2009: Introduction to Crystal Plasticity Modelling (in Englisch), V+Ü: 440101, für Masterstudiengänge an der RuhrUniversität Bochum, with Dr. Ma Anxin.
 WiSe 2007/08: Finite Element Methoden I (in german), L+Ex: 13.1962.1/2, TU Darmstadt.
 SoSe 2007: Finite Element Methoden II (in german), L+Ex: 13.249.1/2, TU Darmstadt.
 WiSe 2006/07: Finite Element Methoden I (in german), L+Ex: 13.196.1/2, TU Darmstadt.
 SoSe 2006: Finite Element Methoden II (in german), L+Ex: 13.249.1/2, TU Darmstadt.
 WiSe 2005/06: Finite Element Methoden I (in german), L+Ex: 13.196.1/2, TU Darmstadt.
 SoSe 2005: Finite Element Methoden II (in german), L+Ex: 13.249.1/2, TU Darmstadt.
 WiSe 2004/05: Finite Element Methoden I (in german), L+Ex: 13.196.1/2, TU Darmstadt.
 WiSe 2000/01: Ex.: Finite Element Methoden I (in german), TU Darmstadt.
 SoSe 1999: Ex.: Finite Element Methoden II (in german), TU Darmstadt.
 19992008: Statik I–IV, TU Darmstadt.
 19921996: Tutor for Engineering Mechanics I–III, Uni Karlsruhe (TH).
Workshops & Summerschools
 08.10.12.10.2012 Stuttgart: SummerSchool "Computational Mechanics of Materials and Structures" (COMMAS), 3 Lectures about "AtomisticContinuum Coupling", Organizer: Universität Stuttgart, Prof. Ch. Miehe.
 03.09.07.09.2012 Bad Herrenalb: "Workshop Advanced Discussion on Multiscale Engineering", Lecturer for "AtomisticContinuum Coupling via the QuasiContinuum Method", Organizer: Karlsruher Institut für Technologie (KIT) and GAMMactivity group "Multiscale Material Modelling" Prof. Böhlke, Prof. Diebels, Prof. Svendsen.
 22.02.05.03.2010 Bochum: MaxPlanckResearch School for Surface and Interface Engineering in Advanced Materials (SURMAT), Lectures about "Multiscale Modelling based on Atomistic CoarseGraining", Organizer: MPI für Eisenforschung and RuhrUniversität Bochum.
 28.06.01.07.2010 Stockholm: SummerSchool "Advanced Discussion on Multiscale Engineering", Head of Section "Hierarchical and Concurrent Multiscale Methods", Organizer: KTH Stockholm, HEROM (Hierarchic Engineering of Industrial Materials) und ICAMS.
 20.03.2009 ICAMSAdvanced Discussions: IndustrySeminar about "Computational Methods in Materials Science", Organizer: ICAMS, RuhrUniversität Bochum.
Career
04.2013  Temporary Professor, Chair of Numerical Mechanics, Institute of Mechanics and Control Engineering, Department of Mechanical Engineering, University of Siegen, Germany 
02.2013  HeisenbergFellow (DFG) 
10.2011  Privatdozent, University of DuisburgEssen 
21.09.2011  Habilitation degree (Dr. Ing. habil.) and venia legendi (Priv. Doz.) for "Mechanics" Title: Modeling and Numerical Analysis of Inelasticity On and Across Multiple Length Scales Reviewers: Prof. Dr.Ing. habil. J. Schröder, Prof. Dr.Ing. habil. P. Steinmann, Prof. Dr. habil. P. Neff 
01/2011  Institute of Mechanics, University of DuisburgEssen 
10/200810/2010  Group Leader "Multiscale Mechanics of Solids", ICAMS, RuhrUniversity Bochum 
10/200405/2008  Oberingenieur, IWMB, TU Darmstadt 
30.09.2004 
Doctoral degree (Dr.Ing.), TU Darmstadt, Faculty of Civil Engineering and Geodesy, Title: "Anisotropic Inelasticity  Modelling, Simulation, Validation" 
02/199909/2004 
Research Assistant, Institut für Statik and Special Collaborative Research Centre SFB 298 "Deformation and Failure of Metallic and Granular Structures", TU Darmstadt 
Publications (peerreviewed)
Eidel, B. & Kuhn, C. (2013), "Is there an orderbarrier p <=2 for time integration in computational elastoplasticity?", submitted for publication. 
Abstract: This paper is devoted to the question, whether there is an order barrier p <= 2 for time integration in computational elastoplasticity. In the analysis we use an implicit RungeKutta (RK) method of order p = 3 for integrating the evolution equations of plastic flow within a nonlinear finite element framework. We show that two novel algorithmic conditions are necessary to overcome the order barrier, (i) total strains must have the same order in time as the time integrator itself, (ii) accurate initial data must be calculated via detecting the elasticplastic switching point (SP) in the predictor step. Condition (i) is for a consistent coupling of the global boundary value problem (BVP) with the local initial value problems (IVP) via displacements/strains. Condition (ii) generates consistent initial data of the IVPs. The third condition, which is not algorithmic but physical in nature, is that (iii) the total strain path in time must be smooth such that condition (i) can be fulfilled at all. This requirement is met by materials showing a sufficiently smooth elasticplastic transition in the stressstrain curve. We propose effective means to fulfil conditions (i) and (ii). We show in finite element simulations that, if condition (iii) is additionally met, the present method yields the full, theoretical convergence order 3 thus overcoming the barrier p <= 2 for the first time. The observed speedup for a 3rd order RK method is considerable compared with Backward Euler. 
BibTeX:
@article{EidelKuhn2012, author = {B. Eidel and C. Kuhn}, title = {Is there an orderbarrier p <=2 for time integration in computational elastoplasticity?}, journal = {submitted for publication}, year = {2013} } 
Spatschek, R. & Eidel, B. (2013), "Driving forces for interphase kinetics and phase field models", International Journal of Solids and Structures. Vol. 1415, pp. 24242436. 
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 = {1415}, pages = {24242436}, 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., TempelStumpf, F. & Schröder, J. (2012), "Finite strain viscoelasticity: how to consistently couple discretizations in time and space on quadraturepoint level for full order p>=2 and a considerable speedup", Computational Mechanics, accepted for publication. 
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 globallocal or spacetime coupling is consistent, if the total strain tensor as the coupling quantity exhibits the same approximation order p in time as the RungeKutta (RK) integration algorithm. To this end we construct interpolation polynomials, based on data at t_n+1, t_n, ... , t_n+2p, 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 lowerorder 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 speedup factors substantiate the improved efficiency compared with BackwardEuler. 
BibTeX:
@article{EidelStumpfSchroeder2012, author = {B. Eidel and F. TempelStumpf and J. Schröder}, title = {Finite strain viscoelasticity: how to consistently couple discretizations in time and space on quadraturepoint level for full order p>=2 and a considerable speedup}, journal = {Computational Mechanics, accepted for publication}, year = {2012}, doi = {http://dx.doi.org/10.1007/s0046601208236} } 
Eidel, B. (2011), "Modeling and Numerical Analysis of Inelasticity On and Across Multiple Length Scales" Habilitation Thesis, University DuisburgEssen. 
BibTeX:
@book{EidelHabil, author = {Eidel, B.}, title = {Modeling and Numerical Analysis of Inelasticity On and Across Multiple Length Scales}, publisher = {Habilitation Thesis, University DuisburgEssen}, year = {2011} } 
Eidel, B. (2011), "Crystal plasticity finiteelement analysis versus experimental results of pyramidal indentation into (001) fcc single crystal", Acta Materialia. Vol. 59(4), pp. 17611771. 
Abstract: Pyramidal microindentation into the (001) surface of an facecentered cubic (fcc) single crystal made of a Nibase superalloy is analyzed in experiment and crystal plasticity finiteelement simulations. The resultant material pileup at the surface reflects the materials 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 pileup 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 pileup 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, wellknown observations for quasiisotropic 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 strainhardening caused by the cumulative response of dislocations. 
BibTeX:
@article{Eidel2011, author = {B. Eidel}, title = {Crystal plasticity finiteelement analysis versus experimental results of pyramidal indentation into (001) fcc single crystal}, journal = {Acta Materialia}, year = {2011}, volume = {59}, number = {4}, pages = {17611771}, 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 ODEcase of viscoelasticity", International Journal for Numerical Methods in Engineering. Vol. 87(11), pp. 10461073. 
Abstract: Time integration is the numerical kernel of inelastic finite element calculations,which largely determines their accuracy and efficiency. If higher order RungeKutta (RK) methods, p >=3, are used for integration in a standard manner, they do not achieve full convergence order but fall back to secondorder 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 RKstages within the considered time interval. We prove that quadratic interpolation of strain based on t_n, t_n+1 and, additionally, t_n1 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 ODEcase of viscoelasticity}, journal = {International Journal for Numerical Methods in Engineering}, year = {2011}, volume = {87}, number = {11}, pages = {10461073}, 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. 158. 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 = {158}, url = {http://link.springer.com/chapter/10.1007%2F9783709102831_1} } 
Fleck, M., Brener, E., Spatschek, R. & Eidel, B. (2010), "Elastic and plastic effects on solidstate transformations: A phase field study", International Journal of Materials Research. Vol. 101(4), pp. 462466. 
Abstract: We discuss a model of diffusion limited growth in solidstate 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 solidstate transformations: A phase field study}, journal = {International Journal of Materials Research}, year = {2010}, volume = {101}, number = {4}, pages = {462466}, 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. 15031512. 
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 coarsegraining of fully atomistic resolution via kinematic constraints, (ii) an approximation of the energy/forces in coarsegrained 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 = {15031512}, 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. 87108. 
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, 18991923]. Opposed to Knap and Ortiz, the energy instead of forces is subject to a clusterbased 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 clusterbased 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 forcedisplacement 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 = {87108}, 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. 172178. 
Abstract: Spherical microindentation into the (001) surface of a FCC single crystal made of the Nibase superalloy CMSX4 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 pileup 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 elastoplasticity 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 pileup/sinkin with the direction dependent pileup 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 = {172178}, doi = {http://dx.doi.org/10.1016/j.commatsci.2006.03.026} } 
Eidel, B. (2004), "Anisotropic Inelasticity  Modelling, Simulation, Validation" , pp. 230pp. PhD Thesis, TUDarmstadt, ShakerVerlag. 
BibTeX:
@book{Eidel2004, author = {B. Eidel}, title = {Anisotropic Inelasticity  Modelling, Simulation, Validation}, publisher = {PhD Thesis, TUDarmstadt, ShakerVerlag}, year = {2004}, pages = {230pp}, url = {http://www.shaker.de/de/content/catalogue/index.asp?ID=8&ISBN=9783832244736} } 
Eidel, B. & Gruttmann, F. (2003), "Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation", Computational Materials Science. Vol. 28(34), pp. 732742. 
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 socalled exponential map which preserves exactly the plastic incompressibility condition. The constitutive equations are implemented in a bricktype 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 = {34}, pages = {732742}, doi = {http://dx.doi.org/10.1016/j.commatsci.2003.08.027} } 
Eidel, B. & Gruttmann, F. (2003), "Deformation and Failure in Metallic Materials" , pp. 5178. 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 socalled 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 lockingfree 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 = {5178}, doi = {http://www.springer.com/materials/mechanics/book/9783540008484} } 
Stand: 07.06.2013
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. 1922. 
BibTeX:
@article{JSBEetal2012, 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 = {1922} } 
Eidel, B. & Kuhn, C. (2012), "RungeKutta methods for time integration in computational inelasticity  how to go beyond order 2", In CDROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 1014, 2012, Vienna, Austria. Publisher: Vienna University of Technology, Austria, ISBN: 9783950248197. 
BibTeX:
@inproceedings{, author = {B. Eidel and C. Kuhn}, title = {RungeKutta methods for time integration in computational inelasticity  how to go beyond order 2}, booktitle = {CDROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 1014, 2012, Vienna, Austria}, publisher = {Publisher: Vienna University of Technology, Austria, ISBN: 9783950248197}, year = {2012} } 
Eidel, B., Stumpf, F. & Schröder, J. (2012), "Effective, higherorder RungeKutta methods for time integration of viscoelastic constitutive models at finite strains", In 10th World Congress on Computational Mechanics (WCCM2012), July 813, 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, higherorder RungeKutta methods for time integration of viscoelastic constitutive models at finite strains}, booktitle = {10th World Congress on Computational Mechanics (WCCM2012), July 813, 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), "EnergyMinimization in AtomictoContinuum ScaleBridging Methods", Proceedings in Applied Mathematics and Mechanics. Vol. 11, pp. 509510. 
BibTeX:
@article{, author = {B. Eidel and A. Stukowski and J. Schröder}, title = {EnergyMinimization in AtomictoContinuum ScaleBridging Methods}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2011}, volume = {11}, pages = {509510}, doi = {http://dx.doi.org/10.1002/pamm.201110246} } 
Eidel, B., Stukowski, A. & Schröder, J. (2011), "Accelerated energyminimization in the quasicontinuum method with application to nanopillar compression", In Proceedings of the XI International Conference on Computational Plasticity (COMPLAS XI)., pp. 360367. 
BibTeX:
@inproceedings{, author = {B. Eidel and A. Stukowski and J. Schröder}, title = {Accelerated energyminimization in the quasicontinuum method with application to nanopillar compression}, booktitle = {Proceedings of the XI International Conference on Computational Plasticity (COMPLAS XI)}, year = {2011}, pages = {360367} } 
Eidel, B. & Schürg, M. (2008), "Pyramidal indentation into fcc single crystals and quasiisotropic polycrystals: similar phenomena, different driving mechanisms", Proceedings in Applied Mathematics and Mechanics. Vol. 8, pp. 1054310544. 
BibTeX:
@article{EidelSchurg2008, author = {B. Eidel and M. Schürg}, title = {Pyramidal indentation into fcc single crystals and quasiisotropic polycrystals: similar phenomena, different driving mechanisms}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2008}, volume = {8}, pages = {1054310544}, 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 singlecrystalline materials", Proceedings in Applied Mathematics and Mechanics. Vol. 7, pp. 40800074080008. 
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 singlecrystalline materials}, journal = {Proceedings in Applied Mathematics and Mechanics}, year = {2007}, volume = {7}, pages = {40800074080008}, 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. 425428. 
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 = {425428} } 
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. 40600254060026. 
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 = {40600254060026}, 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 higherorder methods can this be avoided?", Proceedings of Applied Mathematics and Mechanics. Vol. 7, pp. 20900192090020. 
BibTeX:
@article{KuhnEidel2007, author = {C. Kuhn and B. Eidel}, title = {Time integration of inelastic material models exhibits an order reduction for higherorder methods can this be avoided?}, journal = {Proceedings of Applied Mathematics and Mechanics}, year = {2007}, volume = {7}, pages = {20900192090020}, 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 1822., pp. 167169. 
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 1822}, year = {2006}, pages = {167169} } 
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. 265266. 
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 = {265266}, doi = {http://dx.doi.org/10.1002/pamm.200510109} } 
Eidel, B. & Gruttmann, F. (2005), "Anisotropic pileup pattern at spherical indentation in a CMSX4 single crystal finite element simulation versus experimental results", In Proceedings of the Third M.I.T. Conference on Computational Fluid and Solid Mechanics., pp. 246248. Elsevier. 
BibTeX:
@inproceedings{EidelGruttmann2005a, author = {B. Eidel and F. Gruttmann}, title = {Anisotropic pileup pattern at spherical indentation in a CMSX4 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 = {246248} } 
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. 186187. 
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 = {186187}, 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. 185186. 
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 = {185186}, doi = {http://dx.doi.org/10.1002/16177061} } 
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 712, 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 712, 2002, Vienna, Austria}, year = {2002} } 
Stand: 07.06.2013