Christian Celigoj | Graz University of Technology (original) (raw)

Papers by Christian Celigoj

Research paper thumbnail of Generalized standard materials' and finite deformation coupled thermo-elastoviscoplasticity including damage

Journal of Applied Mathematics and Mechanics, 1998

Research paper thumbnail of Thermomechanical homogenization analysis of axisymmetric inelastic solids at finite strains based on an incremental minimization principle

International Journal for Numerical Methods in Engineering, 2007

The paper presents an attempt to extend homogenization analysis to axisymmetric solids under ther... more The paper presents an attempt to extend homogenization analysis to axisymmetric solids under thermomechanical loading. In axisymmetric solids, under axisymmetric thermomechanical loading and/or torsion, on both scales, macro and micro, the displacement and rotation response is by definition independent of the cylindrical angle coordinate. In homogenization analysis the deformation of the micro-structure is driven by the deformation gradient F of the macro-structure and enhanced by a micro-scale fluctuation fieldũ, such that: x =F • X +ũ and in consequence F =F +F. What is new: on the micro-scale, the fact of independence of the cylindrical angle coordinate imposes the homogeneous or Taylor-assumption on the fluctuation fieldũ of the R(epresentative) V(olume) E(lement) in the radial direction, whereas the other two fluctuation fields, the torsional angle˜ and the axial displacementw, are not affected. The thermomechanical problem on the macroscale is solved via a split approach: an isentropic mechanical phase, an isogeometrical thermal phase, and-in case of inelasticity-an update phase of the internal micro-variables. The homogenization of inelastic solid materials at finite strains is based on an incremental minimization principle, recently introduced by Miehe et al.

Research paper thumbnail of On strong discontinuities in anelastic solids. A finite element approach taking a frame indifferent gradient of the discontinuous displacements

International Journal for Numerical Methods in Engineering, 2000

ABSTRACT

Research paper thumbnail of An assumed enhanced displacement gradient ring‐element for finite deformation axisymmetric and torsional problems

International Journal for Numerical Methods in Engineering, Dec 30, 1998

ABSTRACT

Research paper thumbnail of An augmented Lagrange multiplier approach to continuum multislip single crystal thermo-elasto-viscoplasticity

Communications in Numerical Methods in Engineering, May 9, 2005

The material and structural behaviour of single crystals is going to be investigated. On the cons... more The material and structural behaviour of single crystals is going to be investigated. On the constitutive level the concept of 'generalized standard materials (gsm)' is used to set up the equations for ÿnite deformation multislip single crystal thermo-elasto-viscoplasticity within a continuum slip theory. The only two scalar quantities needed are a thermodynamic potential and a dissipation potential. The resulting evolution equations for the internal (viscoplastic) variables are discretized in time and solved via a backward Euler scheme, using an 'augmented Lagrange multiplier method' for satisfying the multiple constraints, thus circumventing the cumbersome and less robust 'active set strategies'. As a computational reference frame serves the Eulerian setting. The structural behaviour (non-linear coupled thermomechanics) is solved in a staggered algorithm: in an isothermal mechanical phase via q1(displacements)=p0(pressure)=j0(jacobian)-ÿnite elements and in an isogeometric thermal phase via q1(temperatures)-ÿnite elements, followed by an isogeometric and isothermal update phase of the internal variables. Numerical results of the simple isothermal shear test of a single face-centred cubic (fcc) crystal and of the thermomechanical behaviour of a geometrically imperfect strip consisting of initially equally oriented (0=45=30 in Euler angles) fcc-crystals under tension and plane strain conditions are given.

Research paper thumbnail of A Strain-And-Displacement-Based Variational Method Applied to Geometrically Non-Linear Shells

International Journal for Numerical Methods in Engineering, Jul 15, 1996

ABSTRACT

Research paper thumbnail of Finite strain thermoelasto-Thermoviscoplasticity formulated in F_vp_-1 (inverse viscoplastic deformation gradient), xi (accumulated viscoplastiv strain) and eta_vp (viscoplastic entropy) as internal variables

Research paper thumbnail of Ein geometrisch nichtlineares finites Verzerrungs-Weggrößen-Schalenelement

Journal of Applied Mathematics and Mechanics, 1995

Research paper thumbnail of Ein hybrides 4-Knoten-Schalenelement unter Berücksichtigung der Normalenverzerrung

Research paper thumbnail of A total ALE FE formulation for axisymmetric and torsional problems (including viscoplasticity, thermodynamic coupling and dynamics)

International Journal for Numerical Methods in Engineering, 2007

This paper-first-extends a recent 'assumed enhanced deformation gradient' finite ring(segment) el... more This paper-first-extends a recent 'assumed enhanced deformation gradient' finite ring(segment) element (Int. J. Numer. Methods Eng. 2001; 50:899-918.) to Arbitary Lagrange Euler (ALE) computations, by setting up the assumed tensor on the computational configuration, and-second-shows an elegant way of incorporating dynamics into real ALE computations (no splitting into purely-Lagrange steps and thenremeshing steps), by introducing material mesh velocities and accelerations and spatial mesh velocities and accelerations.

Research paper thumbnail of Buckling analysis of carbon nanotubes by a mixed atomistic and continuum model

Computational Mechanics, Jul 28, 2012

A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buc... more A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buckling behavior. Herein, the term "atomistic" refers to the underlying constitutive model that is formulated on the basis of interatomic potentials, whereas "continuum" means the application of the Cauchy-Born rule, which links the bond vectors before and after deformation via the deformation gradient of the continuum. Because the bond vectors are not infinitesimal and the continuum is modeled as surface, the Cauchy-Born rule has to be appropriately adapted to crystalline sheets. This is done via an exponential mapping in a new and surprisingly simple form such that in the analysis the current configuration has never to be left. The numerical buckling analysis of carbon nanotubes using the mixed atomistic and continuum model is carried out by means of the finite element method. For this purpose, the linearization of the equilibrium equations is provided.

Research paper thumbnail of Das Boltzmann-Axiom

Research paper thumbnail of Theory and numerics of anisotropic materials at finite strains (EUROMECH Colloquium 394)

International Journal of Solids and Structures, Dec 1, 2001

The EUROMECH Colloquium 394 on``Theory and Numerics of Anisotropic Materials at Finite Strains'' ... more The EUROMECH Colloquium 394 on``Theory and Numerics of Anisotropic Materials at Finite Strains'' took place on March 29±31st 1999 at the Technical University of Graz. There were 43 participants from nine countries who presented 28 contributions. Following the colloquium the participants were invited to submit full-length papers to be published in the International Journal of Solids and Structures. This special issue contains eleven papers all of which were peer reviewed. The purpose of the colloquium and of this special issue is to provide an overview over the recent progress made in the ®eld considered as well as to present new and signi®cant results. The papers are, in general, concerned with the development of constitutive laws and numerical algorithms for large-strain anisotropy as well as the simulation of the behavior of various materials. Speci®c topics covered are the mathematical, physical and thermodynamical foundations for dierent anisotropic material laws such as hyperelasticity, plasticity and viscoplasticity or damage. Phenomena considered include localization, texture development, phase transitions and shape memory eects. Many contributions introduce new numerical algorithms and models for problems like crystal plasticity, damage mechanics or anisotropic plates and shells. Finally there are contributions dealing with the relation between microscopic and macroscopic properties of materials. The editorial committee would like to thank all the authors for their contributions and the reviewers for helping to guarantee high scienti®c standard of the published papers. Also we would like to extend our gratitude to Professor Charles Steele, the Editor-in-Chief of the International Journal of Solids and Structures, who agreed to publish this special issue.

Research paper thumbnail of A uniquely defined multiplicative elasto-plasticity model with orthotropic yield function and plastic spin

Computer Methods in Applied Mechanics and Engineering, Feb 1, 2021

Abstract A rate-independent model for isotropic elastic–orthotropic plastic material behaviour in... more Abstract A rate-independent model for isotropic elastic–orthotropic plastic material behaviour including the plastic spin is presented in this paper. The plastic spin, as introduced by Dafalias, is the spin of the continuum relative to the material substructure. The model is based on a specific multiplicative decomposition of the deformation gradient tensor, which introduces a uniquely defined intermediate configuration as motivated by Casey. We focus our attention on metal sheets in forming processes, in which pre-existing preferred orientations govern the orthotropic plastic behaviour. As a result, we advocate a Hill-type yield criterion enriched by the notion of plastic spin to describe this material behaviour. Our formulation yields three key findings: firstly, the uniquely defined intermediate configuration, namely a plastically stretched intermediate configuration, allows for a neat implementation of the plastic spin; secondly, the algorithmic formulation is straightforward and shows no additional difficulties in the implementation; and thirdly, a good agreement of our numerical model with experimental and numerical results from in-plane sheet forming processes reported in the literature is achieved.

Research paper thumbnail of Amendment to the Galin Plane Elastoplastic Solution

Journal of Engineering Mechanics-asce, Nov 1, 2013

Research paper thumbnail of Finite deformation coupled thermomechanical problems and ‘generalized standard materials’

International Journal for Numerical Methods in Engineering, Jul 30, 1998

ABSTRACT

Research paper thumbnail of An orthotropic plasticity model at finite strains with plasticity-induced evolution of orthotropy based on a covariant formulation

Computer Methods in Applied Mechanics and Engineering

Research paper thumbnail of Thermomechanical homogenization analysis of axisymmetric inelastic solids at finite strains based on an incremental minimization principle

International Journal for Numerical Methods in Engineering, 2007

The paper presents an attempt to extend homogenization analysis to axisymmetric solids under ther... more The paper presents an attempt to extend homogenization analysis to axisymmetric solids under thermomechanical loading. In axisymmetric solids, under axisymmetric thermomechanical loading and/or torsion, on both scales, macro and micro, the displacement and rotation response is by definition independent of the cylindrical angle coordinate. In homogenization analysis the deformation of the micro-structure is driven by the deformation gradient F of the macro-structure and enhanced by a micro-scale fluctuation fieldũ, such that: x =F • X +ũ and in consequence F =F +F. What is new: on the micro-scale, the fact of independence of the cylindrical angle coordinate imposes the homogeneous or Taylor-assumption on the fluctuation fieldũ of the R(epresentative) V(olume) E(lement) in the radial direction, whereas the other two fluctuation fields, the torsional angle˜ and the axial displacementw, are not affected. The thermomechanical problem on the macroscale is solved via a split approach: an isentropic mechanical phase, an isogeometrical thermal phase, and-in case of inelasticity-an update phase of the internal micro-variables. The homogenization of inelastic solid materials at finite strains is based on an incremental minimization principle, recently introduced by Miehe et al.

Research paper thumbnail of An augmented Lagrange multiplier approach to continuum multislip single crystal thermo-elasto-viscoplasticity

Communications in Numerical Methods in Engineering, 2005

The material and structural behaviour of single crystals is going to be investigated. On the cons... more The material and structural behaviour of single crystals is going to be investigated. On the constitutive level the concept of 'generalized standard materials (gsm)' is used to set up the equations for ÿnite deformation multislip single crystal thermo-elasto-viscoplasticity within a continuum slip theory. The only two scalar quantities needed are a thermodynamic potential and a dissipation potential. The resulting evolution equations for the internal (viscoplastic) variables are discretized in time and solved via a backward Euler scheme, using an 'augmented Lagrange multiplier method' for satisfying the multiple constraints, thus circumventing the cumbersome and less robust 'active set strategies'. As a computational reference frame serves the Eulerian setting. The structural behaviour (non-linear coupled thermomechanics) is solved in a staggered algorithm: in an isothermal mechanical phase via q1(displacements)=p0(pressure)=j0(jacobian)-ÿnite elements and in an isogeometric thermal phase via q1(temperatures)-ÿnite elements, followed by an isogeometric and isothermal update phase of the internal variables. Numerical results of the simple isothermal shear test of a single face-centred cubic (fcc) crystal and of the thermomechanical behaviour of a geometrically imperfect strip consisting of initially equally oriented (0=45=30 in Euler angles) fcc-crystals under tension and plane strain conditions are given.

Research paper thumbnail of Geometrisch quadratische Biegetorsionstheorie gerader elastischer St�be

Ingenieur-Archiv, 1979

ABSTRACT

Research paper thumbnail of Generalized standard materials' and finite deformation coupled thermo-elastoviscoplasticity including damage

Journal of Applied Mathematics and Mechanics, 1998

Research paper thumbnail of Thermomechanical homogenization analysis of axisymmetric inelastic solids at finite strains based on an incremental minimization principle

International Journal for Numerical Methods in Engineering, 2007

The paper presents an attempt to extend homogenization analysis to axisymmetric solids under ther... more The paper presents an attempt to extend homogenization analysis to axisymmetric solids under thermomechanical loading. In axisymmetric solids, under axisymmetric thermomechanical loading and/or torsion, on both scales, macro and micro, the displacement and rotation response is by definition independent of the cylindrical angle coordinate. In homogenization analysis the deformation of the micro-structure is driven by the deformation gradient F of the macro-structure and enhanced by a micro-scale fluctuation fieldũ, such that: x =F • X +ũ and in consequence F =F +F. What is new: on the micro-scale, the fact of independence of the cylindrical angle coordinate imposes the homogeneous or Taylor-assumption on the fluctuation fieldũ of the R(epresentative) V(olume) E(lement) in the radial direction, whereas the other two fluctuation fields, the torsional angle˜ and the axial displacementw, are not affected. The thermomechanical problem on the macroscale is solved via a split approach: an isentropic mechanical phase, an isogeometrical thermal phase, and-in case of inelasticity-an update phase of the internal micro-variables. The homogenization of inelastic solid materials at finite strains is based on an incremental minimization principle, recently introduced by Miehe et al.

Research paper thumbnail of On strong discontinuities in anelastic solids. A finite element approach taking a frame indifferent gradient of the discontinuous displacements

International Journal for Numerical Methods in Engineering, 2000

ABSTRACT

Research paper thumbnail of An assumed enhanced displacement gradient ring‐element for finite deformation axisymmetric and torsional problems

International Journal for Numerical Methods in Engineering, Dec 30, 1998

ABSTRACT

Research paper thumbnail of An augmented Lagrange multiplier approach to continuum multislip single crystal thermo-elasto-viscoplasticity

Communications in Numerical Methods in Engineering, May 9, 2005

The material and structural behaviour of single crystals is going to be investigated. On the cons... more The material and structural behaviour of single crystals is going to be investigated. On the constitutive level the concept of 'generalized standard materials (gsm)' is used to set up the equations for ÿnite deformation multislip single crystal thermo-elasto-viscoplasticity within a continuum slip theory. The only two scalar quantities needed are a thermodynamic potential and a dissipation potential. The resulting evolution equations for the internal (viscoplastic) variables are discretized in time and solved via a backward Euler scheme, using an 'augmented Lagrange multiplier method' for satisfying the multiple constraints, thus circumventing the cumbersome and less robust 'active set strategies'. As a computational reference frame serves the Eulerian setting. The structural behaviour (non-linear coupled thermomechanics) is solved in a staggered algorithm: in an isothermal mechanical phase via q1(displacements)=p0(pressure)=j0(jacobian)-ÿnite elements and in an isogeometric thermal phase via q1(temperatures)-ÿnite elements, followed by an isogeometric and isothermal update phase of the internal variables. Numerical results of the simple isothermal shear test of a single face-centred cubic (fcc) crystal and of the thermomechanical behaviour of a geometrically imperfect strip consisting of initially equally oriented (0=45=30 in Euler angles) fcc-crystals under tension and plane strain conditions are given.

Research paper thumbnail of A Strain-And-Displacement-Based Variational Method Applied to Geometrically Non-Linear Shells

International Journal for Numerical Methods in Engineering, Jul 15, 1996

ABSTRACT

Research paper thumbnail of Finite strain thermoelasto-Thermoviscoplasticity formulated in F_vp_-1 (inverse viscoplastic deformation gradient), xi (accumulated viscoplastiv strain) and eta_vp (viscoplastic entropy) as internal variables

Research paper thumbnail of Ein geometrisch nichtlineares finites Verzerrungs-Weggrößen-Schalenelement

Journal of Applied Mathematics and Mechanics, 1995

Research paper thumbnail of Ein hybrides 4-Knoten-Schalenelement unter Berücksichtigung der Normalenverzerrung

Research paper thumbnail of A total ALE FE formulation for axisymmetric and torsional problems (including viscoplasticity, thermodynamic coupling and dynamics)

International Journal for Numerical Methods in Engineering, 2007

This paper-first-extends a recent 'assumed enhanced deformation gradient' finite ring(segment) el... more This paper-first-extends a recent 'assumed enhanced deformation gradient' finite ring(segment) element (Int. J. Numer. Methods Eng. 2001; 50:899-918.) to Arbitary Lagrange Euler (ALE) computations, by setting up the assumed tensor on the computational configuration, and-second-shows an elegant way of incorporating dynamics into real ALE computations (no splitting into purely-Lagrange steps and thenremeshing steps), by introducing material mesh velocities and accelerations and spatial mesh velocities and accelerations.

Research paper thumbnail of Buckling analysis of carbon nanotubes by a mixed atomistic and continuum model

Computational Mechanics, Jul 28, 2012

A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buc... more A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buckling behavior. Herein, the term "atomistic" refers to the underlying constitutive model that is formulated on the basis of interatomic potentials, whereas "continuum" means the application of the Cauchy-Born rule, which links the bond vectors before and after deformation via the deformation gradient of the continuum. Because the bond vectors are not infinitesimal and the continuum is modeled as surface, the Cauchy-Born rule has to be appropriately adapted to crystalline sheets. This is done via an exponential mapping in a new and surprisingly simple form such that in the analysis the current configuration has never to be left. The numerical buckling analysis of carbon nanotubes using the mixed atomistic and continuum model is carried out by means of the finite element method. For this purpose, the linearization of the equilibrium equations is provided.

Research paper thumbnail of Das Boltzmann-Axiom

Research paper thumbnail of Theory and numerics of anisotropic materials at finite strains (EUROMECH Colloquium 394)

International Journal of Solids and Structures, Dec 1, 2001

The EUROMECH Colloquium 394 on``Theory and Numerics of Anisotropic Materials at Finite Strains'' ... more The EUROMECH Colloquium 394 on``Theory and Numerics of Anisotropic Materials at Finite Strains'' took place on March 29±31st 1999 at the Technical University of Graz. There were 43 participants from nine countries who presented 28 contributions. Following the colloquium the participants were invited to submit full-length papers to be published in the International Journal of Solids and Structures. This special issue contains eleven papers all of which were peer reviewed. The purpose of the colloquium and of this special issue is to provide an overview over the recent progress made in the ®eld considered as well as to present new and signi®cant results. The papers are, in general, concerned with the development of constitutive laws and numerical algorithms for large-strain anisotropy as well as the simulation of the behavior of various materials. Speci®c topics covered are the mathematical, physical and thermodynamical foundations for dierent anisotropic material laws such as hyperelasticity, plasticity and viscoplasticity or damage. Phenomena considered include localization, texture development, phase transitions and shape memory eects. Many contributions introduce new numerical algorithms and models for problems like crystal plasticity, damage mechanics or anisotropic plates and shells. Finally there are contributions dealing with the relation between microscopic and macroscopic properties of materials. The editorial committee would like to thank all the authors for their contributions and the reviewers for helping to guarantee high scienti®c standard of the published papers. Also we would like to extend our gratitude to Professor Charles Steele, the Editor-in-Chief of the International Journal of Solids and Structures, who agreed to publish this special issue.

Research paper thumbnail of A uniquely defined multiplicative elasto-plasticity model with orthotropic yield function and plastic spin

Computer Methods in Applied Mechanics and Engineering, Feb 1, 2021

Abstract A rate-independent model for isotropic elastic–orthotropic plastic material behaviour in... more Abstract A rate-independent model for isotropic elastic–orthotropic plastic material behaviour including the plastic spin is presented in this paper. The plastic spin, as introduced by Dafalias, is the spin of the continuum relative to the material substructure. The model is based on a specific multiplicative decomposition of the deformation gradient tensor, which introduces a uniquely defined intermediate configuration as motivated by Casey. We focus our attention on metal sheets in forming processes, in which pre-existing preferred orientations govern the orthotropic plastic behaviour. As a result, we advocate a Hill-type yield criterion enriched by the notion of plastic spin to describe this material behaviour. Our formulation yields three key findings: firstly, the uniquely defined intermediate configuration, namely a plastically stretched intermediate configuration, allows for a neat implementation of the plastic spin; secondly, the algorithmic formulation is straightforward and shows no additional difficulties in the implementation; and thirdly, a good agreement of our numerical model with experimental and numerical results from in-plane sheet forming processes reported in the literature is achieved.

Research paper thumbnail of Amendment to the Galin Plane Elastoplastic Solution

Journal of Engineering Mechanics-asce, Nov 1, 2013

Research paper thumbnail of Finite deformation coupled thermomechanical problems and ‘generalized standard materials’

International Journal for Numerical Methods in Engineering, Jul 30, 1998

ABSTRACT

Research paper thumbnail of An orthotropic plasticity model at finite strains with plasticity-induced evolution of orthotropy based on a covariant formulation

Computer Methods in Applied Mechanics and Engineering

Research paper thumbnail of Thermomechanical homogenization analysis of axisymmetric inelastic solids at finite strains based on an incremental minimization principle

International Journal for Numerical Methods in Engineering, 2007

The paper presents an attempt to extend homogenization analysis to axisymmetric solids under ther... more The paper presents an attempt to extend homogenization analysis to axisymmetric solids under thermomechanical loading. In axisymmetric solids, under axisymmetric thermomechanical loading and/or torsion, on both scales, macro and micro, the displacement and rotation response is by definition independent of the cylindrical angle coordinate. In homogenization analysis the deformation of the micro-structure is driven by the deformation gradient F of the macro-structure and enhanced by a micro-scale fluctuation fieldũ, such that: x =F • X +ũ and in consequence F =F +F. What is new: on the micro-scale, the fact of independence of the cylindrical angle coordinate imposes the homogeneous or Taylor-assumption on the fluctuation fieldũ of the R(epresentative) V(olume) E(lement) in the radial direction, whereas the other two fluctuation fields, the torsional angle˜ and the axial displacementw, are not affected. The thermomechanical problem on the macroscale is solved via a split approach: an isentropic mechanical phase, an isogeometrical thermal phase, and-in case of inelasticity-an update phase of the internal micro-variables. The homogenization of inelastic solid materials at finite strains is based on an incremental minimization principle, recently introduced by Miehe et al.

Research paper thumbnail of An augmented Lagrange multiplier approach to continuum multislip single crystal thermo-elasto-viscoplasticity

Communications in Numerical Methods in Engineering, 2005

The material and structural behaviour of single crystals is going to be investigated. On the cons... more The material and structural behaviour of single crystals is going to be investigated. On the constitutive level the concept of 'generalized standard materials (gsm)' is used to set up the equations for ÿnite deformation multislip single crystal thermo-elasto-viscoplasticity within a continuum slip theory. The only two scalar quantities needed are a thermodynamic potential and a dissipation potential. The resulting evolution equations for the internal (viscoplastic) variables are discretized in time and solved via a backward Euler scheme, using an 'augmented Lagrange multiplier method' for satisfying the multiple constraints, thus circumventing the cumbersome and less robust 'active set strategies'. As a computational reference frame serves the Eulerian setting. The structural behaviour (non-linear coupled thermomechanics) is solved in a staggered algorithm: in an isothermal mechanical phase via q1(displacements)=p0(pressure)=j0(jacobian)-ÿnite elements and in an isogeometric thermal phase via q1(temperatures)-ÿnite elements, followed by an isogeometric and isothermal update phase of the internal variables. Numerical results of the simple isothermal shear test of a single face-centred cubic (fcc) crystal and of the thermomechanical behaviour of a geometrically imperfect strip consisting of initially equally oriented (0=45=30 in Euler angles) fcc-crystals under tension and plane strain conditions are given.

Research paper thumbnail of Geometrisch quadratische Biegetorsionstheorie gerader elastischer St�be

Ingenieur-Archiv, 1979

ABSTRACT