Variational updates for thermomechanically coupled gradient-enhanced elastoplasticity — Implementation based on hyper-dual numbers

Fohrmeister, Volker; Bartels, Alexander; Mosler, Jörn

doi:10.1016/j.cma.2018.04.047

Cited by 12 publications

(5 citation statements)

References 39 publications

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“…with k = n + 1 for an implicit numerical integration algorithm according to (21) and k = n for a semi-explicit numerical integration algorithm according to (25). In (67) we dropped terms that are associated with previous time t n .…”

Section: Incremental Formulationmentioning

confidence: 99%

“…Alternatively, staggered numerical algorithms were mainly used before which lead to symmetric finite element stiffness matrices for each subproblem, see Simo & Miehe [79] and Armero & Simo [3]. In the recent years, the work of Yang et al [89] has been the basis for further model developments in thermoplasticity, see Stainier & Ortiz [81], Canadija & Mosler [10], Su et al [82], Bartels et al [5], Mielke [55] and Fohrmeister et al [21]. In the latter, a specific phenomenological model of gradient plasticity together with a micromorphic extension in the sense of Forest [22] is considered.…”

Section: Introductionmentioning

confidence: 99%

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A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids – with Applications to Diffusion, Damage and Plasticity

Teichtmeister

Keip

2022

J Elast

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The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical coupling in gradient-extended dissipative materials. It is shown that these principles yield as Euler equations essentially the macro- and micro-balances as well as the energy equation. Starting point is the incorporation of the entropy and entropy rate as canonical arguments into constitutive energy and dissipation functions, which additionally depend on the gradient-extended mechanical state and its rate, respectively. By means of (generalized) Legendre transformations, extended variational principles with thermal as well as mechanical driving forces can be constructed. On the thermal side, a rigorous distinction between the quantity conjugate to the entropy and the quantity conjugate to the entropy rate is essential here. Formulations with mechanical driving forces are especially suitable when considering possibly temperature-dependent threshold mechanisms. With regard to variationally consistent incrementations, we suggest an update scheme which renders the exact form of the intrinsic dissipation and is highly suitable when considering adiabatic processes. It is shown that this proposed numerical algorithm has the structure of an operator split. To underline the broad applicability of the proposed framework, we set up three model problems as applications: Cahn-Hilliard diffusion coupled with temperature evolution, where we propose a new variational principle in terms of the species flux vector, as well as thermomechanics of gradient damage and gradient plasticity. In a numerical example we study the formation of a cross shear band.

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Section: Incremental Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids – with Applications to Diffusion, Damage and Plasticity

Teichtmeister

Keip

2022

J Elast

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show abstract

“…To arrive at (19), we use the result that at equilibrium the thermal driving force T can be identified with the temperature θ, which is an outcome of the mixed variational principle (23)…”

Section: Variational Principle With Entropy Variablementioning

confidence: 99%

“…Alternatively, staggered algorithms were mainly used before that lead to symmetric finite element stiffness matrices for each subproblem, see Simo & Miehe [73] and Simo & Armero [71]. In the recent years the work of Yang et al [81] has been the basis for further model developments in thermoplasticity, see Stainier & Ortiz [74], Canadija & Mosler [9], Su et al [75], Bartels et al [5], Mielke [53] and Fohrmeister et al [19]. In the latter, a specific phenomenological model of gradient plasticity together with a micromorphic extension in the sense of Forest [20] is considered.…”

Section: Introductionmentioning

confidence: 99%

A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids -- with Applications to Diffusion, Damage and Plasticity

Teichtmeister,

Keip

2020

Preprint

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The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical coupling in gradient-extended dissipative materials. It is shown that these principles yield as Euler equations essentially the macro-and micro-balances as well as the energy equation. Starting point is the incorporation of the entropy and entropy rate as additional arguments into constitutive energy and dissipation functions which depend on the gradient-extended mechanical state and its rate, respectively. By means of (generalized) Legendre transformations, extended variational principles with thermal as well as mechanical driving forces can be constructed. On the thermal side, a rigorous distinction between the quantity conjugate to the entropy and the quantity conjugate to the entropy rate is essential here. Formulations with mechanical driving forces are especially suitable when considering possibly temperature-dependent threshold mechanisms. With regard to variationally consistent incrementations, we suggest an update scheme which renders the exact form of the intrinsic dissipation and is highly suitable when considering adiabatic processes. To underline the broad applicability of the proposed framework, we exemplarily set up three model problems, namely Cahn-Hilliard diffusion coupled with temperature evolution as well as thermomechanics of gradient damage and gradient plasticity. In a numerical example we study the formation of a cross shear band.

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“…Finally, parameters for the material models are determined for the chosen confidence interval and these material models are then included in the simulations. Finite element (FE) based calculations are mostly used for the simulations of the temperature dependent stress-strain response and damage accumulation [3,12,22].…”

mentioning

confidence: 99%

A new approach to finite element modelling of cyclic thermomechanical stress-strain responses

Šeruga

Nagode

2019

International Journal of Mechanical Sciences

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Variational updates for thermomechanically coupled gradient-enhanced elastoplasticity — Implementation based on hyper-dual numbers

Cited by 12 publications

References 39 publications

A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids – with Applications to Diffusion, Damage and Plasticity

A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids – with Applications to Diffusion, Damage and Plasticity

A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids -- with Applications to Diffusion, Damage and Plasticity

A new approach to finite element modelling of cyclic thermomechanical stress-strain responses

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