A three-dimensional implicit constitutive relation for a body exhibiting stress softening: part I—theoretical underpinnings

Bustamante, R.; Rajagopal, K. R.

doi:10.1007/s00707-022-03231-5

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…(For another treatment of rate-type models from a thermodynamic point of view see also [10] and the discussion in [15] based on the concept of internal variables, to name a few.) Furthermore, the models in this class have also been employed in modelling the response of various materials, see [32] , [20] , [19] [28] and [4] . We have focused on a generalisation of (1) that describes the standard elastic-perfectly plastic response.…”

Section: Discussionmentioning

confidence: 99%

Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response

Gazca-Orozco¹,

Průša²,

Tůma³

2023

Preprint

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We analyse a numerical scheme for a system arising from a novel description of the standard elastic-perfectly plastic response. The elastic-perfectly plastic response is described via rate-type equations that do not make use of the standard elastic-plastic decomposition, and the model does not require the use of variational inequalities.Furthermore, the model naturally includes the evolution equation for temperature. We present a low order discretisation based on the finite element method. Under certain restrictions on the mesh we subsequently prove the existence of discrete solutions, and we discuss the stability properties of the numerical scheme. The analysis is supplemented with computational examples.

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Section: Discussionmentioning

confidence: 99%

Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response

Gazca-Orozco¹,

Průša²,

Tůma³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…(For another treatment of rate-type models from a thermodynamic point of view see also [33] and the discussion in [34] based on the concept of internal variables, to name a few.) Furthermore, the models in this class have also been employed in modelling the response of various materials, see [14,[35][36][37] and [38]. We have focused on a generalisation of (1) that describes the standard elastic-perfectly plastic response.…”

Section: Discussionmentioning

confidence: 99%

Numerical approximation of a thermodynamically complete rate‐type model for the elastic–perfectly plastic response

Gazca‐Orozco,

Průša,

Tůma

2023

Z Angew Math Mech

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We analyse a numerical scheme for a system arising from a novel description of the standard elastic–perfectly plastic response. The elastic–perfectly plastic response is described via rate‐type equations that do not make use of the standard elastic‐plastic decomposition, and the model does not require the use of variational inequalities. Furthermore, the model naturally includes the evolution equation for temperature. We present a low order discretisation based on the finite element method. Under certain restrictions on the mesh we subsequently prove the existence of discrete solutions, and we discuss the stability properties of the numerical scheme. The analysis is supplemented with computational examples.

show abstract

A three-dimensional implicit constitutive relation for a body exhibiting stress softening: part I—theoretical underpinnings

Cited by 2 publications

References 18 publications

Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response

Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response

Numerical approximation of a thermodynamically complete rate‐type model for the elastic–perfectly plastic response

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