Simulation of inextensible elasto-plastic beams based on an implicit rate type model

Wang, Zhujiang; Srinivasa, Arun R.; Rajagopal, K. R.; Reddy, J. N.

doi:10.1016/j.ijnonlinmec.2017.11.011

Cited by 12 publications

(11 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

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“…Most of the relations presented in this section can be found in classical treatises such as [19,20], and in the case of constitutive equations of the form (4), the interested reader can see the research studies [27][28][29]. The constants E C and E T are in (MPa) [18].…”

Section: Relations For a Beammentioning

confidence: 99%

A beam theory for a new class of constitutive relation for elastic bodies

Bustamante

2022

Mathematics and Mechanics of Solids

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A theory for two-dimensional (2D) beams is presented for the case of considering new constitutive equations, wherein the linearized (infinitesimal) strain tensor is assumed to be a nonlinear function of the Cauchy stress tensor. An incremental formulation is developed to solve numerically the resultant equations. Three constitutive equations for elastic bodies are considered: a model wherein we have strain-limiting behavior, a nonlinear model for rock, and a bimodular constitutive equation for rock (which can also be considered as a nonlinear model for rock). Two boundary value problems are studied: the deformation of a cantilever beam with a point load, and a three-point beam with a point load applied on the middle. The numerical results are compared with the predictions of the classical theory for beams for the case of linearized elastic solids. The results for the stresses can be notoriously different, when comparing the predictions of the nonlinear constitutive equations with the results obtained using the linearized theory of elasticity.

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“…The discussed studies were mainly related to two issues: non-linear analyses of construction elements (mainly reinforced concrete) and non-linear models of hyper-elastic constitutive materials and their utilization. In some cases, the cyclic load of the system that usually generates a hysteretic response is taken under consideration ([ 6 , 10 , 11 , 21 , 30 , 31 ]). The studies feature a common theme that is creating models of constitutive materials or elements—using algebraic or differential mathematical relations describing the stress–strain or moment–curvature relation.…”

Section: Introductionmentioning

confidence: 99%

Matrix Description of Non-Linear Properties of Materials or Structural Components—Idea and Application Examples

Janiak¹

2021

Materials

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Numerical methods are widely used in structural analysis problems. In the cases of the most complex and practical problems, they are often the only way to obtain solutions, as analytical methods prove ineffective. The motivation for this paper was the desire to extend the scope of numerical methods to cover the problems of creating constitutive models of structural materials. The aim of this research was to develop a matrix or numerical discrete constitutive model of materials. It presents the general assumptions of the developed method for modeling the physical properties of materials. The matrix model is only useful with an appropriate numerical algorithm. Such an algorithm was created and described in this paper. Based on its findings, computer software was developed to perform numerical simulations. Presented calculation examples confirmed the effectiveness of the developed method to create constitutive matrix models of various typical materials, such as steel, but also, e.g., hyper-elastic materials. It also presents the usefulness of constitutive matrix models for simulations of simple stress states and analyses of structural elements such as reinforced concrete. All presented examples involved the physical nonlinearity of the materials. It is proved that the developed matrix constitutive model of materials is efficient and quite versatile. In complex analyses of structures made of nonlinear materials, it can be used as an effective alternative to classical constitutive or analytical models based on elementary mathematical functions.

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Simulation of inextensible elasto-plastic beams based on an implicit rate type model

Cited by 12 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

A beam theory for a new class of constitutive relation for elastic bodies

Matrix Description of Non-Linear Properties of Materials or Structural Components—Idea and Application Examples

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