Analytical solutions in elasto-plastic bending of beams with rectangular cross section

Štok, Boris; Halilovic̆, Miroslav

doi:10.1016/j.apm.2008.03.011

Cited by 60 publications

(22 citation statements)

References 18 publications

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“…Simo and Kennedy [31] proposed a framework for modeling elastoplastic deformations within their two-dimensional shell theory. There are several works accounting for elastoplastic deformations within classical linear beam theories [32,33]. Simo et al [34] have pursued the same for planar deformations of their nonlinear beam model.…”

Section: Introductionmentioning

confidence: 99%

A thermoelastoplastic theory for special Cosserat rods

Smriti

Kumar

Großmann

et al. 2018

Mathematics and Mechanics of Solids

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A general framework is presented to model coupled thermoelastoplastic deformations in the theory of special Cosserat rods. The use of the one-dimensional form of the energy balance in conjunction with the one-dimensional entropy balance allows us to obtain an additional equation for the evolution of a temperature-like one-dimensional field variable, together with constitutive relations for this theory. Reduction to the case of thermoelasticity leads us to the well-known nonlinear theory of thermoelasticity for special Cosserat rods. Later on, additive decomposition is used to separate the thermoelastic part of the strain measures of the rod from their plastic counterparts. We then present the most general quadratic form of the Helmholtz energy per unit undeformed length for both hemitropic and transversely isotropic rods. We also propose a prototype yield criterion in terms of forces, moments, and hardening stress resultants, as well as associative flow rules for the evolution of plastic strain measures and hardening variables.

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Section: Introductionmentioning

confidence: 99%

A thermoelastoplastic theory for special Cosserat rods

Smriti

Kumar

Großmann

et al. 2018

Mathematics and Mechanics of Solids

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show abstract

“…The authors include many experimental verifications as well as theoretical results. Elastic-p lastic analysis of beam-like structures of different cross-sections under bending is considered in [2][3][4][5][6][7][8][9][10]. The authors employ different models of non-linear stress-strain idealization.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Rectangular and Circular Cross-section Power Hardening Elements Under Pure Bending

Rimovskis¹,

Sabaliauskas²

2013

IJME

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Eng ineering theory of elastic plastic bending is used in solving a grate variety of strength and durability problems. The accuracy of analysis depends on stress-strain curve idealizat ion model. The elastic linear hardening stress-strain relation is simp le and frequently used. But the actual stress-strain behaviour of ductile material in plastic reg ion is non-linear and, therefore, elastic power hardening material model is more p referab le. Moreover, the properties of monotonic tension and compression as proportional limits and parameters of hardening can differ. In this regard, analytical solution for rectangular and circular cross-section elements loading by monotonic elastic plastic pure bending is presented in the paper. The simp le power relation of stress and strain response is used. The equations describing deviation of the stress neutral axis fro m centroidal axis of an element and dimensionless bending mo ment are derived.

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“…The resulting necessity to address radius of curvature evolution (when employing the generic correlation in Equation 8) is addressed by a few existing analytical approaches; however these approaches, either incorporating an elastic-perfectly-plastic constitutive relationship [18,19] or incorporating strain-hardening rule applicable to metals [20,21,22], may be inaccurate for thermoplastics.…”

Section: Flexure and Cantilever Cae Simulation Trends And Correlationmentioning

confidence: 99%

A modular cantilever fixture and test methodology for thermoplastics: An alternative bending load case for validation of CAE material models

Patham²,

Kavi

et al. 2016

Materials & Design

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Analytical solutions in elasto-plastic bending of beams with rectangular cross section

Cited by 60 publications

References 18 publications

A thermoelastoplastic theory for special Cosserat rods

A thermoelastoplastic theory for special Cosserat rods

Analysis of Rectangular and Circular Cross-section Power Hardening Elements Under Pure Bending

A modular cantilever fixture and test methodology for thermoplastics: An alternative bending load case for validation of CAE material models

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