Folding of a plastic fibre under combined shear and compression

Teng, Xiaoyan; Wierzbicki, Tomasz

doi:10.1016/j.tws.2004.01.002

Cited by 4 publications

(2 citation statements)

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“…We consider a cantilever beam (Figure 4), one fixed end and one free end, of length L , rectangular cross-section, an evenly distributed load w , and a point load P applied at an angle α on the free end [5]. The moment along the neutral axis s described by the forces in Figure 4(b) can be defined as…”

Section: The Beam Modelmentioning

confidence: 99%

“…Lee [3] discussed large deflections of nonlinear Ludwick elastic cantilever beams under combined loading, and, more recently, Borboni and De Santis [4] investigated large deflections of nonlinearly elastic asymmetric Ludwick cantilever beams under multiple combined loading on the free end. The existing body of works in the literature addressing large deflections of uniaxial power-law members under various loadings is extensive and an active topic of research [5–7].…”

Section: Introductionmentioning

confidence: 99%

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Ramberg–Osgood material behavior expression and large deflections of Euler beams

Giardina

Wei

2020

Mathematics and Mechanics of Solids

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Several assumptions are commonly made throughout the literature with regard to the mechanical expression of material behavior under a Ramberg–Osgood material model; specifically, the negligible effects of nonlinearity on the elastic behavior of the material. These assumptions do not reflect the complicated nonlinearity implied by the Ramberg–Osgood expression, which can lead to significant differences in the member model response from the true material behavior curve. With the proposed approach, new explicit results for Ramberg–Osgood materials are achieved without relying on these assumptions of material and model expression. The only assumptions present within the proposed model are the standard mechanical assumptions of an Euler beam. A general nonlinear moment–curvature relationship for monotone material behaviors is constructed. Large deflections of cantilever Euler beams with rectangular cross-sections under a combined loading are modeled. Numerical validation of this new method against results already given in the literature for the special cases of linear and power-law material behaviors are provided. An analysis is presented for three common material behavior relationships, with a focus on how these relationships are expressed through the deflection of members under the application of force within the model; this analysis clearly demonstrates that the sub-yield nonlinear behavior of the Ramberg–Osgood expression can be significant. The distinctions between material behavior expression demonstrated in this analysis have been long overlooked within the literature. This work addresses a gap between the modeling of Ramberg–Osgood material behaviors and the implementation of that model in mechanics.

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