Spherically symmetric deformation of solids with nonlinear stress-state-dependent properties

Ломакин, Е. В.; Beliakova, T.A.

doi:10.1007/s00161-023-01197-w

Cited by 3 publications

(5 citation statements)

References 22 publications

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“…in regions where both characteristic families are curved. In this case, Equation ( 7) allows for p to be determined as ln p sin ϕ + cos ϕ p 0 sin ϕ + cos ϕ = 2(β − α) sin ϕ, (10) where p 0 is constant. It has been shown in [23] that the plastic flow rule is compatible with the ideal flow condition and the stress solution above if…”

Section: System Of Equations In Characteristic Coordinatesmentioning

confidence: 99%

“…In particular, ψ in = 0, and γ = γ', in the case of symmetric dies. It follows from (10) and (11) that…”

Section: Ideal Die Shapesmentioning

confidence: 99%

“…Since σ ξ = 0 on lines AD and AD', it follows from (10) and the first equation in (89) that p 0 = tan χ.…”

Section: Pressure On the Die's Wallsmentioning

confidence: 99%

“…Many materials obey pressure-dependent yield criteria ( [7][8][9][10] among many others). Various plastic flow rules are used in conjunction with such yield criteria.…”

Section: Introductionmentioning

confidence: 99%

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General Planar Ideal Flow Solutions with No Symmetry Axis

Alexandrov,

Mokryakov

2023

Materials

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Bulk ideal flows constitute a wide class of solutions in plasticity theory. Ideal flow solutions concern inverse problems. In particular, the solution determines part of the boundary of a region where it is valid. Bulk planar ideal flows exist in the case of (i) isotropic rigid/plastic material obeying an arbitrary pressure-independent yield criterion and its associated flow rule and (ii) the double sliding and rotation model based on the Mohr–Coulomb yield criterion. In the latter case, the intrinsic spin must vanish. Both models are perfectly plastic, and the complete equation systems are hyperbolic. All available specific solutions for both models describe flows with a symmetry axis. The present paper aims at general solutions for flows with no symmetry axis. The general structure of the solutions consists of two rigid regions connected by a plastic region. The characteristic lines between the plastic and rigid regions must be straight, which partly dictates the general structure of the characteristic nets. The solutions employ Riemann’s method in regions where the characteristics of both families are curvilinear. Special solutions that do not have such regions are considered separately. In any case, the solutions are practically analytical. A numerical technique is only necessary to evaluate ordinary integrals. The solutions found determine the tool shapes that produce ideal flows. In addition, the distribution of pressure over the tool’s surface is calculated, which is important for predicting the wear of tools.

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Section: System Of Equations In Characteristic Coordinatesmentioning

confidence: 99%

“…In particular, ψ in = 0, and γ = γ', in the case of symmetric dies. It follows from (10) and (11) that…”

Section: Ideal Die Shapesmentioning

confidence: 99%

“…Since σ ξ = 0 on lines AD and AD', it follows from (10) and the first equation in (89) that p 0 = tan χ.…”

Section: Pressure On the Die's Wallsmentioning

confidence: 99%

“…Many materials obey pressure-dependent yield criteria ( [7][8][9][10] among many others). Various plastic flow rules are used in conjunction with such yield criteria.…”

Section: Introductionmentioning

confidence: 99%

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General Planar Ideal Flow Solutions with No Symmetry Axis

Alexandrov,

Mokryakov

2023

Materials

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“…Many materials obey pressure-dependent yield criteria. Examples of such materials are soils [12,13], metals [14][15][16], and granular materials [13,17]. Several plasticity models are available for pressure-dependent materials [18,19].…”

Section: Introductionmentioning

confidence: 99%

Design of Dies of Minimum Length Using the Ideal Flow Theory for Pressure-Dependent Materials

Alexandrov,

Mokryakov

2023

Mathematics

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This paper develops the ideal plastic flow theory for the stationary planar flow of pressure-dependent materials. Two rigid plastic material models are considered. One of these models is the double-shearing model, and the other is the double slip and rotation model. Both are based on the Mohr–Coulomb yield criterion. It is shown that the general ideal plastic flow theory is only possible for the double slip and rotation model if the intrinsic spin vanishes. The theory applies to calculating the shape of optimal extrusion and drawing dies of minimum length. The latter condition requires a singular characteristic field. The solution is facilitated using the extended R–S method, commonly employed in the classical plasticity of pressure-independent materials. In particular, Riemann’s method is used in a region where all characteristics are curved. It is advantageous since determining the optimal shape does not require the characteristic field inside the region. The solution is semi-analytical. A numerical procedure is only required to evaluate ordinary integrals. It is shown that the optimal shape depends on the angle of internal friction involved in the yield criterion.

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Stress and strain fields near cracks in solids with stress state-dependent elastic properties under conditions of anti-plane shear

Lomakin,

Korolkova

2024

Acta Mech

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Spherically symmetric deformation of solids with nonlinear stress-state-dependent properties

Cited by 3 publications

References 22 publications

General Planar Ideal Flow Solutions with No Symmetry Axis

General Planar Ideal Flow Solutions with No Symmetry Axis

Design of Dies of Minimum Length Using the Ideal Flow Theory for Pressure-Dependent Materials

Stress and strain fields near cracks in solids with stress state-dependent elastic properties under conditions of anti-plane shear

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