Journal of Applied Mechanics · 1953 · 65 citations · 1 references
Natural SciencesMaterials EngineeringMaterials ScienceFinite Element AnalysisMechanical Behavior Of MaterialsSolid MechanicsPlastic AnalysisPlastic DeformationPlasticityStrain HardeningStress-strain BehaviorWork HardeningAssociated Flow RuleFlow RulesIncremental StrainPlastic FlowSimplificationStrain RelationsStress-strain RelationsWork Hardening Analysis
The Tresca yield condition often yields simpler stress equations than the Mises condition, yet most applications retain the Mises flow rule; this paper discusses the rationale using two examples involving finite plastic deformation of a circular hole in an infinite sheet of perfectly plastic or work‑hardening material. The authors aim to show that adopting the Tresca flow rule further simplifies the analysis. They demonstrate that this approach reduces the complexity of the stress equations in the considered examples.
Abstract It is well known that the use of Tresca’s yield condition frequently leads to a simpler system of equations for the stresses in a plastic solid than the use of the yield condition of Mises. However, in most cases where Tresca’s yield condition has been used, the flow rule associated with the Mises condition has been retained. Following Koiter, it is shown that further simplification results from the use of the flow rule associated with the Tresca condition. The reason for this is discussed in connection with two examples concerning the finite enlargement of a circular hole in an infinite sheet of perfectly plastic or work-hardening material. The second example is probably the first nontrivial case in which a problem of finite plastic deformation of a work-hardening material has been treated in closed form by the use of incremental stress-strain relations.
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