2022/07/26 by Tahar Z. Boulmezaoud, Boualem Khouider, Boulmezaoud, Tahar Z +1
Chemical Engineering · Decision Sciences · Engineering · #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Probabilistic and Robust Engineering Design #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.2207.12719
openalex publication_date 2022/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition with respect to the tangent cone and the normal cone of the yield domain. It is also shown that the stress rate can be seen as the projection on the tangent cone of the elastic stress tensor. This approach leads to a coherent mathematical formulation of the elasto-plastic laws and simplifies the resulting system for the associated flow evolution equations. The cases of one or two yields functions are treated in detail. The practical examples of the von Mises and Tresca yield criteria are worked out in detail to demonstrate the usefulness of the new formalism in applications.