Plasticity
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On this page we conduct numerical studies of plastic deformation by employing the von Mises plasticity model with isotropic hardening. The majority of the theory is explained in detail in Computational Methods for Plasticity - Theory and Applications by EA de Souza Neto [1]. For a more detailed theory description, we strongly recommend reading the book.
Introduction
In physics and materials science, plasticity, also known as plastic deformation, is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation transits from elastic to plastic range.
This demonstration uses the von Mises model, with nonlinear isotropic hardening, due to its computational implementation simplicity and appropriateness for real-world examples.
Theory of plasticity
In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force is applied to the body, the dynamics are described by a second Newton's law \begin{equation} \ \nabla \cdot \bf{sigma} + \bf{f} = 0 \end{equation}
As previously stated, all of the theory is thoroughly explained in Computational Methods for Plasticity - Theory and Applications by EA de Souza Neto [2], mainly chapters 4-7.