Numerical Method for Determining Material Stability Loss During Large Deformation

Source abstract

ABSTRACT Material instability is often associated with the loss of ellipticity for the constitutive equations of the considered material. Determining when ellipticity is lost is crucial for numerical calculations of damage development in materials. For each load increment value of the updated Lagrangian formulation, the algorithm should assess the numerical stability at each point in the material. To check numerical stability, the Jury test is selected. Applying this test, there is no need to transform the approach state matrix formulated in the state space representation from discrete to continuous form. Six different calculation examples described in the paper illustrate the new approach for testing material stability. A comprehensive description of this approach for studying the stability of the Gurson material model is also included.