Students will learn how to solve numerically a set of first-order differential equations subject to an algebraic constraint in the context of stress analysis in metal plasticity. As an introduction, only the classical explicit algorithms and its most recent new developments will be presented.

The assignment is given to a first-year graduate student enrolled in an advanced mechanics of materials course focusing on elastic-plastic deformation analysis of metals and alloys. The student shall complete first learning about the theories of linear elasticity and rate-independent plasticity of isotropic materials.

The student is required to carry out the numerical stress integration of elastic-plastic differential-algebraic equations using the three algorithms implemented in m-files by varying the incremental step size and loading paths. Both graphical visualization and statistical analysis of the output results shall be conducted to evaluate the performance of each algorithm in terms of stability and accuracy.

Additional short m-file scripts shall be developed to compare the computed or estimated stress and plastic strain values with the imposed or true values. A table of summary on the evaluation of all cases (different step sizes, strain paths and algorithms) will be very helpful.

The student's learning about the concepts and algorithms in computational metal plasticity shall be assessed based on the graphs and tables generated by the students in their evaluation of the computational plasticity results.

1. F. Dunne and N. Petrinic. Introduction to Computational Plasticity. Oxford University Press (2005).
2. M. Halilovic, M.Vrh, and B. Stok, NICE-an explicit numerical scheme for efficient integration of nonlinear constitutive equations, Mathematics and Computers in Simulation, Vol. 80 No. 2, pp. 294-313 (2009).
3. S. Yoon and F. Barlat. Non-iterative stress integration method for anisotropic materials. International Journal of Mechanical Science. 242, 108003 (2023).