This course aims at giving a concise introduction to the basic concepts of nonlinear mechanics of solids and at providing the basic ingredients to perform simulations of solid mechanics problems at large strains via the finite element method.
Course Prerequisites
A good knowledge of the basic concepts given within the courses of Mechanics of Solids and Structures, Numerical Analysis, and Computational Mechanics is required.
Teaching Methods
Blackboard lectures, hands-on tutorials in Matlab, Mathematica, AceGen/AceFEM, and commercial finite element software.
Assessment Methods
The exam consists in the assignment of homework and in an oral discussion.
Texts
Suggested references are (among others):
J. Bonet, R.D. Wood. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.
O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. The Finite Element Method: Its Basis and Fundamentals. Elsevier.
O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu. The Finite Element Method for Solid and Structural Mechanics. Elsevier.
P. Wriggers. Nonlinear Finite Element Methods. Springer.
T.J.R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications.
Contents
• Basics of nonlinear mechanics: Kinematics Equilibrium Hyperelastic constitutive laws
• Elements of numerical analysis: Solution of nonlinear equations and systems: theory and Matlab implementation of basic algorithms Nonlinear finite elements
• Application to 1D rods at large strains (and Matlab implementation)
• Application to 2D plane strain problems at large strains (and Matlab implementation)
• Use of a commercial nonlinear finite element code
