Syllabus

Module I - Lagrangian and Eulerian Finite elements in one dimension (10 hours)

Introduction Nonlinear Finite Elements in Design Brief History of Nonlinear Finite Elements Notation Mesh Descriptions Classification of Partial Differential Equations Governing Equations for Total Lagrangian Formulation Weak Form for Total Lagrangian Finite Element Discretization in Total Lagrangian Formulation Element and Global Matrices Governing Equations for Updated Lagrangian Formulation Weak Form for Updated Lagrangian Formulation Element Equations for Updated Lagrangian Formulation Governing Equations for Eulerian Formulation Weak Forms for Eulerian Mesh Equations Finite Element Equations

Module II - Continuum Mechanics (6 hours)

Introduction Deformation and Motion Strain Measures Stress Measures Conservation Equations Lagrangian Conservation Equations Polar Decomposition and Frame-Invariance

Module III - Lagrangian Meshes (8 hours)

Introduction Governing Equations Weak Form: Principle of Virtual Power Updated Lagrangian Finite Element Discretization Implementation Corotational Formulations Total Lagrangian Formulation Total Lagrangian Weak Form Finite Element Semidiscretization

Module IV - Constitutive models (6 hours)

Introduction The Stress–Strain Curve One-Dimensional Elasticity Nonlinear Elasticity One-Dimensional Plasticity Multiaxial Plasticity Hyperelastic–Plastic Models Viscoelasticity Stress Update Algorithms Continuum Mechanics and Constitutive Models

Module V - Solution methods and stability (6 hours)

Introduction Explicit Methods Equilibrium Solutions and Implicit Time Integration Linearization Stability and Continuation Methods Numerical Stability Material Stability

To provide the fundamentals of non-linear analysis.

To understand updated lagrangian formulation.

To understand total lagrangian formulation.

To learn fundamentals of constitutive models in FEM.
To understand stability of the numerical methods.

Students will develop skills in non-linear finite element analysis.

Students will analyse complex problems involving geometric non-linearity.

Students will execute non-linear material modeling.

Students will implement material models in FEM framework.

Students will know the issues of numerical stability in FEM algorithms.

Ted Belytschko, Wing Kam Liu, Brian Moran, Khalil Elkhodary, ents for Continua and Structures, John Wiley and Sons Ltd , 2014

René de Borst, Mike A. Crisfield, Joris J. C. Remmers, Clemens V., Non-Linear Finite Element Analysis of Solids and Structures, John Wiley and Sons Ltd. , 2012

K.J. Bathe, Finite Element Procedures, Pearson Inc. , 1998

International Journal for Numerical Methods in Engineering

Journal of the Mechanics and Physics of Solids