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Understanding Applied Nonlinear Elasticity Through Examples

Understanding the theory and principles of nonlinear elasticity or nonlinear mechanics is tough for students and also tough for practicing engineers. Although the governing equations in the traditional CAE (linear or nonlinear finite element) tools such as ANSYS, ABAQUS, LS-DYNA, SolidWorks, etc., use 1D or 2D or 3D linear/nonlinear elasticity formulations, students see little or no use to actually learn and understand the solution of the governing theoretical equations that use advanced numerical methods. The developers of CAE programs are obviously expected to deeply understand the assumptions made and the associated limitations in order to implement the solution processes to solve the theoretical equations. Offering more user-friendly CAE environment is still more challenging that involves experts from different fields of engineering and mathematical sciences. Research schools typically expect the students to write their own solution codes and validate those by using an appropriate CAE tool. What is the best method to teach a nonlinear elasticity course at a predominantly teaching school while also to demonstrate real life applications of the basic nonlinear theory? Automotive industry routinely use CAE tools to perform linear or nonlinear analysis of their very complex components and assemblies. Nonlinearity arises due to geometry changes during deformation, material property changes, and changing loads (for example in dynamic environment). The purpose of this paper is to discuss the above-mentioned difficulties and limitations and also to provide few examples that demonstrate the nonlinear theoretical principles. The teaching and learning experiences of the author in delivering this course and also presenting invited talks on this topic at conferences will be discussed in detail in this paper.