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About this book

This volume demonstrates the use of FORTRAN for numerical computing in the context of the finite element method. FORTRAN is still an important programming language for computational mechanics and all classical finite element codes are written in this language, some of them even offer an interface to link user-code to the main program. This feature is especially important for the development and investigation of new engineering structures or materials. Thus, this volume gives a simple introduction to programming of elasto-plastic material behavior, which is, for example, the prerequisite for implementing new constitutive laws into a commercial finite element program.

Table of Contents

Frontmatter

Chapter 1. Theoretical Foundation

Abstract
This introduction discusses a general approach to model elasto-plastic materials. A mathematical model is established based on the governing equations of elasto-plasticity.
Michael Trapp, Andreas Öchsner

Chapter 2. One-Dimensional Continuum Approach

Abstract
In this chapter, the elasto-plastic material model is analyzed with numerical methods. For this purpose, simple tensile tests are carried out. The test geometry is modeled in the simplest way, as a one-dimensional continuum. After the theory, example numerical algorithms are discussed for different test setup conditions.
Michael Trapp, Andreas Öchsner

Chapter 3. One-Dimensional Finite Element Approach

Abstract
This chapter presents a different approach to compute problems of plasticity, using a finite element formulation. Again, simple one-dimensional virtual tensile tests are considered for the numerical analysis.
Michael Trapp, Andreas Öchsner

Chapter 4. Three-Dimensional Finite Element Approach

Abstract
In this chapter, a mathematical model of the material for the three-dimensional case is discussed. Therefore, the governing equations for the one-dimensional case are generalized and modified. Many quantities that were scalars in the one-dimensional case are arranged as vector quantities now.
Michael Trapp, Andreas Öchsner

Chapter 5. Summary and Outlook

Abstract
This chapter summarizes the most important aspects of the previous chapters and gives an outlook for further potential research.
Michael Trapp, Andreas Öchsner

Chapter 6. FORTRAN Source Codes

Abstract
This chapter discusses the Fortran source codes for the numerical analysis.
Michael Trapp, Andreas Öchsner

Backmatter

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