I plan to explore the Saint-Venant torsion problem applied to prismatic bars with elastic-plastic behavior. Wagner and Gruttmann have developed a finite element method to obtain the elastic/plastic stresses of a bar using a single load step. In particular, I will present the constitutive model that they have developed, and then use ABAQUS to apply Wagner and Gruttmann’s model to various cross-sections. I will try to reproduce their results for some simple cross-sections, as well as exploring some more complicated cross sections. I will compare my numerical results with analytical results for the various cross-sections.

The mechanical performance of a homogeneous material can be varied by the addition of second-phase particles. In this project, we will model a planar composite under plastic deformation. As shown on the following figure, the composite consists of matrix material and randomly-distributed inclusion particles. The matrix is assumed to be an elastic-plastic material with isotropic or kinematic hardenings, and the inclusion particle pure elastic with a higher Young’s modulus. The stress/strain field throughout the composite will be calculated numerically with finite element method. The effective constitutive behavior of the composite will be evaluated and compared with theoretical and experimental results from literature [1, 2].

Due to maturity of FEM package, slip-line field theory is not widely used these days. However, we shall keep in mind that slip-line field analysis can provide analytical solutions to a number of very difficult problem which may involve huge deformations or velocity discontinuities, e.g. many metal forming processes. To evaluate these two analytical and numerical methods for plasticity I will try a simple example, compare these two solutions and finally get into a conclusion of my own.

http://imechanica.org/node/add/imageI propose to investigate an elastic-viscoplastic constitutive model proposed by Anand and Gurtin [1] for the large deformation of amorphous solids.  Specifically, I will present the constitutive framework proposed for elastic-plastic amorphous materials, I will implement the constitutive equations into Abaqus/Explicit, and I will compare numerical results with experimental results for polycarbonate [2]. 

Each student creates a project that addresses a phenomenon or issue in plasticity theory, and presents it in class after the winter break. The scope of the projects is very wide: experimental, computational, or a critical discussion of one or more papers. The project contributes 30% of the grade, distributed as follows:

• 5%: November 30 Thursday. Post your project proposal in iMechanica.

1. Title. ES 246 project: e.g. Plastic buckling of plates.
2. Tags. Use the following tags: ES 246, plasticity, Fall 2006, project
3. Body. (i) Describe the project. (ii) Cite at least 1 journal article.

• 5%: December 7 Thursday. Post a comment to critique the project proposal of at least 1 classmate.