ES 246

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.

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.

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.

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.