1. ES 246 Project: Effective Properties of Planar Composites under Plastic Deformation

2. 1. Effective Properties of Composite Materials 2. Model Description 3. Model Validation 4. Effect of Inclusion Shapes 5. Isotropic/Kinematic Hardening 6. Conclusion and Future Work Outline

3. 1. Effective Properties of Composite Materials Objective of the Research: 2. To formulate equations for accurate prediction of the effective properties of composite materials. (Boyce M. et al: rubber particles to improve the toughness of the polymer) 1. By introducing small amount of inclusion phase to improved the bulk properties of the matrix. (Evans A. : Low-dielectric high-stiffness porous silica) Torquato S. et al: Mean Field Theory for Effective Modulus of Linear Elastic Composite

4. 2. Model Description -Composite Generation Criteria for Inclusion Phase: 1. Random coordination 2. Random orientation 3. No overlap Shape of Inclusion Phase: 1. Triangular 2. Square 3. Circular Volume fraction of Inclusion Phase: 0.2 Inclusion number: 30 1cm

5. MatrixInclusion E (GPa)100200 (GPa)24 n (-)0.5 Constitutive Law: 2. Model Description -Materials Properties

6. 2. Model Description -Finite Element Mesh Triangular InclusionCircular InclusionRectangular Inclusion Element Type: 4-Noded-Element Dominant Element Size (Edge length): ~0.1 mm Mesh Sensitivity: Refined-mesh model gives similar results.

7. :bulk modulus of the matrix and inclusion :shear modulus of the matrix and inclusion :volume fraction of the inclusion phase 3. Model Validation -Effective Modulus of the Composite (Based on Mean Field Theory for Linear Elastic Material)

8. Simulated: Theoretical: 3. Model Validation -Theoretical and Simulated Young’s Modulus

9. Effective Electric Conductivity with High Conductivity Inclusions: Triangular > Square > Circle (Both Experiments and Theory) Effective Tangent Modulus with Stiffer Inclusions: Triangular > Square > Circle Still True? 3. Model Results -Effects of Inclusion Shapes

10. Effective Tangent Modulus Triangular = Square = Circle 3. Model Results -Effects of Inclusion Shapes

11. 3. Model Results -Von Mises Stress Distribution Circular Inclusion Triangular Inclusion Rectangular Inclusion Max: 12.605 GPa Max: 9.629 GPa Max: 8.827 GPa

12. 3. Model Results - Isotropic or Kinematic Hardening (circular inclusion) (Bilinear constitutive relations assumed for matrix and inclusion)

13. 3. Model Results - Isotropic or Kinematic Hardening (triangular inclusion)

14. 3. Model Results - Isotropic or Kinematic Hardening (Effective Plastic Strain)

15. 1. We calculate the effective elastoplastic properties of composite material with an stiffer inclusion phase. The volume ratio of the inclusion is 0.2. 2. The shape of the inclusion phase has no effect on the effective tangent modulus of the material. 3. The triangular inclusion phase gives the highest maximum Von Mises stress in the matrix, and followed by the rectangular inclusion phase. The circular inclusion phase gives the most uniform stress distribution. 4. The hardening type of the composite is dominant by the matrix phase. Conclusion

16. 4. Future Work -3D Modeling is Possible