Finite Element Modeling of Nacre Austen Motily with Dr. Mark Garnich Sponsored by the Department of Mechanical Engineering and EPSCoR

Nacre Also known as mother of pearl Composite material found in mollusk shells Two phases Aragonite Organic protein matrix Barthelat et al. [1]

Nacre Unique periodic arrangement About 95% aragonite “repeating” structure Hexagonal platelets About 95% aragonite Brittle Doesn’t absorb much energy About 5% organic protein Ductile Easily deformed Barthelat et al. [1]

Fracture Toughness The amount of energy a material can absorb before it breaks Nacre has a high fracture toughness 95 % of the nacre is not very tough The unique arrangement of nacre results in its increased toughness

Why is Toughness important? Materials must be resistant to flaws Tough materials resist rapid crack propagation Energy absorption is important in structural stability Katti et al. [2]

Finite Element Modeling Create a model of the structure Separate the model into small elements Use the finite element method to predict material behavior Analyze the results Abaqus® was used for this research Marks, Laurence [3]

Representative Volume Element (RVE) Nacre platelets are about one micron thick Would be almost impossible to model thousands of layers of Nacre Create a small volume representative of overall behavior Zuo and Wei [4]

Representative Volume Element (RVE) Difficulties Conceptually more difficult Must implement correct boundary conditions Have to achieve symmetry

Two-Dimensional (2D) Model Create a model to compare to results of Zuo and Wei Tension test Simplify as much as possible Start with elastic behavior Implement plastic behavior of organic protein phase Zuo and Wei [4]

Results of 2D Elastic Simulation Verify correct geometrical behavior Achieve symmetry

Results of 2D Plastic Simulation Protein: elastic linear-plastic material Equivalent to model of Zuo and Wei

Results of 2D Plastic Simulation Similar general behavior

Three-Dimensional (3D) Model Include depth in the model Elastic-plastic behavior of protein Verify correct implementation of boundary conditions Stress-strain behavior should be the same

Results of 3D Simulation Same geometrical behavior as 2D simulation

Results of 3D Simulation

Results of 3D Simulation

Comparison of 2D and 3D Simulations Same stress-strain behavior for the two simulations

Comparison of Stress-strain curves Plastic portion slopes are different

Discrepancy Between Stress Strain Curves Distribution of stress along vertical axis Protein behavior converted from shear stress/strain Abaqus® requires normal stress-strain behavior for input Difference in slope of plastic portion of stress-strain curve is too large to be attributed to these factors

Verification Using the Mathematical Model Solve the differential equation used by Zuo and Wei Use Matlab® to solve the differential equation Create stress-strain curve and compare to results of Zuo and Wei

Verification Using the Mathematical Model Similar to Abaqus® simulation results

Next Steps Simulate nacre under shear loading Compare with experimental results from Menig et al. The tension test produced a lot of shearing action in model New simulation will contain different boundary conditions indicative of a shear simulation Menig et al. [5]

Next Steps More advanced models that incorporate the complex hexagonal platelet arrangement Implement a more realistic elastic- plastic model for the organic protein phase Simulate other loading scenarios such as bending or compression Menig et al. [5]

References Barthelat F, Dastjerdi AK, Rabiei R. 2013 An improved failure criterion for biological and engineered staggered composites. Journal of The Royal Society Interface 10, 1-10. Katti DR, Katti KS, Sopp JM, Sarikaya M. 2001 3D Finite Element Modeling of Mechanical Response in Nacre-Based Hybrid Nanocomposites. Computational and Theoretical Polymer Science 11, 397-404. Marks L. 2012 Bolted Joints in Finite Element Models. SSA Limited. Zuo S, Wei Y. 2008 Microstructure observation and mechanical behavior modeling for limnetic nacre. Acta Mechanica Sinica 24, 83-89. Menig R, Meyers MH, Meyers MA, Vecchio KS. 2000 Quasi-Static and Dynamic Mechanical Response of Haliotis Rufescens (Abalone) Shells. Acta Materialia 48, 2383-2398.