TAMU Mechanics

Current Research Projects

MODELING AND OPTIMIZATION OF NACRE-LIKE MATERIALS

Nasra Al-Maskari, D. A. McAdams, and J. N. Reddy

BACKGROUND

  • Natural or biological material are made from weak constituents that have evolved hundreds of millions year thus having outstanding mechanical properties
  • Biological Material vs. Engineering Material
    nasra-1
    nasra-2
  • Nacre, which is an inner layer in sea shells, is composed of microscopic mineral polygonal tablets bonded by a tough biopolymer (organic layer)
    -95% mineral = calcium carbonate (aragonite CaCO3)
    -5% proteins and polysaccharides (Chitin)

  • Nacre has a remarkable toughness due to sliding and waviness of the tablets
nasra-3

MOTIVATIONS

  • Mimicking the high toughness and stiffness into engineering materials is desired.
  • Models in literature assumes the tablets are flat and don’t account for tablet waviness.
  • Designing of bio-inspired materials is done currently by trial and error.
  • The improvement in toughness relative to its main constituent is not as in biological materials.
  • No clear way of selecting materials and geometry of the structure.

OBJECTIVES

  • Build an improved model of a biological hard material (Nacre) to predict the mechanical properties in order to aid in designing of a bio-inspired material.
  • The waviness should be included in the model.
  • The model should predict stiffness & toughness.
  • The model should be able to predict the optimal material and geometry of the tablets and interface (matrix) to produce the optimal mechanical properties (stiffness, strength and toughness)

WAVINESS STIFFNESS & TOUGHNESS MODEL

  • Representative volume element (RVE) that includes waviness as dovetail feature.
nasra-4-1
nasra-4-2
  • Stress- strain equation is

        \[ \bar{ \sigma } _x = \frac{G_i \cos \theta}{th} \left[ L_0 h \tan \theta + \bar{ \varepsilon}_x (L_0+L_c)(L_0-h \tan \theta) - \bar{ \varepsilon }_x^2(L_0+L_c)^2 \right] \]

  • Toughness is quantified using J-integral
  • Bridging and process zone: toughening mechanisms are considered
    • nasra-5
  • Nacre has shown to exhibit a raising resistance curve (R-curve)
  • R-curve is given by

        \[J_T = J_B + \left[ \sigma _x \left( \frac{L_0 \theta}{h+t} - \frac{ \sigma _x}{E} \right) + \sigma _y \left( \frac{u_{max}}{L} - \frac{\sigma_y}{E} \right) \right] wF \left( \frac{dw}{da} \right)\]

    where

        \[ J_B = \begin{cases} \left( \frac{a}{ \lambda } \right) \frac{L}{2t} \tau_s u_{max} \cos \theta & \quad 0 \leq a \leq \lambda \\ \frac{L}{2t} \tau_s u_{max} \cos \theta & \quad a> \lambda \end{cases} \]

    and

  • R-curve plot comparison

        \[F(n) = \left[ 2 \frac{(1+n) \sqrt{1+2n} }{n} - n \cot^{-1}\left( \frac{n}{ \sqrt{1+2n} } \right) - \frac{(1+2n)^{3/2}}{n^2} \ln \left( \frac{1+2n}{1+n} \right) \right]\]

nasra-6
nasra-7

APPLICATIONS

  • Nacre like-materials can replace materials and composites in applications that require high stiffness and toughness with less weight in areas such as material science, biomaterials development, civil and nanotechnology
  • Nacre-like materials and coatings have been developed for biomedical applications such as development of better performance implant materials.
  • Researchers are looking into using cement paste, which is concrete’s binding ingredient, with the structure and properties of natural materials such as nacre, bone and deep-sea sponge.

OPTIMIZATION OF NACRE-LIKE MATERIALS

  • Multi-objective Optimization Formulation
  • Maximize:

        \[E= \frac{t}{2t+h} \frac{E_t h t}{E_t h t + L_c G_i (L_0 - h \theta)} \frac{G_i}{th} L (L_0 - h \theta) \]

        \[ \sigma _s = \frac{L_0}{t+h} \tau _s \]

        \[J= \frac{0.5 \tau _s u_{max} L/t}{1- \frac{E \tau _s}{4 \sigma _s^2} \left[ \frac{u_s - L_0}{L_c} \left( \frac{L_0 \theta}{h+t} - \frac{ \tau _s (u_s -L_0) }{EL_c} \right) \theta + \frac{L_0 - u_s}{t} \left( \frac{u_{max}}{L} - \frac{ \tau _s (L_0 - u_s) }{tE} \right) \right] } \]

    Subjected to:

        \[\frac{L}{t} < 0.56 \frac{K_{IC}}{ \tau _s \sqrt{t} }, \quad \frac{L_0}{t+h} > \sqrt{3}, \quad 0< \frac{L_0}{L} \leq 0.5, \quad L \geq t, \quad t \geq h\]

  • Genetic Algorithm based on no-dominated sorting genetic algorithm II (NSGA II) is used
  • MATLAB optimization tool box is used to solve the optimization problem
  • Sample of solution were plotted in Ashby charts indicating the performance of nacre-like material relative to existing engineering materials
nasra-8
nasra-9

REFERENCES

  • M. A. Meyers, P.-Y. Chen, A. Y.-M. Lin, and Y. Seki,” Progress in Materials Science, vol. 53, pp. 1-206, 2008.
  • U. G. K. Wegst and M. F. Ashby, Philosophical Magazine, vol. 84, pp. 2167-2186, 2004/07/21 2004.
  • D. Zhu and F. Barthelat, in Mechanics of Biological Systems and Materials, Volume 2, T. Proulx, Ed., ed: Springer New York, 2011, pp. 181-187.
  • S. P. Kotha, Y. Li, and N. Guzelsu, Journal of Materials Science, vol. 36, pp. 2001-2007, 2001/04/01 2001.
  • X. Wei, M. Naraghi, and H. D. Espinosa, ACS Nano, vol. 6, pp. 2333-2344, 2012/03/27 2012.
  • F. Barthelat, H. Tang, P. D. Zavattieri, C. M. Li, and H. D. Espinosa, Journal of the Mechanics and Physics of Solids, vol. 55, pp. 306-337, 2// 2007
  • F. Barthelat and R. Rabiei, Journal of the Mechanics and Physics of Solids, vol. 59, pp. 829-840, 4// 2011.
  • B. Seyed Mohammad Mirkhalaf Valashani and Francois, Bioinspiration & Biomimetics, vol. 10, p. 026005, 2015.
  • R. Rabiei, S. Bekah, and F. Barthelat, Acta Biomaterialia, vol. 6, pp. 4081-4089, 10// 2010.