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


  • 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
  • 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


  • 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.


  • 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)


  • Representative volume element (RVE) that includes waviness as dovetail feature.
  • 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

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


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


  • R-curve plot comparison

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



  • 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.


  • 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


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