246
plays a crucial role in its overall mechanical performance (Fratzl and Weinkamer
2007 ). For example, how neighbouring scales interact to minimize skin defl ection
and, fi nally, to prevent penetration is not known (Vernerey and Barthelat 2010 ).
Little is also known about the mechanical properties of extinct fi sh dermal armor
and scales, as well as the specifi c mechanical roles (Bruet 2008 ) of the mathematical properties for “material form variations (e.g. gradients) both within and between
various layers, the number of layers, the layer and junction thickness, structures
and geometries, the constitutive laws of each layer, and the relationship of these
parameters to larger scale biomechanical performance and environmental stresses,”
(Bruet 2008 ).
Recently, Vernerey and Barthelat ( 2010 ) proposed one idealized model of fi sh
scale structure. Scale deformation is described in terms of homogeneous curvature j . During bending, the support shape is “described as an arc circle of radius
R = 1 / j (Fig . 5.10 ), which results in the rotation and deformation of scales and the
development of contact forces between adjacent scales. The elastic energy stored in
this deformed confi guration determines the bending stiffness of the fi sh-structure.
To further simplify the system, one may take advantage of two distinct features of
fi sh scale structures: (i) the fi sh scale structure is made of a periodic pattern and (ii)
during uniform bending deformation, every scale undergoes the same deformation,”
(Vernerey and Barthelat 2010 ).
The free-body diagram of a fi shscale subjected to several applied forces and
moments arising from scale-scale and dermis-scale interactions are depicted in
Fig. 5.10 . In particular, the authors consider:
– “The force exerted by the left scale applied at the point of contact. This force is
comprised of a normal force f
L
n and a tangential force f
L
t resulting from
friction.
– The force exerted by the right scale applied at the right extremity of the principal
scale. This force can also be decomposed into a normal f
R
n and tangential f
R
t
component, with respect to the right scale. Because of the periodicity argument,
the magnitude of these forces is equal and opposite to f
L
n and f
L
t .
– A moment m
D resisting scale rotation around its support,” (Vernerey and
Barthelat 2010 ).
Generally, results obtained by Vernerey and Barthelat ( 2010 ) indicate that:
– “Strain-stiffening characteristic increases with increasing scale density and
decreasing scale-dermis attachment rotational stiffness (relative to a scale’s
bending stiffness);
– The contact force (relative to macroscopic moment) between scales increases
exponentially with a measure of scale density;
– The average macroscopic bending stiffness increases in a nonlinear fashion with
the ratio K
D
/ EI (angular stiffness to scale stiffness);
– Finally, shear deformation of the scale tends to decrease both the average stiffness and the strain-stiffening characteristic of the fi sh scale response,” (Vernerey
and Barthelat 2010 ).
5 Materials Design Principles of Fish Scales and Armor
plays a crucial role in its overall mechanical performance (Fratzl and Weinkamer
2007 ). For example, how neighbouring scales interact to minimize skin defl ection
and, fi nally, to prevent penetration is not known (Vernerey and Barthelat 2010 ).
Little is also known about the mechanical properties of extinct fi sh dermal armor
and scales, as well as the specifi c mechanical roles (Bruet 2008 ) of the mathematical properties for “material form variations (e.g. gradients) both within and between
various layers, the number of layers, the layer and junction thickness, structures
and geometries, the constitutive laws of each layer, and the relationship of these
parameters to larger scale biomechanical performance and environmental stresses,”
(Bruet 2008 ).
Recently, Vernerey and Barthelat ( 2010 ) proposed one idealized model of fi sh
scale structure. Scale deformation is described in terms of homogeneous curvature j . During bending, the support shape is “described as an arc circle of radius
R = 1 / j (Fig . 5.10 ), which results in the rotation and deformation of scales and the
development of contact forces between adjacent scales. The elastic energy stored in
this deformed confi guration determines the bending stiffness of the fi sh-structure.
To further simplify the system, one may take advantage of two distinct features of
fi sh scale structures: (i) the fi sh scale structure is made of a periodic pattern and (ii)
during uniform bending deformation, every scale undergoes the same deformation,”
(Vernerey and Barthelat 2010 ).
The free-body diagram of a fi shscale subjected to several applied forces and
moments arising from scale-scale and dermis-scale interactions are depicted in
Fig. 5.10 . In particular, the authors consider:
– “The force exerted by the left scale applied at the point of contact. This force is
comprised of a normal force f
L
n and a tangential force f
L
t resulting from
friction.
– The force exerted by the right scale applied at the right extremity of the principal
scale. This force can also be decomposed into a normal f
R
n and tangential f
R
t
component, with respect to the right scale. Because of the periodicity argument,
the magnitude of these forces is equal and opposite to f
L
n and f
L
t .
– A moment m
D resisting scale rotation around its support,” (Vernerey and
Barthelat 2010 ).
Generally, results obtained by Vernerey and Barthelat ( 2010 ) indicate that:
– “Strain-stiffening characteristic increases with increasing scale density and
decreasing scale-dermis attachment rotational stiffness (relative to a scale’s
bending stiffness);
– The contact force (relative to macroscopic moment) between scales increases
exponentially with a measure of scale density;
– The average macroscopic bending stiffness increases in a nonlinear fashion with
the ratio K
D
/ EI (angular stiffness to scale stiffness);
– Finally, shear deformation of the scale tends to decrease both the average stiffness and the strain-stiffening characteristic of the fi sh scale response,” (Vernerey
and Barthelat 2010 ).
5 Materials Design Principles of Fish Scales and Armor