very low (0.0025 nN m). This dramatic bending stiffness change facilitates stress
localization leading to the buckling of longitudinal ribbons. On the contrary,
a= 45° design creates a uniform distribution of effective bending stiffnessDL,
therefore, the electronics can bend homogeneously. Secondly, thisa= 45° design
decreasesDTand increaseDLso that the mesh is more readily to bend and roll-up
into tubular structure going through the needle and less readily buckle in the lon-
gitudinal direction.
We conductedfinite element modeling (FEM) analysis to simulate the bending
stiffness for mesh bending in two directions. Notably, reducing theDTand increases
DLis benefit to the injection process. Figure5.1is the schematic showing how to
select unit cells from the periodic mesh structure for simulation. The relation of
angleato bending stiffness was investigated. The white dashed lines indicate the
boundary for unit cells from mesh for simulation. We define effective bending
stiffness of mesh as the stiffness required a homogenous beam to achieve the same
bending under the same moment. Therefore, every unit cell has the same bending
stiffness and we use a unit cell to calculate the effective bending stiffness of the
structure from the simulations. The results (Fig.5.11) show that increasingafrom
0° to 60°,DTdecreases from 0.0036 to 0.0013 nN m andDLincreases from 0.0051
to 0.0167 nN m. The bending stiffness ratio between bending in transverse and
longitudinal direction increases for 8.7 times (1.46–12.8). Altogether, those results
show that increasing theacan significantly facilitate the rolling of electronics in the
needle in transverse direction to form a tubular structure and prevent bending in the
longitudinal direction.
We use simulations to further estimate the strain distribution in the electronics
during injections in needles with different sizes. We only simulate the bending of a
unit cell to the curvature of the needle, since every unit cell behaves similarly. The
inset of Fig.5.5b shows a bending structure of a representative unit cell inside a
200-μm diameter needle. The color mode shows the contour plot of the maximal
principle strain. The maximal value is reached on the junction between the trans-
verse and longitudinal ribbons. Simulation results (Fig.5.5b) show the dependence
of the maximal principal strain of the unit cell on the curvature of the needles 1/r,
and a linear relation canfit the dependence. The two colors correspond to two
different sizes of the mesh structures used for needle inner diameter larger or
Fig. 5.11 Mechanical
analysis for injection process.
Bending stiffness in
longitudinal and transverse
direction of the mesh with
change of ribbons angle in
Fig.5.1
84 5 Syringe Injectable Electronics