5.2.5 Mechanical Analysis............................
Bending stiffness: We estimate the bending stiffness of the devices with different
structures byfinite element software ABAQUS. A unit cell is used for the simu-
lation, and the tilt angleais defined in Fig.5.1. The devices are modeled with shell
elements. The longitudinal ribbons are partitioned into a one-layer part and a
three-layer part. A homogeneous section with 700-μm thick SU-8 is assigned to the
transverse ribbons, while a composite section with three layers of 300-nm thick
SU8, 100-nm thick gold and another 300-nm thick SU-8 is assigned to the
three-layer part of the longitudinal ribbons. Both SU-8 and gold are modeled as
linear elastic material, with Young’s modulus 2 and 79 Gpa respectively [ 12 ]. To
calculate the longitudinal and transverse bending stiffness, afixed boundary con-
dition is set at one of the ends parallel with the bending direction, and a small
vertical displacement,d, is added at the other end. The external work,W, to bend
the device is calculated. We define the effective bending stiffness of the device as
the stiffness required of a homogenous beam to achieve the same external work
Wunder the displacementd. Therefore, the effective bending stiffness per width of
the device can be estimated as
D¼
2 Wl^3
3 d^2 b; ð 5 : 1 Þwithbthe width of the unit cell parallel with the bending direction, andlthe length
of the unit cell perpendicular to the bending direction.
Injection process: We further simulate a unit cell with the tilted anglea= 45°
going through a needle (Fig.5.4a). The unit cell is bent by a rigid shell with radius
of curvatureR(Fig.5.4b). Afixed boundary condition is set on one of the end of
the device parallel with the bending direction. The distribution of the maximal
principal strainemis shown in the inset of Fig.5.4b. When the radius of the needle
Ris 300μm, the highest maximal principal strain is as small as 0.167%; when the
radius of the needleRis 100μm,emreaches around 0.531%. The dependence of the
highest maximal principal strainemof the unit cell on the curvature 1/Ris linear as
shown in Fig.5.4b. The two colors correspond to two different sizes of the mesh
structures. The two correspondingfitting relations areem= 0.499/R andem=
0.473/Rrespectively.
Dimensional analysis of mesh electronics with cells: Flexibility of electronics
implanted into biological system has been proved to be a critical factor for the level
of provoked immunoresponse from the surrounding tissue, especially in long-term
implantations [ 24 ]. If the structure of electronics is rigid, daily movements between
electronics and tissues will introduce sever mechanical damage to the tissue. Here,
we analyze this mechanical mismatch through definition of a dimensionless number
D/cL^2 , whereDis the bending stiffness per width of the ribbons in our mesh
electronics or representing feature of other implantable electronics,cis the mem-
brane tension of cells andLis the length of the electronics. Since the bending
72 5 Syringe Injectable Electronics