ABSTRACT
D.1 Shear modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 D.2 Area expansion modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 D.3 Comment on differences in implementations of local area forces 225
When using regular triangular spring networks, one would like to relate the spring stiffness constants to the physical membrane constants defining the shear modulus µ0 and the area compression/extension modulus K. Adopting the notation from [40] we have the situation depicted in Figure 4.5. Vectors a and b define the geometry of the network and denoting c = b − a = [bx − ax, by − ay] we have the following relations:
a = |a| = √ a2x + a
2 y, b = |b| =
√ b2x + b
c = |c| = √
(bx − ax)2 + (by − ay)2 (D.1)
For areas of the triangles we have
A0 = A1 = A2 = A = 1
2 |a× b| = 1
2 |axby − aybx|.
