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5 Contraction
Applying these conditions to the above expression for u(X) yields the solution
u(X) = C 1 sinh αX,
(5.19)
where
C 1 =
K − 1
α cosh αL + β sinh αL
.
Results
Illustrative results are shown for L = 1, A 0 = 0.01, c a = 1, and K = 0.5. Values
of k and k n are indicated on the plots.
First, consider the case where the stress fiber is not attached to the nucleus (k n =
0). In this case, the stress must vanish at the right end of the fiber for all values of
k. Moreover, since this implies λ ∗ = 1, λ = K = 0.5 at that end. The results in
Fig. 5.6a,b are consistent with these observations. If the contracting fiber is also not
attached to the cytoskeleton (k = 0), it simply shortens to λ = 0.5 without stress.
Fig. 5.6 Results from stress fiber model shown in Fig. 5.5b. Total stretch ratio λ and Cauchy stress
σ are plotted versus deformed axial coordinate x. (a, b) Without nucleus (k n = 0). (c, d) With
nucleus (k n = 1). The colors defined in (a) correspond to different values of cytoskeletal stiffness
k and apply to all plots