Capturing 3D large-strain Euler-bending filament dynamics in fibrous media simulations; sample case of compression collapse in dendritic actin network

Abstract

Cytoskeletal networks to transmission towers are comprised of slender elements. Slender filaments bend and buckle more easily than stretch. Therefore a deforming network is expected to exhaust all possible bending-based modes before engaging filament stretch. While the large-strain bending critically determines fibrous-media response, simulations use small-strain and jointed approximations. At low resolution, these approximations inflate bending resistance and delay buckling onset. The proposed string-of-continuous-beams (SOCB) approach captures 3D nonlinear Euler bending of filaments with high fidelity at low cost. Bending geometry (i.e. angles and its differentials) is solved as primary variables, to fit a 5 th order polynomial of the contour angle. Displacement, solved simultaneously as length conservation, is predicted with C3 and C6 smoothness between and within segments, using only 2 nodes. In the chosen analysis frame, in-plane and out-plane moments can be decoupled for arbitrarily-curved segments. Complex crosslink force-transfers can be specified. Simulations show that when a daughter branch is appended, the buckling resistance of a filament changes from linear to nonlinear before reversible collapse. An actin outcrop with 8 generations of mother-daughter branching produced the linear, nonlinear, and collapse regimes observed in compression experiments. ‘Collapse’ was a redistribution of outcrop forces following the buckling of few strands.

Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix

“…Scalebar: ratio of deformed to undeformed density. about the post-buckling behaviour of individual collagen or fibrin fibers in compression 22 , as λ decreases from 1 toward 0 (total collapse). This depends on their bending behaviour, which is difficult to characterise, because of their inhomogeneous, hierarchical structure 18 as bundles of loosely connected fibrils.…”

“…Modelling the force-stretch relation of a single fiber depends on the post-buckling behaviour of a flexible beam, which can be quite complicated as buckling is a bifurcation/instability phenomenon. There are typically three main types of post-buckling response S(λ), depending on whether stability is maintained or lost on the bifurcating branch of buckled states 22 , and whether it is later regained if lost: (i) Stable post-buckling, where stiffness is diminished but load carrying capacity in compression is not lost (as λ decreases below 1). An example is S(λ) = k(λ 3 −1) with k > 0 a constant (Fig.…”

“…2b). (iii) Snap-through post-buckling, where stability is first lost but eventually regained at higher compression 22 , for example S(λ) = k (λ 5 − 3λ 3 /2 + λ/2) (qualita-tively as in Fig. 2e).…”

“…We assume S(λ) stiffens in tension (its slope increases with λ > 1) as is common for biopolymers [26][27][28]. Aside from direct observation of buckling [29][30][31], very little is known about the post-buckling behaviour of individual collagen or fibrin fibres in compression [32], as λ decreases from 1 toward 0 (total collapse). This depends on their bending behaviour, which is difficult to characterize, because of their inhomogeneous, hierarchical structure [28] as bundles of loosely connected fibrils.…”

Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix

“…Modelling the force-stretch relation of a single fiber depends on the post-buckling behaviour of a flexible beam, which can be quite complicated as buckling is a bifurcation/instability phenomenon. There are typically three main types of post-buckling response S(λ), depending on whether stability is maintained or lost on the bifurcating branch of buckled states 22 , and whether it is later regained if lost: (i) Stable post-buckling, where stiffness is diminished but load carrying capacity in compression is not lost (as λ decreases below 1). An example is…”