Dynamic filopodial forces induce accumulation, damage, and plastic remodeling of 3D extracellular matrices
Fig 7
A strain-dependent plastic softening with elastic damage constitutive law recapitulates the effect of crosslinking in fibrous matrices.
(a) Schematic of the constitutive viscoplasticity of the Norton Van’t Hoff type used to model the ECM. (Parameters provided in S2 Table). (b) The model is modified and alternatively tested to include phenomenologically the features of damage, simulating breakage of crosslinks with tensile strain, and plastic softening, simulating the drop in yield stress with plastic strain. (c) The constitutive model is implemented in the commercial finite element solver ABAQUS using existing standard viscoplastic material models and custom subroutine implementation for the damage model. An axisymmetric mesh is shown to model the ECM around a contracting cell. The zoom inset shows the surface where the load is applied to simulate the action of filopodia farther away from the edge. (d) Von Mises equivalent stress and (e) displacement length for the continuum viscoplasticity cases with or without damage and softening. Displacement lengths are calculated at the cell-ECM interface, and Von Mises stresses are calculated at approximately 5μm from the loading surface (toward the ECM), which exhibits mostly tensile stress states. In (d) the boundary applied loading history is plotted, with * showing the typical time discretization for the FE analysis. Loading starts at 0 and stops at the normalized time of 1. (f) Recoverability index at the cell-ECM interface (elastic deformation divided by total deformation) for the cases with or without damage and softening, along with the experimental data from Fig 1E for comparison. (g) Plastic equivalent strain for the cases with or without damage and softening, all calculated at the cell-ECM interface. (h) Recoverability index and damage radius, i.e. the radius up to regions with half-max damage (as pictured in S10 Fig), as a function of the magnitude of the applied load p. (i) Recoverability index and damage radius as a function of the creep loading time during which the load is kept constant (p = 0.1 kPa).