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Nonlinear stiffening is a ubiquitous property of major types of biopolymers that make up the extracellular matrices (ECM) including collagen, fibrin, and basement membrane. Within the ECM, many types of cells such as fibroblasts and cancer cells have a spindle-like shape that acts like two equal and opposite force monopoles, which anisotropically stretch their surroundings and locally stiffen the matrix. Here, we first use optical tweezers to study the nonlinear force-displacement response to localized monopole forces. We then propose an effective-probe scaling argument that a local point force application can induce a stiffened region in the matrix, which can be characterized by a nonlinear length scale R* that increases with the increasing force magnitude; the local nonlinear force-displacement response is a result of the nonlinear growth of this effective probe that linearly deforms an increasing portion of the surrounding matrix. Furthermore, we show that this emerging nonlinear length scale R* can be observed around living cells and can be perturbed by varying matrix concentration or inhibiting cell contractility. [ABSTRACT FROM AUTHOR]

The Mohr-Coulomb criterion is widely used in geosciences and solid mechanics to relate the state of stress at failure to the observed orientation of the resulting faults. This relation is based on the assumption that macroscopic failure takes place along the plane that maximizes the Coulomb stress. Here, this hypothesis is assessed by simulating compressive tests on an elastodamageable material that follows the Mohr-Coulomb criterion at the mesoscopic scale. We find that the macroscopic fault orientation is not given by the Mohr-Coulomb criterion. Instead, for a weakly disordered material, it corresponds to the most unstable mode of damage growth, which we determine through a linear stability analysis of its homogeneously damaged state. Our study reveals that compressive failure emerges from the coalescence of damaged clusters within the material and that this collective process is suitably described at the continuum scale by introducing an elastic kernel that describes the interactions between these clusters. [ABSTRACT FROM AUTHOR]

Nonlinear stiffening is a ubiquitous property of major types of biopolymers that make up the extracellular matrices (ECM) including collagen, fibrin, and basement membrane. Within the ECM, many types of cells such as fibroblasts and cancer cells have a spindle-like shape that acts like two equal and opposite force monopoles, which anisotropically stretch their surroundings and locally stiffen the matrix. Here, we first use optical tweezers to study the nonlinear force-displacement response to localized monopole forces. We then propose an effective-probe scaling argument that a local point force application can induce a stiffened region in the matrix, which can be characterized by a nonlinear length scale R * that increases with the increasing force magnitude; the local nonlinear force-displacement response is a result of the nonlinear growth of this effective probe that linearly deforms an increasing portion of the surrounding matrix. Furthermore, we show that this emerging nonlinear length scale R * can be observed around living cells and can be perturbed by varying matrix concentration or inhibiting cell contractility.