Abstract
Indentation is often used to measure the stiffness of soft materials whose main structural component is a network of filaments, such as the cellular cytoskeleton, connective tissue, gels, and the extracellular matrix. For elastic materials, the typical procedure requires fitting the experimental force-displacement curve with the Hertz model, which predicts that $f=k \delta ^{1.5}$ and $k$ is proportional to the reduced modulus of the indented material, $E/(1-\nu^2)$ . Here we show using explicit models of fiber networks that the Hertz model applies to indentation in network materials provided the indenter radius is larger than approximately $12 l_c$, where $l_c$ is the mean segment length of the network. Using smaller indenters leads to a relation between force and indentation displacement of the form $f=\delta^q$, where $q$ is observed to increase with decreasing indenter radius. Using the Hertz model to interpret results of indentations in network materials using small indenters leads to an inferred modulus smaller than the real modulus of the material. The origin of this departure from the classical Hertz model is investigated. A compacted, stiff network region develops under the indenter, effectively increasing the indenter size and modifying its shape. This modification is marginal when large indenters are used. However, when the indenter radius is small, the effect of the compacted layer is pronounced as it changes the indenter profile from spherical towards conical. This entails an increase of exponent $q$ above the value of 1.5 corresponding to spherical indenters.
Jacob Merson
Assistant Professor of Mechanical Engineering
loves to scale multiphysics simulations onto leadership class supercomputers
