Compression stiffening of fibrous networks with stiff inclusions

Tissues commonly consist of cells embedded within a fibrous biopolymer network. Whereas cell-free reconstituted biopolymer networks typically soften under applied uniaxial compression, various tissues, including liver, brain, and fat, have been observed to instead stiffen when compressed. The mechanism for this compression stiffening effect is not yet clear. Here, we demonstrate that when a material composed of stiff inclusions embedded in a fibrous network is compressed, heterogeneous rearrangement of the inclusions can induce tension within the interstitial network, leading to a macroscopic crossover from an initial bending-dominated softening regime to a stretching-dominated stiffening regime, which occurs before and independently of jamming of the inclusions. Using a coarse-grained particle-network model, we first establish a phase diagram for compression-driven, stretching-dominated stress propagation and jamming in uniaxially compressed 2- and 3-dimensional systems. Then, we demonstrate that a more detailed computational model of stiff inclusions in a subisostatic semiflexible fiber network exhibits quantitative agreement with the predictions of our coarse-grained model as well as qualitative agreement with experiments.

Nonaffine rubber elasticity for stiff polymer networks

We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces (``stretching). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic characterization of the deformation field in terms of ``floppy modes -- low-energy bending excitations that retain a high degree of non-affinity. The length-scale characterizing the emergent non-affinity is given by the ``fiber length $l_f$, defined as the scale over which the polymers remain straight. The calculated scaling properties for the shear modulus are in excellent agreement with the results of recent simulations obtained in two-dimensional model networks. Furthermore, our theory can be applied to rationalize bulk rheological data in reconstituted actin networks.

Stiffest Elastic Networks

The rigidity of a network of elastic beams crucially depends on the specific details of its structure. We show both numerically and theoretically that there is a class of isotropic networks which are stiffer than any other isotropic network with same density. The elastic moduli of these textit{stiffest elastic networks} are explicitly given. They constitute upper-bounds which compete or improve the well-known Hashin-Shtrikman bounds. We provide a convenient set of criteria (necessary and sufficient conditions) to identify these networks, and show that their displacement field under uniform loading conditions is affine down to the microscopic scale. Finally, examples of such networks with periodic arrangement are presented, in both two and three dimensions.

Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers

Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.

High-pressure structural and elastic properties of Tl2O3

The structural properties of Thallium (III) oxide (Tl2O3) have been studied both experimentally and theoretically under compression at room temperature. X-ray powder diffraction measurements up to 37.7 GPa have been complemented with ab initio total-energy calculations. The equation of state of Tl2O3 has been determined and compared to related compounds. It has been found experimentally that Tl2O3 remains in its initial cubic bixbyite-type structure up to 22.0 GPa. At this pressure, the onset of amorphization is observed, being the sample fully amorphous at 25.2 GPa. The sample retains the amorphous state after pressure release. To understand the pressure-induced amorphization process, we have studied theoretically the possible high-pressure phases of Tl2O3. Although a phase transition is predicted at 5.8 GPa to the orthorhombic Rh2O3-II-type structure and at 24.2 GPa to the orthorhombic a-Gd2S3-type structure, neither of these phases were observed experimentally, probably due to the hindrance of the pressure-driven phase transitions at room temperature. The theoretical study of the elastic behavior of the cubic bixbyite-type structure at high-pressure shows that amorphization above 22 GPa at room temperature might be caused by the mechanical instability of the cubic bixbyite-type structure which is theoretically predicted above 23.5 GPa.