Abstract
Biological tissues experience mechanical compression under various physiological and pathological conditions and often exhibit compression stiffening, in which their stiffness increases during compression, a phenomenon that plays a crucial role in regulating cell behavior and maintaining mechanical homeostasis. However, most isolated biopolymer networks, such as fibrin and collagen hydrogels that form the extracellular matrix and actin network that forms the internal cytoskeleton, undergo compression softening, raising questions about how tissues achieve compression stiffening despite the softening properties of their extracellular and intracellular matrix components. Previous studies have shown that spherical inclusions at large volume fractions can induce compression stiffening in biopolymer networks, but they do not account for the effects of aggregation and irregular morphologies of cellular assemblies or other components in tissues. Here, we demonstrate a novel mode of compression stiffening induced by aggregated or irregularly shaped inclusions that occurs at significantly lower volume fractions. Using carbonyl iron particles and coffee ground particles, we find that the morphological diversity of inclusions enables tissue-like compression stiffening at a low volume fraction of inclusions. Through a set of experiments and computational analyses, we demonstrate that these particles can percolate at low volume fractions. We further show that the percolation of stiff inclusions creates a stress-supporting network and enables tension-dominated stress propagation in fibrin fibers, both of which drive macroscopic stiffening during compression. These findings provide insights into the regulation of tissue stiffness and have implications for designing biomaterials with physiologically relevant mechanical properties for biomedical applications. SIGNIFICANCE STATEMENT: Biological tissues experience a variety of mechanical forces. Many tissues, such as brain, liver, fat, and blood clots, become stiffer under physiological compressive loads, a property known as compression stiffening. In contrast, most biopolymer networks, which are the primary structural components for tissues, soften under compression. Here, we show that incorporating a small amount of aggregated or irregularly shaped particles into biopolymer gels induces robust compression stiffening. These inclusions percolate through the gel and rearrange non-affinely under compression, stretching surrounding fibers and contributing to mechanical reinforcement. Together, these effects reproduce tissue-like compression stiffening. Our findings not only provide new physical models for understanding tissue mechanics but also offer insights for designing biomaterials to achieve physiologically relevant mechanical responses.