Stochastic continuum model for mycelium-based bio-foam

Abstract

Mycelium, the root structure of fungi, grows naturally as a biodegradable filamentous material. This unique material has highly heterogeneous microstructure with pronounced spatial variability in density and exhibits strongly non-linear mechanical behavior. In this work we explore the material response in compression, under cyclic deformation, and develop an experimentally-validated multiscale model for its mechanical behavior. The deformation localizes in stochastically distributed sub-domains which eventually percolate to form macroscopic bands of high density material. This is reflected in the stress-strain curve as strain softening. Cycling at fixed macroscopic strain leads to deformation history dependence similar to the Mullins effect. To capture this behavior, we use a two-scale model. At the micro-scale, a random fiber network is used, while at the macroscale the spatial density fluctuations are captured using a stochastic continuum model. The density-dependent local constitutive behavior is defined by the microscale model. An empirical damage model is incorporated to account for the experimentally observed cyclic softening behavior of mycelium. The model is further validated by comparison with a separate set of experimental results. The model can be used to explore the effect of mesoscale density fluctuations on the overall mechanical behavior and to design mycelium-based products with desired mechanical performance.