Hydrogels are being used in an ever-widening range of applications. Although there is a large variety of hydrogel types, one common feature of them has been their lack mechanical strength, which presents a considerable limitation to their application. By adding a secondary microstructure to the material, enzymatic calcification addresses this and can produce materials capable of withstanding high loads, such as when they serve as a pressure boundary in filtration, or as a tissue scaffold in vitro or in vivo.

In such cases diffusion plays a critical role to the use case, especially where biological cells depend on it for sustenance. The new heterogeneous microstructure affects the way solutes diffuse through the gel and the effect is nonlinear. The scale of the structure is much smaller than the application scale, which prohibits direct simulation. We develop a method for two calcified hydrogels based on asymptotic homogenisation and show how the multiscale heterogeneities can be accounted for in a homogenised material model. The results can be used to guide the production process and target specific material diffusivities.