An irregular structure/topology as the solution is preferred.
Not only straight fibers, but also curved fibers and fiber curvature that could come from fibers being entangled should be considered.
If an anisotropic topology/structure is identified, please note that the uniaxial compression could come from any direction and the air phase should stay continuous in any space direction.
Even if you cannot prove that your topology/structure is ideal, topologies that are substantially better than typical structures are of interest.
Problem – Ideal Topology of a Fibrous Porous Material
Consider a porous medium in three space dimensions consisting of circular cross section fibers and air. The fibers are solid. The space between the fibers is filled with air. Fibers should have given properties such as modulus, poison ratio, elastic and plastic deformation, fiber breaking, fiber to fiber coefficient of friction, and fiber diameter. The porous medium could be in sheet form (relatively thin in one- dimension, infinite length in the two other dimensions). A nonwoven or a woven would be specific embodiments of such a porous material.
What is the topology (configuration of fibers?) of said porous medium that maintains one continuous air phase, even under uniaxial load in the direction that is realtively thin (compression at very slow strain rates, viscosity of air may be neglected), for the highest uniaxial stress?
For the ideal topology identified, what are the fiber properties that are important to maintain continuous air phase even under high uniaxial stress?
What is the porosity of the ideal topology identified at the transition from continuous to discrete air phase?