The work is focused on the mechanical behavior description of porous filled composites that is not based on simulations or exact physical models, including different assumptions and simplifications with further comparison with real behavior of materials with different extents of accordance. The proposed process begins by measurement and further fitting of data by spatial exponential function z_c = z_m · p₁^b · p₂^c, where z_c/z_m is mechanical property value for composite/nonporous matrix, p₁/p₂ are suitable dimensionless structural parameters (equal to 1 for nonporous matrix) and b/c are exponents ensuring the best fitting. The fitting is followed by interpolation of b and c, which are logarithmic variables based on the observed mechanical property value of nonporous matrix with additions of further properties of matrix in some cases. The work is dedicated to the utilization of further suitable pairs of structural parameters to one pair published earlier. The proposed mathematical approach was demonstrated for PUR/rubber composites with a wide range of rubber filling, various porosity, and different polyurethane matrices. The mechanical properties derived from tensile testing included elastic modulus, ultimate strength and strain, and energy need for ultimate strain achievement. The proposed relationships between structure/composition and mechanical behavior seem to be suitable for materials containing randomly shaped filler particles and voids and, therefore, could be universal (and also hold materials with less complicated microstructure) after potential following and more exact research.

This study describes a new mathematical approach to the relationship between mechanical properties (tensile modulus, ultimate strength, and strain), composition as well as structure of porous-filled reinforced composites. The composite system consisted of a polyurethane matrix, a rubber filler, and a small amount of polyethylene terephthalate as a reinforcement. The newly proposed equations are based on a special mixing rule with the same basic form for all studied properties. The mixing rule contains a correction parameter η, which differs in different filler content in the filled part of the composite. Here, a cubic exponential function including the product of suitable structural parameters and exponents ensuring the best fitting and describable by matrix properties were successfully defined to fit the different values of correction parameter. The proposed equations should be a suitable step to obtain a relationship for describing the mechanical behavior of porous-filled and reinforced composites in the case of a small amount of reinforcement.

The work focuses on researching relationships between structure/properties and mechanical behavior of porous composites. The primary data comes from tensile testing. The observed properties include elastic modulus, ultimate strength, ultimate strain, and energy need for ultimate strength achievement. The studied materials include composites based on different polyurethane matrices and one rubber filler with various filler and porosity contents. Presented work expands the possibilities of an approach based on measured data fitting by a suitable function followed by obtained parameters interpolation. The utilization of new structural parameters leads to a spatial linear function shape instead of spatial exponential. The newly introduced equation is z _c = z _m + z _m · (b · p ₁ + c · p ₂), where z _c /z _m is generally labeled mechanical property value for composite/nonporous matrix, p ₁/p ₂ are suitable structural parameters, and b/c are fitting parameters subjected to interpolations by logarithmic function containing values of properties typical for matrices. The work focuses on studying the case of different matrices and one kind of filler. The work includes all potentially valuable interpolations for earlier mentioned properties with the most interesting results in cases of pairs p ₁/p ₂ containing two from three parameters: n (porosity), 1 − v _m (v _f + porosity), and v _f (filler volume fraction).