if one is going to vary the porosity, or uses different structures such as square, rectangular, structure with circular holes etc. while the material remains the same, So how it will affect the elastic modulus of the material?
If the internal structure of a material is altered, so to is the internal stresses and strains of the material.
if changes to the internal structure (such as heat treatment) of a material increase the stiffness of a material, the value for the elastic modulus will be higher, and vice versa.
increasing the porosity of a material would reduce the stiffness of the structure and result in a lower elastic modulus.
with regards to varying they actual shape of the material i.e square, rectangular etc etc, the elastic modulus would remain uniform (theoretically) and they only variance would be the location of material fatigue and failure.
We know Elastic modulus is equal to stress/strain ratio or slope of stress vs. strain curve within elastic / proportional limit. So, if stress-strain pattern change then definitely, the slope of the curve changed so Elastic modulus also will change.
Generally stress is the internal resistance force by cross-sectional area. The internal resistance and cross-section should highly depended on size and shape of the porosity which have a effect on cross-sectional area. So, here I feel the slope of stress-strain curve will change and hence Elastic modulus should change.
https://www.researchgate.net/publication/226613781_Correlation_between_Young's_Modulus_and_Porosity_in_Porous_Materials
Article Correlation between Young's Modulus and Porosity in Porous Materials
Young's modulus is derived by the stress /strain relationship of a material. apart from it's application in Engineering, the principle can be applied to many areas such as in compaction of pharmaceutical materials, soil and many more.
During powder/formulation compaction, crystalline particles continually undergo consolidation and /or fragmentation and in the case of fragmentation, the original rigid structure of the materials is truncated into smaller bits of the original material which in some cases induces weakness to the material. Reduction in particle size can overcomes the material stiffening tendencies which is also its ability to withstand deformation (Young's modulus) but increases the chances of the compaction event to produce a robust tablet hence the young's modulus being an important compaction parameter used to evaluate material behaviour.
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