Quantum mechanics

Anisotropy

Phase (matter)

Random field

Pure mathematics

Statistics

Materials science

Field (mathematics)

Porosity

Physics

Mathematics

Porous medium

Composite material

Compaction

Fracture (geology)

Brittleness

International Journal of Solids and Structures

Heterogeneous materials with randomly distributed pores are ubiquitous, such as sintered silver nanoparticles, concrete materials, 3D printed polymers, and natural bones. Recent experimental investigations have revealed that porosity and also pore-related geometries (size, number, shape, distribution and alignment) have significant impacts on the mechanical behavior of random porous materials. However, existing studies focus on the porosity effect while ignoring other pore features such as pore size and pore shape. Our research is dedicated to a computational framework for generating isotropic/anisotropic random porous materials using Gaussian random fields with stochastic pore size and shape factor and addressing the mechanical properties and behavior of brittle fractures using a fracture phase-field model with a preferred degradation function. Sintered silver nanoparticles with typical randomly distributed pores, as representative porous materials, are chosen for their promising applications in emerging fields such as power electronics and wearable devices. In order to emphasize the effect of pore size and shape, 420 random samples with a fixed porosity were generated to discuss the stress–strain response during fracture and to establish statistical relationships between pore feature distributions and mechanical properties such as Young's modulus, UTS, and average historical energy. Our findings suggest that the statical attributes of the pore sizes and shape factors significantly affect the material performance related to the mechanical properties and fracture behavior, which could give a better understanding of the random porous materials and guide reliability-based material design optimization.

Statistical effects of pore features on mechanical properties and fracture behaviors of heterogeneous random porous materials by phase-field modeling