Hybrid homogenization theory with surface effects: Application to columnar nanoporous materials

• Published in: European journal of mechanics, A, Solids Vol. 101; p. 105050
• Main Authors: Yin, Shizhen, Pindera, Marek-Jerzy
• Format: Journal Article
• Language: English
• Published: Elsevier Masson SAS 01.09.2023
• Subjects: Gurtin–Murdoch theory; Homogenization; Nanocomposites; Surface/interface effect; Homogenization; Nanocomposites; Surface/interface effect; Gurtin–Murdoch theory
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2023.105050

Nanocomposites, including nanoporous ceramics, metals and polymers, are being widely used in various engineering applications. At the nanoscale, surface/interface effects have significant influence on the homogenized properties and local stresses. To account for these nanoscale effects, the well-established Gurtin–Murdoch theory of surface elasticity is typically incorporated into classical elasticity-based micromechanics schemes and numerical approaches based on the finite-element and most recently finite-volume methods. Whereas the classical micromechanics models either neglect the interactions of adjacent fibers/pores or account for the interactions in an average sense, the finite-element and finite-volume based approaches require high discretization to capture the large stress/strain gradients around the interface/surface. In contrast, the recently proposed hybrid homogenization theory (HHT) combines elements of locally-exact elasticity and finite-volume approaches and is both accurate and efficient, enabling rapid generation and analysis of ordered and quasi-random fiber or pore arrays. Herein, a continuous bulk matrix layer of arbitrary size endowed with a two-dimensional energetic surface is introduced between fiber/pore and discretized matrix region that enables exact calculation of stress jump conditions in the Young–Laplace equations of the Gurtin–Murdoch model. The enhanced HHT with interface/surface effects is validated by comparison with the stress concentration factors obtained using a classical elasticity solution and point-wise stress fields predicted by the locally-exact and finite-volume homogenization theories, exhibiting stable solutions even for very thin bulk matrix layers. The enhanced theory is then employed to study the influence of random nanopore microstructures with random pore radii on the complete set of homogenized moduli of porous silicon used in the electronics industry. •Authors’ hybrid homogenization theory generalized to include energetic surface effects.•Generalization enables exact treatment of jump conditions in the Young–Laplace equations.•Solution of multiple inclusion/pore unit cell stable even for extremely thin matrix layers with energetic surfaces.•Effect of pore distributions and pore radius randomness on homogenized moduli of porous silicon quantified.