Maxwell homogenisation methodology for evaluation of effective elastic constants of weakly-nonlinear particulate composites

The far-field methodology, developed by J. C. Maxwell in 1873 for the evaluation of the electrical conductivity of a particle-reinforced material, is utilised to estimate the effective third order elastic constants of composite media containing a random distribution of spherical particles. The results are explicit analytical relationships derived using a perturbation solution, that are in a broad agreement with previous studies employing different homogenisation schemes. In contrast to other homogenisation schemes, Maxwell's methodology relies only on the far-field asymptotics. Therefore, the methodology may be more suitable for the evaluation of effective mechanical and physical properties of composites where the far-field asymptotics are known or can be derived. The main fundamental result of this work is the first demonstration that the Maxwell methodology may be applied to weakly nonlinear problems. Therefore, it can offer a new, simple method to analyse homogenisation problems in many other fields.

Automated summary

The far-field methodology, developed by J.C. Maxwell, is utilized to estimate the effective third order elastic constants of composite media containing random distribution of spherical particles. The results agree with previous studies and can be applied to homogenization problems in other fields.