Mindlin second-gradient elastic properties from dilute two-phase Cauchy-elastic composites Part II: Higher-order constitutive properties and application cases

• Published in: International journal of solids and structures Vol. 50; no. 24; pp. 4020 - 4029
• Main Authors: Bacca, M., Bigoni, D., Dal Corso, F., Veber, D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2013
• Subjects: Composite materials; Derivation; Dilute distribution of spherical and circular inclusions; Effective non-local continuum; Higher-order elasticity; n-Polygonal holes; Effective non-local continuum; n-Polygonal holes; Composite materials; Higher-order elasticity; Dilute distribution of spherical and circular inclusions
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2013.08.016

Starting from a Cauchy elastic composite with a dilute suspension of randomly distributed inclusions and characterized at first-order by a certain discrepancy tensor (see part I of the present article), it is shown that the equivalent second-gradient Mindlin elastic solid: (i) is positive definite only when the discrepancy tensor is negative defined; (ii) the non-local material symmetries are the same of the discrepancy tensor, and (iii) the non-local effective behaviour is affected by the shape of the RVE, which does not influence the first-order homogenized response. Furthermore, explicit derivations of non-local parameters from heterogeneous Cauchy elastic composites are obtained in the particular cases of: (a) circular cylindrical and spherical isotropic inclusions embedded in an isotropic matrix, (b) n-polygonal cylindrical voids in an isotropic matrix, and (c) circular cylindrical voids in an orthotropic matrix.