title: Effective elastic properties of a composite containing multiple types of anisotropic ellipsoidal inclusions, with the application to the attachment of tendon to bone.
abstract: Estimates of the effective stiffness of a composite containing multiple types of inclusions are needed for the design and study of functionally graded systems in engineering and physiology. While excellent estimates and tight bounds exist for composite systems containing specific classes and distributions of identical inclusions, these are not easily generalized to complex systems with multiple types of inclusions. For example, three-point parameters are known for only a few inclusion shapes and orientations. The best estimate available for a composite containing multiple classes of inclusions arises from the Kanaun-Jeulin approach. However, this method is analogous to a generalized Benveniste approach, and therefore suffers from the same limitations: while excellent for low volume fractions of inclusions, the Kanaun-Jeullin and Benveniste estimates lie outside of three-point bounds at higher volume fractions. Here, we present an estimate for composites containing multiple classes of aligned ellipsoidal inclusions that lies within known three-point bounds at relatively higher volume fractions of inclusions and that is applicable to many engineering and biological composites.
authors.affiliation: Department of Mechanical Engineering & Materials Science, Washington University, St. Louis, MO 63130, USA.
authors.forename: Fatemeh
authors.initials: F
authors.lastname: Saadat
authors.affiliation: Engineering Education Center, Missouri University of Science and Technology, St. Louis, MO 63131, USA.
authors.forename: Victor
authors.initials: V
authors.lastname: Birman
authors.affiliation: Department of Orthopaedic Surgery, Washington University School of Medicine, St. Louis, MO 63130, USA.
authors.forename: Stavros
authors.initials: S
authors.lastname: Thomopoulos
authors.affiliation: Department of Mechanical Engineering & Materials Science, Washington University, St. Louis, MO 63130, USA.
authors.forename: Guy M
authors.initials: GM
authors.lastname: Genin
keywords: Tendon-to-bone insertion site; composite materials; enthesis; homogenization methods