Multiscale modeling and evaluation of effective properties of cortical bone

• Grant number: 14/21836-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2015
• End date: June 01, 2018
• Field of knowledge: Engineering - Biomedical Engineering - Bioengineering
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Adair Roberto Aguiar
• Grantee: Uziel Paulo da Silva
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 15/16219-7 - Multiscale modeling of effective properties of cortical bone, BE.EP.PD

Abstract

We wish to employ a multiscale approach to determine the effective electromechanical properties of cortical bones. First, we will model cortical bone as a two-phase composite containing a periodic distribution of circular cylindrical holes in a piezoelectric matrix of symmetry class 6. Each hole in the matrix is centered in a regular hexagonal cell. We will employ the Asymptotic Homogenization Method (MHA) on the corresponding boundary value problem to evaluate the effective electromechanical constants of the resulting homogenized medium. Next, instead of circular cylindrical holes and the MHA, we will consider ellipsoidal voids and the method of Mori-Tanaka (MT) to evaluate the effective electromechanical constants of the resulting homogenized medium. In the case of cylindrical voids with circular cross sections, the constants obtained via MT will be compared with the effective constants obtained via MHA. Subsequently, we will model cortical bone as a hierarchical structure and will employ both the MHA and the MT in each hierarchical level of the structure to evaluate the effective electromechanical constants for that level. Besides modeling cortical bone tissues, we also wish to model other piezoelectric biological tissues, such as cartilage. Mathematical modeling of boundary value problems that lead to the determination of the effective piezoelectric properties of biological tissues is difficult and requires the involvement of research groups with different backgrounds. This motivates and justifies the candidate's initiative to spend some time abroad with a research group that has extensive experience in multiscale modeling of hierarchical structures. Finally, we will model cortical bone as an inhomogeneous piezoelectric structure containing a random distribution of voids. Again, it will be assumed that the material of this structure belongs to the crystalline symmetry class 6. Green tensor is then used to evaluate the effective electromechanical constants. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

AGUIAR, ADAIR ROBERTO; BRAVO-CASTILLERO, JULIAN; DA SILVA, UZIEL PAULO. Application of Mori-Tanaka method in 3-1 porous piezoelectric medium of crystal class 6. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, v. 123, p. 36-50, FEB 2018. (14/21836-2)

AGUIAR, ADAIR ROBERTO; BRAVO-CASTILLERO, JULIAN; DA SILVA, UZIEL PAULO; RODRIGUEZ-RAMOS, REINALDO. Effective Electromechanical Properties of 622 Piezoelectric Medium With Unidirectional Cylindrical Holes (vol 80, 050905, 2013). JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, v. 85, n. 2, p. 2-pg., 2018-02-01. (14/21836-2)

AGUIAR, ADAIR ROBERTO; THEOPHILO PRADO, EDMAR BORGES; DA SILVA, UZIEL PAULO. Analysis of Boundary Layer Influence on Effective Shear Modulus of 3-1 Longitudinally Porous Elastic Solid. LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES, v. 17, n. 8, SI, 2020. (14/21836-2)