Determination of Effective Elastic Coefficients Using the Standard Mechancis Approach: Application to Trabecular Bone Tissue

A.A. IBARRA PINO ; A. P. CISILINO

Foz do Iguacu

Congreso; XI Pan-American Congress of Applied Mechanics; 2010

Universidad de Sao Paulo, Brazil

Abstract. The human bone tissue is a natural composite material with a complex microstructure optimized for withstanding functional loads. It is extremely difficult to analyze the mechanical response of the trabecular bone considering each structural entity due to its high degree of heterogeneity. The typical way to overcome this difficulty is to find an equivalent material model that characterizes the average material mechanical behavior in the macroscopic scale. It is presented in this paper a method to compute the macroscopic effective stiffness matrix of the trabecular bone via the so-called standard mechanics approach. To this end, the finite element (FE) method is used to conduct a stress analysis a representative volume element (RVE) of the trabecular microstructure. The FE results are processed in order to compute the local structure tensor M, which relates the local tissue strain tensor to the average strain tensor. Finally, the M tensor is used to compute the elastic coefficients for the equivalent continuum material in the macroscopic level. The method is used to obtain the equivalent elastic coefficients for idealized trabecular geometries in 2D. The effect of the RVE size is analyzed and discussed.