Mathematical modeling of heterogeneous materials. Applications

Time: 09:00 to  10:30 Ngày 20/01/2017

Venue/Location: C2-714

Speaker: Reinaldo Rodríguez Ramos

Content:

Effective moduli closed-form analytical expressions of two-phase fibrous periodic heterogeneous media with perfect and imperfect adhesion at the interface are obtained by means of the Asymptotic Homogenization Method (AHM) for a parallelogram array of circular cylinders. A doubly period- parallelogram array of cylindrical inclusions is studied. The behavior of the effective coefficients is studied for several cell geometry arrays with different contacts at the interface. Numerical examples and comparisons with other theoretical results demonstrate that the present model is efficient for the analysis of heterogeneous structures in which the periodic cell is rectangular,rhombic or a parallelogram. The effect of the arrangement of the cells on the effective property is discussed. The present method can provide benchmark results for other numerical and approximate methods. Sometimes heterogeneous materials may be regarded as an idealized model of certain biological tissue comprising tubular cells, such as skeletal muscle, bones, etc and to explore the applications of new theoretical models for heterogeneous structures to biological tissue is of great interest. On the other hand, the study of tumor growth within the framework of Continuum Mechanics, considering a tumor as a specific case of a growing soft tissue or a special type of heterogeneity is motivation of different works in the last years.