Microcontinuum approach in biomechanical modeling

The living organs consist of tissues characterized by the hierarchical, very complex inner structure. One of theories taking this into account is the microcontinuum theory elaborated by Eringen [Microcontinuum Field Theories: Foundation and Solids, 1998]. The corresponding mathematical formulation is rather complicated, and therefore, the numerical application is still in progress. In this contribution, the boundary value problem for micropolar and microstretch linear continuum is defined. Using the author’s formalism [ZAMM 65 (1985) 417; J. Computat. Appl. Math. 53 (1995) 307] which is based on Bufler’s work [Ingenieur-Arch. 45 (1976) 17] the corresponding variational principles are developed. These are used for the numerical implementation. The code for micropolar continuum is tested on some examples and used for the bone modeling.