Numerical homogenization techniques applied to growth and remodelling phenomena

Materials with inherent microstructures like granular media, foams or spongy bones often show a complex constitutive behaviour on the macroscale while the microscopic constitutive equations may be formulated in a simple fashion. Applying homogenization procedures allows to transfer the information from the microlevel to the macrolevel. In the present contribution the porous structure of hard biological tissues, i.e. of spongy bones, is investigated. On the macroscale the approach is embedded into an extended continuum mechanical setting in order to capture size effects. The constitutive equations are formulated on the microscopic level taking into account growth and reorientation of the microstructural elements. By application of a strain-driven numerical homogenization procedure the macroscopic stress response is obtained.