Mechanical modelization of anisotropic porous materials with a homogenization method. Application to aerated concretes

摘要

This study deals with the modelization of the mechanical behavior of an anisotropic porous material made up of ellipsoidal pores uniaxially oriented according to the geometric parameters that characterize porosity. To do so we used a homogenization technique based on the method of finite elements and the coupling of porosity parameters was taken into account. This approach made possible both the introduction of the quantitative and qualitative aspects of porosity and the transcription of mechanical anisotropy due to geometric anisotropy. We thus determined the homogenized elasticity moduli, which traduce rigidity of the material both parallel and perpendicular to the flattening of the pores according to their shape coefficient and the porosity. We noticed that with equal porosity a material made up of ellipsoidal pores is more rigid on the mechanical level -- parallel to the flattening of pores--than a material made up of spherical pores. Higher rigidity linked to geometric anisotropy varies according to the porosity and to the shape coefficient of the pores. It may reach a factor of 4 for a 20/100 porosity. So the results of modelization show the advantage of anisotropy in the case of building materials such as aerated concretes. Moreover, experimental results confirm, on a qualitative level, optimization potentialities of aerated concretes mechanical efficiency by varying the geometrical configuration of porosity.