Multiscale structure mechanics

We are mainly working on three subjects here. The first one refers to the numerical computation of the microscopic stress-strain behavior and effective material properties of composite or porous materials. We apply homogenization methods which allow for the computation of average (effective) elastic, viscoelastic, and plastic material properties, accounting for the microstructure and the different constitutive laws. The computation of effective free temperature deformation, swelling, and shrinkage is also possible. The second subject deals with contact problems with micro-rough surfaces, which can also be solved by homogenization methods. Finally, within the third problem complex we consider time-dependent processes for composite bodies, whose macro strength and durability are examined with respect to fatigue, creep strain, impact load, and wear.

Homogenization methods are applied if the composite material shows strongly differing size scales. In this case, a direct computation of properties and effects on the macro scale is mostly impossible due to the enormous efforts, which are necessary if the microstructure is to be accounted for. The homogenization method, which is applied here, works with an asymptotic expansion of the entire problem with respect to the length ratio of the micro and macro scales. In the limit, the result is an equivalent homogeneous problem, which includes only mean effective properties. The solution of this homogenized problem finally represents an approximation of the exact solution.

Compared to other, simpler averaging methods, such as self-consistent methods according to Hashin and Eshelby, which can only be applied to special geometric types, asymptotic homogenization methods have the essential advantage that they can be applied to arbitrary microstructures and many different material laws.