Mathematical analysis and homogenization of the torsion problem
This paper starting from the standard equations of elastic equilibrium, presents the limitations of the classical formulation of the torsion problem of bars consisting of different materials. The classical theory requires that the surface separating the different materials are sufficiently smooth. Weak and variational formulations of the torsion problem defined on Sobolev spaces enable the authors to relax this requirement and is suitable for obtaining bounds on the torsional rigidity and analyzing the limit torsional behavior of composite materials when the characteristic length of the microstructures (e.g. the diameter of the fibers) tends to zero. The analysis is based on the homogenization method in both the periodic and stochastic setting. The theoretical results are explained with numerical computations.
scientific article; zbMATH DE number 5310050