Grid based procedures for the mechanical analysis of heterogeneous solids The importance of modern simulation methods in the mechanical analysis of heterogeneous solids is presented in detail. Thereby the problem is noted that even for small bodies the required high resolution analysis reaches the limits of todays computational power in terms of memory demand as well as acceptable computational effort. A further problem is that frequently the accuracy of geometrical modelling of heterogeneous bodies is inadequate. The present work introduces a systematic combination and adaption of grid based methods for achieving an essentially higher resolution in the numerical analysis of heterogeneous solids. Grid based methods are as well primely suited for developing efficient and numerically stable algorithms for flexible geometrical modeling. A key aspect is the uniform data management for a grid which can be utilized to reduce the effort and complexity of almost all concerned methods. A new finite element program called Mulgrido was just developed to realize this concept consistently and to test the proposed methods. ...