The paper by Ekkehart Kröner from the Institute of Theoretical and Applied Physics, University of Stuttgart, discusses the calculation of elastic constants of polycrystals from single-crystal constants. Using the concept of elastic polarizability, the elastic constants of a macroscopically isotropic polycrystal can be accurately calculated from single-crystal constants. For a polycrystal composed of cubic grains, the shear modulus can be derived from a cubic equation (equation 22), where combinations of single-crystal elastic constants appear as coefficients. Experimental results deviate slightly from the calculated values, indicating that the experiments did not meet the ideal conditions required by the theory. Further applications of the method are discussed. Recent summaries of the topic show that the theoretical and experimental elastic constants of polycrystals seem well-ordered. However, a closer examination reveals that the associated calculations are not strongly theoretically grounded. The uncertainty is increased because it is often difficult to select the necessary experimental data from the variety of results, which often differ significantly. The concept of elastic polarizability, introduced by Eschenbacher and used by the author, allows for the calculation of polycrystal elastic constants on a solid theoretical basis without ad hoc assumptions. Before describing the method, the most important previous works are briefly reviewed with some important comments for later use. The paper introduces notation for stress and strain tensor components, Euler angles, and orientation symbols. It also defines elastic constants for single crystals and polycrystals, including isotropic elastic constants. The paper discusses the relationship between single-crystal elastic constants and the isotropic elastic constants of a polycrystal composed of cubic grains. It also presents previous results, including Voigt's approximation, which assumes all grains experience the same deformation, leading to inaccuracies in the calculated moduli. The paper concludes with a discussion of the method's potential applications.The paper by Ekkehart Kröner from the Institute of Theoretical and Applied Physics, University of Stuttgart, discusses the calculation of elastic constants of polycrystals from single-crystal constants. Using the concept of elastic polarizability, the elastic constants of a macroscopically isotropic polycrystal can be accurately calculated from single-crystal constants. For a polycrystal composed of cubic grains, the shear modulus can be derived from a cubic equation (equation 22), where combinations of single-crystal elastic constants appear as coefficients. Experimental results deviate slightly from the calculated values, indicating that the experiments did not meet the ideal conditions required by the theory. Further applications of the method are discussed. Recent summaries of the topic show that the theoretical and experimental elastic constants of polycrystals seem well-ordered. However, a closer examination reveals that the associated calculations are not strongly theoretically grounded. The uncertainty is increased because it is often difficult to select the necessary experimental data from the variety of results, which often differ significantly. The concept of elastic polarizability, introduced by Eschenbacher and used by the author, allows for the calculation of polycrystal elastic constants on a solid theoretical basis without ad hoc assumptions. Before describing the method, the most important previous works are briefly reviewed with some important comments for later use. The paper introduces notation for stress and strain tensor components, Euler angles, and orientation symbols. It also defines elastic constants for single crystals and polycrystals, including isotropic elastic constants. The paper discusses the relationship between single-crystal elastic constants and the isotropic elastic constants of a polycrystal composed of cubic grains. It also presents previous results, including Voigt's approximation, which assumes all grains experience the same deformation, leading to inaccuracies in the calculated moduli. The paper concludes with a discussion of the method's potential applications.