Analysis of beams composed of bimodulus materials treated by granular micromechanics

In this study, we examine the behavior of beam composed of bimodulus materials using a granular micromechanics-based continuum model. The results are also compared with available experimental data. Both statically determinate and hyperstatic beam cases are considered. Numerical results demonstrate the following interesting findings. (1) The model confirms the validity of the rigidity of the cross-sectional area that is typical of the Euler–Bernoulli beam theory. (2) The neutral axis shifts toward the compression region of the cross-sectional area as the stiffness in compression increases with respect to that in tension. (3) Jourawski's formula must be generalized to a parabolic-type shape for shear stress distribution, where the maximum shear shifts with the neutral axis position. (4) In certain hyperstatic beam configurations, additional axial reaction forces arise due to the imbalance between tension and compression stresses across the cross-section. (5) The transition of axial stiffness from tension to compression regions is smooth and not abrupt as in other bimodulus models. (6) The tension and compression principal stress trajectories reveal crack propagation paths that differ from those observed under tension/compression symmetry. These findings demonstrate that modeling bimodulus materials using the granular micromechanic approach provides a comprehensive framework for analyzing beams and other structural members under various loading and boundary conditions.