Material-defined two-dimensional numerical model for grain-scale nonlinear elasticity

Understanding the acoustic manifestations of nonlinear mesoscopic elastic material is essential for characterizing complex granular media. This work develops a numerical model defined using properties of Berea Sandstone that captures nonlinear elastic wave behavior under cyclic loading conditions. The material consists of crystalline, linearly stiff elastic grains, embedded within an amorphous diagenetic matrix that exhibits spatially varying nonlinear stress-strain behavior. When performing quasi-static loading scenarios, the soft matrix governs the rate-independent hysteresis response and reproduces behavior commonly observed experimentally in resonant bar and acousto-elastic testing. For physical insight the model enables detailed local tracking of the material matrix to identify essential force pairs that control hysteresis and are consistent with phenomenological models. The results demonstrate that physically motivated microstructural modeling provides insight towards explaining experimentally observed nonlinear acoustic wave phenomena. This approach advances modeling efforts beyond phenomenological descriptions of acoustic nonlinearity in solids for a more detailed understanding.