2013年1月，MatDEM的第一篇论文发表于JGR-Solid Earth。JGR主编评价“This is an interesting paper - I look forward to seeing future work on this topic and I hope someday our computers can do this in 3D”。Analytical solutions and numerical tests of elastic and failure behaviors of close-packed lattice for brittle rocks and crystals Liu et al., 2013, JGR-Solid Earth Analytical solutions of elastic properties and failure modes of a two‐dimensional close‐packed discrete element model are proposed. Based on the assumption of small deformation, the conversion formulas between five inter‐particle parameters of the lattice model and rock mechanical properties were derived. Using the formulas, the inter‐particle parameters can be determined by Young's modulus (E), Poisson's ratio (v), tensile strength (Tu), compressive strength (Cu), and coefficient of intrinsic friction (μi). The lattice defined by the parameters simulates the elastic and failure behaviors of rocks and crystals and therefore can be used to investigate the initiation and development of geological structures quantitatively. Furthermore, the solutions also provide a theoretical basis for the calibration of parameters of random discrete assemblies. The model of quartz was used as an example to validate the formulas and test the errors. The simulated results show that E and v converge to theoretical values when particle number increases. These elastic properties are almost constant when the magnitude of strain is lower than 10−3. The simulated Tu and Cu of a single three‐element unit are also consistent with the formulas. However, due to the boundary effects and stress concentrations, Tu and Cu of lattices with multiple units are lower than the values predicted by the formulas. Therefore, greater Tu and Cu can be used in the formulas to counteract this effect. The model is applicable to the simulation of complicated structures that involve deformation and failure at different scales. Fig. 1 A vertical force Fy acts on a three-particle unit. The deformation of the basic triangular unit is used to inves-tigate the mechanical properties of the lattice model.
Fig. 2 Relationships between elastic properties (G, l, E, and v) of close-packed model and the normal stiffness (Kn) and shear stiffness (Ks).
Fig.3 Test results for Young’s modulus and Poisson’s ratio of one unit (three particles) agree with the theoretical values, 90 GPa and 0.16, respectively. Deviations of elastic properties of other lattices in-crease with the increasing magnitude of strain and decrease with increasing particle number. (a) Young’s modulus; (b) Poisson’s ratio.
Fig.4 (a) Simulated uniaxial compressive strength (Cu) and (b) tensile strength (Tu) with different pa
Liu C., Pollard D.D., Shi B. 2013. Analytical solutions and numerical tests of elastic and failure behaviors of close-packed lattice for brittle rocks and crystals. Journal of Geophysical Research- Solid Earth, 118, 71-82.
