## 1 Introduction  
Montmorillonite (MMT) consists of well-defined layers separated by interlayer spaces and has great water absorption potential [1; 2; 3; 4]. Thus, it is often used as clay barriers or adsorption material in environmental geotechnical engineering, for example, the backfill in the nuclear waste disposal and the cushion in the landfill [5; 6; 7; 8; 9; 10]. It is very challenging to directly measure the fundamental mechanical properties of MMT [11; 12]. Atomic force acoustic microscopy is used to determine the elastic properties of clay mineral aggregates by measuring adhesion forces [13; 14; 15]. Nanoindentation and ultrasonic pulse velocity technology (UPV) are also used to measure the elastic stiffness constants of clays and shale samples [16; 17; 18]. However, these techniques are powerless to measure the anisotropic mechanical properties of MMT, due to the complications in sample preparation and even the testing process. In contrast to difficulty in experimental methods, molecular dynamics (MD) simulation is a supplemental way to model and understand the properties of hydrated clay minerals on an atomic scale [1; 19; 20; 21]. With the development of polymer-clay nanocompositesin recent years, several studies on the nanomechanical properties of MMT minerals or hydrated MMT systems have emerged. The authors in [18] reported for the first time the stress-strain response of rock-forming minerals by MD simulation. The authors in [22] performed MD simulations to study the flexibility and the mechanical behavior of a single clay layer in a completely exfoliated state and found that the critical stress of a clay layer bending fracture is 0.8 MPa in both in-plane directions. In [23], the authors presented results for the elastic properties of a single lamella of MMT by MD simulation and further pointed out that the elastic constants characteristic of a thin plate is closely related to the thickness of the nanoplate. Based on the analogous minerals and modulus-density relations, ref. [24] deduced a convergence of opinion in the range 178-265 GPa for the elastic moduli of smectite clay platelets. The authors in [25] systematically simulated the structure and the thermomechanical properties of an isolated clay nanoplate and MMT crystals intercalated by water or polyethylene oxide. In [26], the authors clarified the linear elastic properties including tensile moduli, shear moduli, and potential failure mechanisms as a function of cation density and stress for the minerals pyrophyllite, MMT, and mica. In [27], the authors examined the mechanism of bending, the stored energy, and the failure of several clay minerals. They revealed that molecular contributions to the bending energy include bond stretching and bending of bond angles in the mineral as well as rearrangements of alkali ions on the surface of the layers. The authors in [28] further simulated the elastic and structural properties of muscovite as a function of temperature, pressure, and strain. The results demonstrate that the elastic properties of muscovite depend on both temperature and pressure. MD with the CLAYFF force field was used in [29] to simulate isothermal isobaric water adsorption of interlayer MMT, and nanoscale elastic properties of the clay-interlayer water system are calculated from the potential energy of the model system. Similar simulations have also been carried out on MMT by implementing the elastic bath method [30]. The mechanical properties of Na-MMT were investigated in [31] from the view of water content by MD, and the hysteresis phenomena of elastic constant during the swelling and shrinking was found. In addition, researchers found that the mechanical behavior of MMT crystal exhibits a clear dissymmetry between compression and tension and an important dependency on mean stress [32]. The above simulation studies are generally based on the strain method, that is, the stress is calculated by changing the size of the simulation box. The stress method and the large-scale fluctuation method are also usually adopted.