An atomistic entropy based finite element multiscale method for modeling amorphous materials

A new concurrent multiscale method based on the maximum entropy statistical method is proposed for the analysis of amorphous materials. In addition to reducing the number of degrees of freedom, any irregular structure of amorphous materials can be accurately analyzed. The amorphous structure is generated from a solid crystalline structure by a heating/cooling process without the need for any specific independent technique to create such a random structure. The method is expected to perform efficiently because of its entropic and irregular intrinsic. Regions with moderate conditions are discretized by the entropy-based finite element method while the severe parts are simulated by the present atomistic-based multiscale technique. The new proposed approach allows for accurate analysis of amorphous structures across multiple scales and does not suffer from conventional complications such as the standard Cauchy Born rule and consistency of the molecular structure with the standard finite element geometries. The conventional Cauchy-Born rule cannot be directly used due to the non–crystalline microstructure of the material. A remedy is proposed based on the meshfree techniques by constructing a continuous atomic deformation field from the imposed macro deformation gradient. The resultant deformation gradient and the stress field remain consistent in micro scales. In addition, a genetic algorithm-based method, which has less sensitivity to the choice of initial point and number of parameters, is adopted for the maximization of the entropy function. The silicon amorphous structure is considered for MD simulations. It is obtained by quenching from a melted sample. The MD-obtained structure is further analyzed and the predicted displacements and stress contours, as well as the density and radial distribution functions are examined to assess the state of the material. Then, the proposed meshfree technique is applied to construct the continuous form of the deformation gradient on the MD model to improve the accuracy of the solution. The proposed concurrent multiscale method is verified and then employed to simulate an amorphous silicon specimen. Finally, the effects of sample size, strain rate and quenching speed on rupture stress and strain in different 3D tensile simulations are investigated by the proposed multiscale method.