Methods and systems for numerically simulating structural behaviors of embedded bi-materials are disclosed. At least first and second grid models are created independently for an embedded bi-material that contains an immersed material embedded entirely within a base material. First group of meshfree nodes represents the entire domain (i.e., base plus immersed materials). Second group of meshfree nodes represents the immersed or embedded material, which includes all interface nodes and nodes located within a space bordered by the material interface. Numerical structural behaviors of the embedded bi-material are simulated using the first and second set of meshfree nodes with a meshfree method that combines two meshfree approximations. The first meshfree approximation covers the first set of meshfree nodes and is based on properties of the base material, while the second meshfree approximation covers the second set of meshfree nodes and is based on a differential between the immersed and base materials.