## RVE Analysis vs Mechanics of Structure Genome

RVE analysis is a popular method for micromechanical modeling of heterogeneous materials. It can be used to perform a homogenization analysis to obtain effective properties and it can also be used to perform a dehomogenization analysis to obtain the local fields and failure of the material. Its popularity is mainly due to the maturity and acceptance of commercial finite element software. Various boundary conditions (BCs) can be used for the RVE analysis as long as they satisfy the Hill-Mandel macrohomogeneity condition. The three common types of BCs are: kinematically uniform BCs (KUBCs), statically uniform BCs (SUBCs), and periodic BCs (PBCs). Both KUBCs and SUBCs are fairly easy to apply. PBCs can be applied using coupled equation constraints. It has been shown that KUBCs provide the upper bound, SUBCs provide the lower bound. With the increase of RVE size, these two types of BCs will converge to the results computed using PBCs. In other words, PBCs are the best BCs to be used for RVE analysis unless the one or more dimensions of the RVE are the same as the macro structural dimension such as laminate made of one woven fabric through the thickness. In this case traction free BCs should be used on the top and bottom surfaces and PBCs should be used for the boundary surfaces along the in-plane directions. Applying PBCs rigorously requires paired nodes on the corresponding surfaces which is not easy to generate, particularly for irregular microstructures. RVE analysis usually requires a 3D domain to obtain 3D properties and local fields. If a 2D RVE is used, only 2D properties and local fields are obtained. To obtain the complete set of properties, multiple analysis is needed. For example, to obtain the complete stiffness matrix, six 3D RVE analyses are needed. To perform dehomogenization, another analysis is needed based on the global information.

The recently discovered mechanics of structure genome (MSG), when specialized to 3D structures, can provide a general-purpose micromechanics theory for predicting the effective properties and local fields of heterogeneous materials. MSG carries out homogenization/dehomogenization analysis over structure genome (SG) which is defined to be the smallest mathematical building block of the material.

MSG is more versatile than the RVE analysis. MSG can handle all materials: periodic, partially periodic or aperiodic materials and material with arbitrary shapes while RVE must have straight edges. MSG uses a finite element mesh to describe the microstructure which enjoys the same versatility of the finite element method for geometry modeling.

MSG is much more efficient than the RVE analysis. First, for heterogeneous materials made of layer microstructure such as composite laminates, MSG only needs to perform ONE 1D analysis to compute all 3D properties and local fields. For heterogeneous materials featuring 2D heterogeneity such as unidirectional fiber reinforced composites, MSG only needs to perform ONE 2D analysis to compute all 3D properties and local fields. Even for materials featuring 3D heterogeneity such as particle reinforced composites, MSG only needs to perform ONE 3D analysis to obtain all 3D properties and local fields. For dehomogenization, MSG only performs simple matrix multiplications without resolving the linear system. Hence, if RVE analysis and MSG uses the same mesh, MSG is at least six times faster in theory. Moreover, because MSG is a semi-analytical method, it computes material properties directly without computing stress/strain fields first. Significant reduction in computing time and modeling complexity is possible without losing accuracy comparing to the RVE analysis.

MSG is much simpler to use. Because one does not have to apply BCs in terms of displacements/tractions. No preprocessing and/or postprocessing are needed. All it requires is a finite element mesh, then the properties and local fields are just one click away. MSG is implemented in a general-purpose multiscale modeling code called SwiftComp. It can be freely launched in the cloud at https://cdmhub.org/resources/scstandard. In other words, one can run a super-efficient "RVE analysis" on any devices including smart phones and tablets connected to Internet via a browser. Various GUIs are available for users to choose from including Gmsh, TexGen, ANSYS, ABAQUS, and NASTRAN, all of which are freely available on cdmHUB.org to anybody.

MSG also provides a systematic and straightforward approach for computing equivalent structural properties for beams, plates, and shells. It is not trivial to use RVE analysis to do so. Some carefully crafted boundary conditions are needed for RVE analysis.

### Comments on this entry

1. Dear Dr. Wenbin Yu,

I'm trying to use ABAQUS-Swiftcomp GUI to obtain homogenised RVE properties. It is my first use, and I'm happy with the ABAQUS interface and processing time, in addtion, matrix construction.

I used RVE method with periodic boundary conditions, Chamis equations (rule of mixture as a ref. point) will give relative results. On the other hand, with Swiftcomp, the results are:

• Consistent with the above methods for E1, but significantly different for E2 and E3 (when using Hex elements);
• Consistent in E2 and E3, but 50% less for E1 (when using Tet elements).

Kindly note that I did not use and special type elements. My RVE is set to be periodic, 3D.

Any advice would be great.

Thank you in advance…

Best regards