NASA NTRS2014
It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).