Towards Automated Determination of USERMAT for the Nonlinear Constitutive Behavior of Composites
Over the last 30 years NRL's Composite Materials and Structures (CMS) group has been developing a data driven system identification inverse approach for characterizing the constitutive behavior of polymer matrix composites (PMCs). The core concept in this approach has been the experimental identification of a dissipated energy density (DED) function. This is achieved through establishing a non-linear optimization scheme for determining the free coefficients of the sum of the basis functions that are used to construct the DED function and is based on the energy balance of the specimen under test. The method used was based on using massive amounts of experimental data that would be produced by exposing PMC specimens to multidimensional loading paths with the help of custom made multi-axial computer-controlled testing machines. The analytical and numerical implementation that has been followed up to now has been developed within various custom environments and this has been one of the main stumbling blocks in transferring this technology to end users in the design and material communities. Recent advances in finite element techniques and design optimization integration technologies along with the parallel hardware and software evolution have directed the CMS group to turn its attention to utilizing "of the shelf" technology of achieving the same goals. Thus, the “Z-mat” and "Z-Optim" packages from Northwest Numerics, Inc., have been utilized to extract the non-linear constitutive response from the available experimental data in an integrated and automated manner and in conjunction with the ANSYS/Mechanical infrastructure. The automation lies on the fact that the process automatically generates the code of a "USERMAT" subroutine that it can be subsequently used with any geometry and loading specification definable within the limits of ANSYS' non-linear element library. The geometry of the single notched specimen of NRL's In Plane has been used for developing and verifying the process.