MAP123: A data-driven approach to use 1D data for 3D nonlinear elastic materials modeling

Solving three-dimensional boundary-value engineering problems numerically requires material laws. However, it is difficult to build the material laws in three dimension, since the material behaviors are usually measured by one-dimensional uniaxial tension/compression experiments. In this way, the material behavior in the three-dimension is ‘compressed’ into one-dimensional data. Here we propose a new method, coined MAP123 (map data from one-dimension to three-dimension), to decompress the one-dimensional data into three dimension for nonlinear elastic material modeling without the construction of analytic mathematical function for the material law. The decomposition of stress and strain into deviatoric and spherical parts for isotropic nonlinear elastic materials at finite deformation makes this data-driven approach work quite well. Several examples are used to demonstrate the capability of MAP123, such as a rectangular plate with a circular hole under uniaxial tension. Corresponding experiments are also carried out to further verify the MAP123 method. Based on the proposed approach, uniaxial experiment is suggested to measure the deformation in three directions not only the force and extension along the loading direction. Limitation of the proposed MAP123 approach is also discussed.