Derivation of the Orthotropic Nonlinear Elastic Material Law Driven by Low-Cost Data (DDONE)

Orthotropic nonlinear elastic materials are common in nature and widely used by various industries. However, there are only limited constitutive models available in today's commercial software (e.g., ABAQUS, ANSYS, etc.) that adequately describe their mechanical behavior. Moreover, the material parameters in these constitutive models are also difficult to calibrate through low-cost, widely available experimental setups. Therefore, it is paramount to develop new ways to model orthotropic nonlinear elastic materials. In this work, a data-driven orthotropic nonlinear elastic (DDONE) approach is proposed, which builds the constitutive response from stress–strain data sets obtained from three designed uniaxial tensile experiments. The DDONE approach is then embedded into a finite element (FE) analysis framework to solve boundary-value problems (BVPs). Illustrative examples (e.g., structures with an orthotropic nonlinear elastic material) are presented, which agree well with the simulation results based on the reference material model. The DDONE approach generally makes accurate predictions, but it may lose accuracy when certain stress–strain states that appear in the engineering structure depart significantly from those covered in the data sets. Our DDONE approach is thus further strengthened by a mapping function, which is verified by additional numerical examples that demonstrate the effectiveness of our modified approach. Moreover, artificial neural networks (ANNs) are employed to further improve the computational efficiency and stability of the proposed DDONE approach.