Multiscale Progressive Damage and Nonlinear Analysis of Composite Materials and Structures

This dissertation first presents a multiscale progressive damage analysis framework for composite materials and structures based on the mechanics of structure genome (MSG) theory. MSG is a multiscale theory that provides a unified approach to link microscale behaviors with the macroscopic responses, ensuring optimal local stress field recovery through the principle of information loss. The theory is particularly effective for dimensionally reducible structures such as beams and plates. In the proposed framework, continuum damage mechanics is employed to model the damage evolution in the constituents at the microscale. The damage model features separate damage variables for matrix and fiber in tension and compression to capture the distinct failure mechanisms. Mesh objectivity is achieved using the crack band model. The effectiveness of the developed approach is demonstrated through several numerical examples, including the strength prediction of unnotched and open-hole composite laminates. The results show good agreement with experimental data. The developed multiscale damage analysis framework provides an accurate and efficient tool for progressive failure analysis and strength prediction of composite structures. 

The framework is also extended to model the elastoplastic behavior of Composites, addressing the limitations inherent in existing approaches. The proposed method incorporates nonlinear hardening laws and leverages the multiscale capabilities of MSG, enabling accurate prediction of nonlinear elastoplastic stress-strain behavior. To better represent the nonlinear behavior of the matrix, a multi-linear hardening law is employed. The model is calibrated through a systematic approach that combines experimental data and multiscale simulations. Validation of the proposed method is conducted through comparisons with both experimental data and high-fidelity direct numerical simulations. The results exhibit excellent agreement with experimental observations. These findings demonstrate that the MSG-based elastoplastic method provides a robust and reliable tool for analyzing and designing composite structures that undergo nonlinear deformation.

Additionally, a new machine learning model, the Numerical Regression Transformer (NRT), is developed to enhance the efficiency in composite design. This model supports both forward and inverse predictions within a single trained model. By employing a specialized embedding technique and a strategic two-phase training approach, the model effectively maps constituent properties and microstructure parameters with composite properties. The NRT model can simultaneously predict material properties from design parameters and determine optimal design parameters for desired composite properties. Validation results show excellent accuracy in forward prediction tasks, with correlation coefficients above 0.99, while inverse design performance varies based on the number of unknown parameters. This approach significantly enhances design efficiency by enabling rapid exploration of design spaces and parameter sensitivity analysis through a single trained model.

The ultimate goal of this research is to develop an accurate, efficient, and versatile computational framework for the progressive damage and nonlinear analysis of composite materials and structures. By integrating state-of-the-art modeling techniques and machine learning algorithms, this study aims to accelerate the development and adoption of composite technologies across various industries.