PARAMETRICALLY HOMOGENIZED CONTINUUM DAMAGE MECHANICS (PHCDM) MODELS FOR UNIDIRECTIONAL FIBER-REINFORCED COMPOSITES
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Fiber reinforced composites are widely used in aerospace, energy, protective armors and other applications that require materials with high strength-to-weight ratios, impact resistance, durability, etc. Damage in such heterogeneous materials exhibits multi-scale phenomena across various length scales – microscopic damage mechanisms such as fiber-matrix interfacial debonding and micro-cracking in matrix phase subsequently lead to macroscopic failure behaviors such as structural stiffness degradation and crack propagation. The multi-scale phenomena in heterogeneous materials make their macroscopic constitutive behaviors strongly influenced by the corresponding microstructures. Understanding and modeling such microstructure-dependent material constitutive behaviors are of great importance for improving structural performance through the material design process. However, due to the prohibitive computational cost associated with explicit representation of microstructural details, the microstructural effects on structural performance are often ignored in engineering practice. In order to realize the microstructural effects during structural scale analysis, it is imperative to develop computationally efficient, microstructure-integrated multi-scale constitutive models. The Parametrically Homogenized Continuum Damage Mechanics (PHCDM) models are developed in this dissertation for such purpose. They are thermodynamically consistent, reduced order constitutive models with coefficients that are explicit functions of microstructural descriptors and evolving material damage variables. The microstructural descriptors, which characterize important microscopic features that affect macroscopic material responses, are strategically determined and optimally expressed as representative aggregated microstructural parameters or RAMPs. The functional representation of PHCDM coefficients in terms of RAMPs and evolving material damage variables are obtained by physics-informed machine learning operating on a microstructural response database created from detailed micromechanical simulations. The developed PHCDM models exhibit high accuracy and significant computational efficiency compared with conventional homogenized micromechanical (HMM) approaches. The microstructure-integrated PHCDMs can be easily implemented via user-interface (UMAT/VUMAT) in any FEM code for analyzing damage responses in composite structures across multiple material length scales. These capabilities make PHCDMs indispensable tools for understanding the multi-scale damage phenomena in composites and subsequent material-by-design process. Following similar framework, parametrically homogenized constitutive models (PHCMs) can be developed for other material systems as well.