Development of constitutive relation for multiscale modeling of carbon fiber reinforced polymer composites under uncertainty
This dissertation presents development of constitutive relations for progressive damage analysis of laminated composites and efficient computational implementation of a multiscale computational framework. All the numerical studies presented in this dissertation consider quasi-static tensile and compressive loadings. A continuum damage mechanics-based constitutive model for the constituent materials contained in a unidirectional carbon fiber reinforced polymer composite material is presented. The model is formulated to be consistent with the thermodynamics theory of material damage. All model parameters are directly calibrated using experimental data and are updated to monitor the evolution of damage as a function of the strain state. Although quality control techniques are utilized by manufacturers, composite materials entail variability in both the constituent materials as well as the involved processes. In addition to variability, a mechanics-based computational model also has epistemic uncertainty due to lack of knowledge about model parameters, model form and solution errors. In this study the epistemic uncertainty is quantified with respect to model parameters. Furthermore, a multiscale crack band model is proposed to alleviate spurious mesh size dependence in the application of the constitutive model. The formulation and dissipated energy regularization within the multiscale modeling framework is considered. Improvement in computational cost of the microscale analysis is achieved by efficient use of parallel computing tools.