An Inverse Computational Approach for the Identification of the Parameters of the Constitutive Model for Damaged Ceramics Subjected to Impact Loading

Abstract

In the present study, a computational method was developed, validated and applied for the determination of parameters of a constitutive model for a ceramic material. An optimization algorithm, based on a direct search method, was applied to the determination of the load-displacement response of the specimen, and for the identification of the parameters of the constitutive model.A one-dimensional nonlinear initial-boundary value problem of wave propagation in a composite bar made of dissimilar materials was formulated and solved numerically. Convergence of the numerical scheme was studied, and range of convergence was established. Numerical scheme was validated for a number of benchmark problems with known analytical solutions, and for the problems solved using finite element method. Investigation of the accuracy of the displacement and strain responses was conducted; known limitations of the Kolsky's method for split Hopkinson pressure bar were revealed. For numerical examples considered in the present study, comparison of performance of the optimized finite-difference solver and of the finite element code LS-DYNA showed that the finite-difference code is about 10 times faster.Developed method and solutions were applied for the identification of the parameters of the Johnson-Holmquist constitutive model for five sets of experimental data for aluminum oxide AD995. Results of analysis revealed significant sensitivity of stress response to variation of fractured strength model parameters and damage model parameters.For the determined values of parameters, detailed parametric study of stress field, damage accumulation, and velocity field, was conducted with the help of the finite element method.It was found that the accuracy of the simulation using the JH-2 constitutive model changes with the rate of damage accumulation in the ceramic material.The damage patterns and history of damage development, obtained numerically, agreed qualitatively with the fracture history and its patterns, observed in the recovered Macor ceramics available in the literature.A method for image analysis of the photographic images of the lateral sides of the recovered specimen was proposed. It was used to quantify density of the damage in the specimen and to establish a better integral approach to predict amount of damage inside the specimen.