Uncertainty Quantification of Composite Laminate Damage with the Generalized Information Theory

This work presents a survey of five theories to assess the uncertainty of projectile impact induced damage on multi-layered carbon-epoxy composite plates. Because the types of uncertainty dealt with in this application are multiple (variability, ambiguity, and conflict) and because the data sets collected are sparse, characterizing the amount of delamination damage with probability theory alone is possible but incomplete. This motivates the exploration of methods contained within a broad Generalized Information Theory (GIT) that rely on less restrictive assumptions than probability theory. Probability, fuzzy sets, possibility, and imprecise probability (probability boxes (p-boxes) and Dempster-Shafer) are used to assess the uncertainty in composite plate damage. Furthermore, this work highlights the usefulness of each theory. The purpose of the study is not to compare directly the different GIT methods but to show that they can be deployed on a practical application and to compare the assumptions upon which these theories are based. The data sets consist of experimental measurements and finite element predictions of the amount of delamination and fiber splitting damage as multilayered composite plates are impacted by a projectile at various velocities. The physical experiments consist of using a gas gun to impact suspended plates with a projectile accelerated to prescribed velocities, then, taking ultrasound images of the resulting delamination. The nonlinear, multiple length-scale numerical simulations couple local crack propagation implemented through cohesive zone modeling to global stress-displacement finite element analysis. The assessment of damage uncertainty is performed in three steps by, first, considering the test data only; then, considering the simulation data only; finally, performing an assessment of total uncertainty where test and simulation data sets are combined. This study leads to practical recommendations for reducing the uncertainty and improving the prediction accuracy of the damage modeling and finite element simulation

Estimating the error in simulation prediction over the design space

This study addresses the assessrnent of accuracy of simulation predictions. A procedure is developed to validate a simple non-linear model defined to capture the hardening behavior of a foam material subjected to a short-duration transient impact. Validation means that the predictive accuracy of the model must be established, not just in the vicinity of a single testing condition, but for all settings or configurations of the system. The notion of validation domain is introduced to designate the design region where the model's predictive accuracy is appropriate for the application of interest. Techniques brought to bear to assess the model's predictive accuracy include test-analysis coi-relation, calibration, bootstrapping and sampling for uncertainty propagation and metamodeling. The model's predictive accuracy is established by training a metalnodel of prediction error. The prediction error is not assumed to be systcmatic. Instead, it depends on which configuration of the system is analyzed. Finally, the prediction error's confidence bounds are estimated by propagating the uncertainty associated with specific modeling assumptions

Model calibration and validation of an impact test simulation

This paper illustrates the methodology being developed at Los Alamos National Laboratory for the validation of numerical simulations for engineering structural dynamics. The application involves the transmission of a shock wave through an assembly that consists of a steel cylinder and a layer of elastomeric (hyper-foam) material. The assembly is mounted on an impact table to generate the shock wave. The input acceleration and three output accelerations are measured. The main objective of the experiment is to develop a finite element representation of the system capable of reproducing the test data with acceptable accuracy. Foam layers of various thicknesses and several drop heights are considered during impact testing. Each experiment is replicated several times to estimate the experimental variability. Instead of focusing on the calibration of input parameters for a single configuration, the numerical model is validated for its ability to predict the response of three different configurations (various combinations of foam thickness and drop height). Design of Experiments is implemented to perform parametric and statistical variance studies. Surrogate models are developed to replace the computationally expensive numerical simulation. Variables of the finite element model are separated into calibration variables and control variables, The models are calibrated to provide numerical simulations that correctly reproduce the statistical variation of the test configurations. The calibration step also provides inference for the parameters of a high strain-rate dependent material model of the hyper-foam. After calibration, the validity of the numerical simulation is assessed through its ability to predict the response of a fourth test setup