Anisotropic nonlinear elasticity in a spherical bead pack: influence of the fabric anisotropy

Stress-strain measurements and ultrasound propagation experiments in glass bead packs have been simultaneously conducted to characterize the stress-induced anisotropy under uniaxial loading. These measurements, realized respectively with finite and incremental deformations of the granular assembly, are analyzed within the framework of the effective medium theory based on the Hertz-Mindlin contact theory. Our work shows that both compressional and shear wave velocities and consequently the incremental elastic moduli agree fairly well with the effective medium model by Johnson et al. [J. Appl. Mech. 65, 380 (1998)], but the anisotropic stress ratio resulting from finite deformation does not at all. As indicated by numerical simulations, the discrepancy may arise from the fact that the model doesn't properly allow the grains to relax from the affine motion approximation. Here we find that the interaction nature at the grain contact could also play a crucial role for the relevant prediction by the model; indeed, such discrepancy can be significantly reduced if the frictional resistance between grains is removed. Another main experimental finding is the influence of the inherent anisotropy of granular packs, realized by different protocols of the sample preparation. Our results reveal that compressional waves are more sensitive to the stress-induced anisotropy, whereas the shear waves are more sensitive to the fabric anisotropy, not being accounted in analytical effective medium models.Comment: 9 pages, 8 figure

Resource Allocation Framework: Validation of Numerical Models of Complex Engineering Systems against Physical Experiments

An increasing reliance on complex numerical simulations for high consequence decision making is the motivation for experiment-based validation and uncertainty quantification to assess, and when needed, to improve the predictive capabilities of numerical models. Uncertainties and biases in model predictions can be reduced by taking two distinct actions: (i) increasing the number of experiments in the model calibration process, and/or (ii) improving the physics sophistication of the numerical model. Therefore, decision makers must select between further code development and experimentation while allocating the finite amount of available resources. This dissertation presents a novel framework to assist in this selection between experimentation and code development for model validation strictly from the perspective of predictive capability. The reduction and convergence of discrepancy bias between model prediction and observation, computed using a suitable convergence metric, play a key role in the conceptual formulation of the framework. The proposed framework is demonstrated using two non-trivial case study applications on the Preston-Tonks-Wallace (PTW) code, which is a continuum-based plasticity approach to modeling metals, and the ViscoPlastic Self-Consistent (VPSC) code which is a mesoscopic plasticity approach to modeling crystalline materials. Results show that the developed resource allocation framework is effective and efficient in path selection (i.e. experimentation and/or code development) resulting in a reduction in both model uncertainties and discrepancy bias. The framework developed herein goes beyond path selection in the validation of numerical models by providing a methodology for the prioritization of optimal experimental settings and an algorithm for prioritization of code development. If the path selection algorithm selects the experimental path, optimal selection of the settings at which these physical experiments are conducted as well as the sequence of these experiments is vital to maximize the gain in predictive capability of a model. The Batch Sequential Design (BSD) is a methodology utilized in this work to achieve the goal of selecting the optimal experimental settings. A new BSD selection criterion, Coverage Augmented Expected Improvement for Predictive Stability (C-EIPS), is developed to minimize the maximum reduction in the model discrepancy bias and coverage of the experiments within the domain of applicability. The functional form of the new criterion, C-EIPS, is demonstrated to outperform its predecessor, the EIPS criterion, and the distance-based criterion when discrepancy bias is high and coverage is low, while exhibiting a comparable performance to the distance-based criterion in efficiently maximizing the predictive capability of the VPSC model as discrepancy decreases and coverage increases. If the path selection algorithm selects the code development path, the developed framework provides an algorithm for the prioritization of code development efforts. In coupled systems, the predictive accuracy of the simulation hinges on the accuracy of individual constituent models. Potential improvement in the predictive accuracy of the simulation that can be gained through improving a constituent model depends not only on the relative importance, but also on the inherent uncertainty and inaccuracy of that particular constituent. As such, a unique and quantitative code prioritization index (CPI) is proposed to accomplish the task of prioritizing code development efforts, and its application is demonstrated on a case study of a steel frame with semi-rigid connections. Findings show that the CPI is effective in identifying the most critical constituent of the coupled system, whose improvement leads to the highest overall enhancement of the predictive capability of the coupled model

Reduced Order Numerical Modeling for Calibration of Complex Constitutive Models in Powder Pressing Simulations

Numerical simulations of different ceramic production phases often involve complex constitutive models, with difficult calibration process, relying on a large number of experiments. Methodological developments, proposed in present paper regarding this calibration problem can be outlined as follows: assessment of constitutive parameters is performed through inverse analysis procedure, centered on minimization of discrepancy function which quantifies the difference between measurable quantities and their computed counterpart. Resulting minimization problem is solved through genetic algorithms, while the computational burden is made consistent with constraints of routine industrial applications by exploiting Reduced Order Model (ROM) based on proper orthogonal decomposition. Throughout minimization, a gradual enrichment of designed ROM is used, by including additional simulations. Such strategy turned out to be beneficial when applied to models with a large number of parameters. Developed procedure seems to be effective when dealing with complex constitutive models, that can give rise to non-continuous discrepancy function due to the numerical instabilities. Proposed approach is tested and experimentally validated on the calibration of modified Drucker-Prager CAP model, frequently adopted for ceramic powder pressing simulations. Assessed values are compared with those obtained by traditional, time-consuming tests, performed on pressed green bodies

Reduced Order Numerical Modeling for Calibration of Complex Constitutive Models in Powder Pressing Simulations

Numerical simulations of different ceramic production phases often involve complex constitutive models, with difficult calibration process, relying on a large number of experiments. Methodological developments, proposed in present paper regarding this calibration problem can be outlined as follows: assessment of constitutive parameters is performed through inverse analysis procedure, centered on minimization of discrepancy function which quantifies the difference between measurable quantities and their computed counterpart. Resulting minimization problem is solved through genetic algorithms, while the computational burden is made consistent with constraints of routine industrial applications by exploiting Reduced Order Model (ROM) based on proper orthogonal decomposition. Throughout minimization, a gradual enrichment of designed ROM is used, by including additional simulations. Such strategy turned out to be beneficial when applied to models with a large number of parameters. Developed procedure seems to be effective when dealing with complex constitutive models, that can give rise to non-continuous discrepancy function due to the numerical instabilities. Proposed approach is tested and experimentally validated on the calibration of modified Drucker-Prager CAP model, frequently adopted for ceramic powder pressing simulations. Assessed values are compared with those obtained by traditional, time-consuming tests, performed on pressed green bodies