Brittle structures, such as masonry buildings, present significant challenges in the digitalization of the mechanical problem due to the nonlinearities that arise under extreme loading conditions. Classical methods, like the Finite Element Method, struggle to accurately capture these nonlinear behaviors. The use of advanced theories such as peridynamics overcome these issues. The theory offers a more accurate and straightforward representation of material discontinuities and nonlinearities and do not require complex constitutive equations incorporating fracture mechanics; fracture emerges naturally from the restoring force formulation in the equations of motion. However, the computational complexity of peridynamics, especially when using ultra-high-fidelity models, can become prohibitive for practical applications. In response to these challenges, the authors propose an innovative approach that combines active learning techniques and computational mechanics to develop digital models with varying levels of fidelity. In the proposed work, optimal experimental design is used to adaptively select a set of parameters that maximize or minimize specific task objectives. This adaptive selection allows for efficient exploration of the parameters space, optimizing the use of computational resources. The ultra-high-fidelity model is used for a limited number of simulations, ensuring a high level of accuracy, while low-fidelity models, which are less accurate but much more efficient, are employed for a larger number of simulations. This process improves the predictive capabilities of the less detailed models, allowing for the correction of discrepancies and refinement of damage representation without resorting to costly large-scale simulations. In this way, a solution is generated that is both computationally efficient and accurate, capable of being used in practical applications for different purposes that need predicting damage distribution in masonry structures subjected to external loads.

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Optimal Experimental Design for Multi-fidelity Optimization in Peridynamic Models

  • Gaetano Miraglia,
  • Rosario Ceravolo

摘要

Brittle structures, such as masonry buildings, present significant challenges in the digitalization of the mechanical problem due to the nonlinearities that arise under extreme loading conditions. Classical methods, like the Finite Element Method, struggle to accurately capture these nonlinear behaviors. The use of advanced theories such as peridynamics overcome these issues. The theory offers a more accurate and straightforward representation of material discontinuities and nonlinearities and do not require complex constitutive equations incorporating fracture mechanics; fracture emerges naturally from the restoring force formulation in the equations of motion. However, the computational complexity of peridynamics, especially when using ultra-high-fidelity models, can become prohibitive for practical applications. In response to these challenges, the authors propose an innovative approach that combines active learning techniques and computational mechanics to develop digital models with varying levels of fidelity. In the proposed work, optimal experimental design is used to adaptively select a set of parameters that maximize or minimize specific task objectives. This adaptive selection allows for efficient exploration of the parameters space, optimizing the use of computational resources. The ultra-high-fidelity model is used for a limited number of simulations, ensuring a high level of accuracy, while low-fidelity models, which are less accurate but much more efficient, are employed for a larger number of simulations. This process improves the predictive capabilities of the less detailed models, allowing for the correction of discrepancies and refinement of damage representation without resorting to costly large-scale simulations. In this way, a solution is generated that is both computationally efficient and accurate, capable of being used in practical applications for different purposes that need predicting damage distribution in masonry structures subjected to external loads.