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Second-Order Homogenization of BCC Lattice Structures to Strain-Gradient Continuum with the Aid of Machine Learning

Taghizadeh, Sina | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56956 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen
  7. Abstract:
  8. Engineering of properties was previously not possible. With the advent of additive manufacturing, it became possible to produce structures with architected microstructures, known as lattice structures. The popularity of these structures, due to their lightweight and tunable properties, has increased the importance of their optimal mechanical analysis. Since direct analysis of these structures is computationally prohibitive due to their high level of detail, homogenization methods have been proposed as an alternative. Since these methods couldn't capture size effects, higher-order homogenization methods were introduced. However, despite their good accuracy, these methods are still rarely used in industry. Therefore, this research aims to facilitate the use of these methods by employing machine learning techniques. To this end, the present study proposes a surrogate model for BCC lattice structures with a linear elastic, homogeneous, and isotropic constituent material under small deformations. The model takes as input the overall dimensions and strut radius of the BCC structure, as well as the Young's modulus and Poisson's ratio of the constituent material, and outputs the equivalent tensors in a fraction of a second. In this model, the relations between the overall dimensions and Young's modulus of the structure and the equivalent tensors are found analytically. To find the relations between the strut radius and Poisson's ratio and the equivalent tensors, a database is generated and machine learning methods are employed. The required database is generated through repeated simulations of the second-order homogenization problem, and the training process of the predictive model is performed using nonlinear polynomial functions. Finally, the final model is verified and an error of about 1% is observed for most of its influential parameters. A comparison with direct solution shows that the second-order homogenization method based on the proposed model also has acceptable accuracy, with an error of 0.62% compared to direct solution, while the error of classical homogenization was 7.02%
  9. Keywords:
  10. Size Effect ; Machine Learning ; Body Center Cubic (BCC)Lattice Structures ; Asymptotic Homogenization ; Second-Order Homogenization ; Optimal Mechanical Analysis ; Gradient-Based Equivalent Continuum

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