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Communication Dans Un Congrès Année : 2023

Sensitivity with respect to uncertainties of a particle-based homogeneous and isotropic second-gradient continuum model

Gabriele La Valle
B.E. Abali
  • Fonction : Auteur

Résumé

Particle-based models cover a wide range of applications. Among the others, particle-based models can be adapted to simulate the mechanical behavior of specific biological systems such as cell aggregates, describe certain biomaterials used in tissue engineering and regenerative medicine, and develop implants in ceramics or granular composites that can be used in dental materials. This study focuses on the stochastic modeling of the geometric and constitutive microscale parameters related to the interactions between particles in a particle-based material. Specifically, the research aims to incorporate these parameters into an existing granular second-gradient model [1]. To tackle this task, a probabilistic approach based on the Maximum entropy (MaxEnt) principle derived from Information Theory is employed and the strategy used by [2] in the field of classic elasticity is adopted. After defining and enhancing the selected granular second-gradient continuum model, it is demonstrated that, in the case of homogeneous and isotropic materials, the microscale parameters involved are statistically independent. Specifically, the distance between two consecutive particles in a particle-pair follows a uniform distribution, while the specific microscale stiffness parameters follow a Gamma distribution. To illustrate this concept, a 2D concrete plate is considered, subjected to an axial load. A stochastic solver based on Monte Carlo (MC) numerical simulation is employed, and its convergence is examined. Furthermore, the propagation of uncertainties is discussed, revealing that the statistical fluctuations in the macro mechanical response are significant. [1] Misra, A., Placidi, L., dell’Isola, F., Barchiesi, E., 2021. Identification of a geometrically nonlinear micromorphic continuum via granular micromechanics. Zeitschrift für angewandte Mathematik und Physik 72, 1–21. [2] Guilleminot, J., Soize, C., 2013. On the statistical dependence for the components of random elasticity tensors exhibiting material symmetry properties. Journal of Elasticity 111, 109–130.
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Dates et versions

hal-04129267 , version 1 (15-06-2023)

Identifiants

  • HAL Id : hal-04129267 , version 1

Citer

Gabriele La Valle, B.E. Abali, Giovani Falsone, Christian Soize. Sensitivity with respect to uncertainties of a particle-based homogeneous and isotropic second-gradient continuum model. Workshop Mathematical modelling in biology and medicine, May 2023, Arpino, Italy. ⟨hal-04129267⟩
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