Search

Artificial Neural Networks (NNWs) are appealing functions to substitute high dimensional and non-linear history-dependent problems in computational mechanics since they offer the possibility to drastically reduce the computational time. This feature has recently been exploited in the context of multi-scale simulations, in which the NNWs serve as surrogate model of micro-scale finite element resolutions. Nevertheless, in the literature, mainly the macro-stress-macro-strain response of the meso-scale boundary value problem was considered and the micro-structure information could not be recovered in a so-called localization step. In this work, we develop Recurrent Neural Networks (RNNs) as surrogates of the RVE response while being able to recover the evolution of the local micro-structure state variables for complex loading scenarios. The main difficulty is the high dimensionality of the RNNs output which consists in the internal state variable distribution in the micro-structure. We thus propose and compare several surrogate models based on a dimensionality reduction: i) direct RNN modeling with implicit NNW dimensionality reduction, ii) RNN with PCA dimensionality reduction, and iii) RNN with PCA dimensionality reduction and dimensionality break down, i.e. the use of several RNNs instead of a single one. Besides, we optimize the sequential training strategy of the latter surrogate for GPU usage in order to speed up the process. Finally, through RNN modeling of the principal components coefficients, the connection between the physical state variables and the hidden variables of the RNN is revealed, and exploited in order to select the hyper-parameters of the RNN-based surrogate models in their design stage.

In the modelling process of cardiovascular diseases, one often comes across the numerical simulation of the blood vessel wall. When the vessel geometry is patient-specific and is obtained in vivo via medical imaging, the stress distribution throughout the vessel wall is unknown. However, simulating the full physiological pressure load inside the blood vessel without incorporating the in vivo stresses will result in an inaccurate stress distribution and an incorrect deformation of the vessel wall. In this work a computational method is formulated to restore the zero-pressure geometry of patient-specific blood vessels, and to recover the in vivo stress field of the loaded structures at the moment of imaging. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations. As only an update of the mesh is required, the formulation of this method allows for a straightforward implementation in combination with existing structural solvers, even if the structural solver is a black box.

The macroscopic behavior of complex heterogeneous materials is strongly governed by the interactions between their elementary constituents within their microstructure. Beside experimental efforts characterizing the behaviors of such materials, there is growing interest, in view of the increasing computational power available, in building models representing their microstructural systems integrating the elementary behaviors of their constituents and their geometrical organization. While a large number of contributions on this aspect focus on the investigation of advanced physics in material parameter studies using rather simple geometries to represent the spatial organization of heterogeneities, few are dedicated to the exploration of the role of microstructural geometries by means of morphological parameter studies.The critical ingredients of this second type of investigation are (I) the generation of sets of representative volume elements ( RVE ) describing the geometry of microstructures with a satisfying control on the morphology relevant to the material of interest and (II) the discretization of governing equations of a model representing the investigated physics on those RVEs domains. One possible reason for the under-representation of morphologically detailed RVEs in the related literature may be related to several issues associated with the geometrical complexity of the microstructures of considered materials in both of these steps. Based on this hypothesis, this work is aimed at bringing contributions to advanced techniques for the generation and discretization of microstructures of complex heterogeneous materials, focusing on geometrical issues. In particular, a special emphasis is put on the consistent geometrical representation of RVEs across generation and discretization methodologies and the accommodation of a quantitative control on specific morphological features characterizing the microstructures of the covered materials.While several promising recent techniques are dedicated to the discretization of arbitrary complex geometries in numerical models, the literature on RVEs generation methodologies does not provide fully satisfying solutions for most of the cases. The general strategy in this work consisted in selecting a promising state-of-the-art discretization method and in designing improved RVE generation techniques with the concern of guaranteeing their seamless collaboration. The chosen discretization technique is a specific variation of the generalized / extended finite element method that accommodates the representation of arbitrary input geometries represented by level set functions. The RVE generation techniques were designed accordingly, using level set functions to define and manipulate the RVEs geometries. The RVE methodologies developed are mostly morphologically motivated, incorporating governing parameters allowing the reproduction and the quantitative control of specific morphological features of the considered materials. These developments make an intensive use of distance fields and level set functions to handle the geometrical complexity of microstructures. Valuable improvements were brought to the RVE generation methodologies for several materials, namely granular and particle-based materials, coated and cemented geomaterials, polycrystalline materials, cellular materials and textile-based materials. RVEs produced using those developments have allowed extensive testing of the investigated discretization method, using complex microstructures in proof-of-concept studies involving the main ingredients of RVE-based morphological parameter studies of complex heterogeneous materials. In particular, the illustrated approach offers the possibility to address three crucial aspects of those kinds of studies: (I) to easily conduct simulations on a large number of RVEs covering a significant range of morphological variations for a material, (II) to use advanced constituent material behaviors and (III) to discretize large 3D RVEs. Based on those illustrations and the experience gained from their realization, the main strengths and limitations of the considered discretization methods were clearly identified., Doctorat en Sciences de l'ingénieur, info:eu-repo/semantics/nonPublished