This research work focuses on understanding structural morphologies at different scales and studying their mechanical behavior in the context of the development of topology optimization by the concern of creation and valuation of new porous and architectured materials in fields of industrial, aerospace, and even medical applications. We focused on developing a multi-scale modeling approach of porous and architectural structures allowing the production of the structure by Additive Manufacturing for aeronautical and medical applications.
Therefore, we demonstrated an approach based on 3D printing of structure production by displaying the numerical and experimental results in the aerospace and medical field. Firstly, we introduced the design stage of the CAD model equivalent for the designed turbine blade. By applying the method of Topology Optimization for finding the optimal density distribution of lattice structures and selecting the proposed technique for manufacturing the lattice structures. Numerical simulations have been carried out for gas turbine blades and obtaining the deformation and stress values under thermomechanical loads, present some results, and discuss them. On another hand, created a new design based on three lattice structures from triply periodic minimal surfaces (TPMS) with a different volume porosity to replace cancellous bone based on predicting the mechanical stiffness. Finally, present some results and their interpretations and discuss them.

Due to the high degree of randomness in the microstructure of real closed-cell foams, many reported numerical models in the literature are not able to capture precisely the local morphological features found in solid foams geometry. This is still the main impediment that restricts the investigation of this novel material and motivates the development of a sophisticated 3D solid model, which describes properly the complex geometry of real closed-cell foams. In this regard, this paper presents an original approach to generate a realistic and accurate 3D computational model of irregular closed-cell foams with relative density control and detailed finite element analysis of their mechanical performance under quasi-static loading up to densification. The solid model is constructed based on spherical particles inflation simulation. It resembles the real foams in terms of local features such as cell walls irregularities and thickness variation. The modeling approach was successfully
verified by comparing cell-morphological details of the generated models with those produced experimentally available in the literature and by the high-quality of obtained 3D printed models containing complex shapes and irregular cell wall thickness distribution. The evolution of spherical particles during the inflation process is analyzed based on finite element (FE) simulations. It was found that it can produce varying relative densities of foam due to the gradual decrease in the gap between the inflated particles, this makes the geometrical model of the foam suitable for studying the effect of local morphological characteristics on the mechanical performance of closed-cell foam material. To demonstrate that the compressive performance of the proposed closed-cell foam models can be controlled by relative density, 3D foam models were extracted from different inflation times and then subjected to quasi-static compression tests up to densification using the Abaqus software. The results confirm that the plateau stress can be expressed as a function of foam relative density, its accuracy is validated by comparing it to the closed-cell aluminum foam power law equation existing in the literature.
The new design method offers suitable numerical models for AM technology, plenty of experimental works on closed-cell foam can be reduced for engineering applications.

Lotus-type porous materials (LTPMs) are considered as a new category of engineering materials. They are porous materials characterized by long, straight, unidirectional cylindrical pores, and are obtained via unidirectional solidification from a melt under hydrogen and argon atmospheres. The anisotropic pore morphology of lotus-type materials results in the anisotropy of their mechanical and physical properties. This study aims at investigating the effect of cross-sectional pore shapes on the effective Young's modulus (EYM) of LTPMs. The representative volume element-based finite element homogenization method was used to compute the effective bulk and shear moduli. Subsequently, the EYM was deduced from the effective bulk and shear moduli. The numerical results of the circular pores were validated by comparing them with experimental results. Because the results indicated that the EYM is extremely sensitive to the variation in the pore shapes, a formula for estimating the EYM of LTPMs by considering the pore shapes was developed and validated.

The concept of equivalent morphology has received much consideration in recent decades. The importance of this concept is reflected in the fact that an inclusion of any morphology can be replaced by a circular one in simulation. If this concept is confirmed, it will facilitate the modeling and simulation of complex configuration microstructures.

To decide on this concept, an in–depth study is carried out in this work, trying to answer it in a clear and definitive way by trying to identify all the possible situations. For this the two types of composites, namely, periodic interpreted by an elementary cell and random interpreted by a Representative Volume Element (RVE) with 200 inclusions are considered. To be sure that the isotropy is provided by the RVE of the periodic microstructure, two types of elementary cells were treated: one circular and the other square. In order to cover all possible situations, the inclusion of the elementary cell is considered with several situations, centered position with different orientations at constant and random steps, random position with orientation at constant steps and random position and orientation at random steps. For each situation, the effective property is determined by the average of 20 cases are processed for elementary cells, while for the large RVE, the properties are obtained by a unit realization. To take into account the effect of contrast, two situations are considered, namely, rigid inclusion case and rigid matrix case. Several results are obtained and given in the conclusion.