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Homogenization
Published in Georgios A. Drosopoulos, Georgios E. Stavroulakis, Nonlinear Mechanics for Composite Heterogeneous Structures, 2022
Georgios A. Drosopoulos, Georgios E. Stavroulakis
More recently, an asymptotic homogenization approach is applied in [177] to the equations describing the dynamic response of heterogeneous materials with evolving micro-structures, depicting an hyperelastic behaviour. A second-order reduced asymptotic homogenization scheme is developed in [75], to capture the non-linear response of heterogeneous materials with large periodic microstructure. In [193] a reduced-order asymptotic expansion homogenization technique is proposed, for the simulation of the inelastic, damaged behaviour of heterogeneous materials.
A novel stiffness prediction method with constructed microscopic displacement field for periodic composite plates
Published in Mechanics of Advanced Materials and Structures, 2023
Yahe Gao, Zhiwei Huang, Yufeng Xing
For the equivalent property prediction of periodic composite structures, the Asymptotic Homogenization Method (AHM) [1–4] is one of the widely used homogenization methods with rigorous mathematical foundations. However, the AHM faces challenges when dealing with composite plates. This is because the omnidirectional periodicity assumption, which is very crucial for the establishment of the AHM [5], is generally not satisfied for plate-like structures with fewer unit cells in the thickness direction. Many studies [6–8] on the cell size effects have also validated the limitations of this homogenization method. To improve the performance at low-scale separation ratios, higher-order expansion terms were considered [9, 10]. Besides, relieving periodicity in the thickness direction, being consistent with the real free-traction boundaries of unit cell problems, has been proved important [11].
A hierarchical asymptotic homogenization approach for viscoelastic composites
Published in Mechanics of Advanced Materials and Structures, 2021
Oscar Luis Cruz-González, Ariel Ramírez-Torres, Reinaldo Rodríguez-Ramos, Raimondo Penta, Julián Bravo-Castillero, Raúl Guinovart-Díaz, José Merodio, Federico J. Sabina, Frederic Lebon
A general methodology in the use of the three-scale Asymptotic Homogenization Method (AHM) is considered for modeling non-aging, quasi-periodic, hierarchical and linear viscoelastic composite materials. The present work takes into account the stratified functions in the homogenization procedure allowing the study with more general periodic structures. The analytical solution for the local problems and the expressions of the effective coefficients for hierarchical laminated composites with anisotropic components and perfect contact at the interfaces are derived. Also, the interconnection between the effective relaxation modulus and the effective creep compliance is performed. The approach is applied to study the overall viscoelastic behavior of the dermis. The results shown in Table 3 and Figure 3 could have a special interest in clinical applications, for instance, in the study of the epidural anesthesia procedure and in the development of haptic devices used in surgical operations. Its study is important in order to provide a location as accurate as possible for the insertion of the needle and the mechanical response of the skin (see Ref. [44]). The results can be used in the automation of the needle insertion procedure (see Ref. [45]).
Relating mechanical properties of vertebral trabecular bones to osteoporosis
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2020
R. Cesar, J. Bravo-Castillero, R. R. Ramos, C. A. M. Pereira, H. Zanin, J. M. D. A. Rollo
The asymptotic homogenization technique presented here is based on (Galka et al. 1999). The method of asymptotic homogenization it is a mathematical technique for investigating macroscopic behavior of periodic heterogeneous media (Papanicolau et al. 1978; Sanchez-Palencia 1980; Bakhvalov and Panasenko 1989; Oleinik et al. 1992). The method allows transform equations with periodic and rapidly oscillating coefficients in equations with constants coefficients. Such coefficients, which are called the effective coefficients, characterize the macroscopic properties of a homogeneous medium “equivalent” to the original heterogeneous medium. From a mathematical point of view, the “equivalence” means that the solution of the original problem converges to the solution of the homogenized problem as the microstructure period goes to zero.