Periodic boundary condition and its numerical implementation algorithm for the evaluation of effective mechanical properties of the composites with complicated micro-structures

Tian, Wenlong; Qi, Lehua; Chao, Xujiang; Ji, Liang; Fu, Ming

doi:10.1016/j.compositesb.2018.10.053

Cited by 127 publications

(37 citation statements)

References 26 publications

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“…The models were meshed using Hypermesh 13.0, and the detailed element parameters are listed in Table 1 . Numerical homogenization method was used to determine the mechanical properties of the thick and thin lamellae ( Vercher et al, 2014 ; Tian et al, 2019 ). Differences in mineral content among the four quadrants of the mid-femoral neck in the elderly and young models were considered in the modeling process.…”

Section: Methodsmentioning

confidence: 99%

A Comparative Study on the Multiscale Mechanical Responses of Human Femoral Neck Between the Young and the Elderly Using Finite Element Method

Cen

Gong

Liu

et al. 2022

Front. Bioeng. Biotechnol.

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Background: Femoral neck fracture (FNF) is the most serious bone disease in the elderly population. The multiscale mechanical response is a key to predicting the strength of the femoral neck, assessing the risk of FNF, and exploring the role of mechanosensation and mechanotransmission in bone remodeling, especially in the context of aging bone.Methods: Multiscale finite element (FE) models of the proximal femur for both young and elderly people were developed. The models included organ scale (proximal femur), tissue scale (cortical bone), tissue element scale (osteon), and cell scale [osteocyte lacuna-canalicular network (LCN) and extracellular matrix (ECM), OLCEM]. The mechanical responses of cortical bone and osteocytes in the mid-femoral neck and the differences in mechanical responses between these two scales were investigated.Results: The mechanical responses of cortical bone and osteocyte showed significant differences between the elderly and the young. The minimum principal strains and mean SEDs of cortical bone in the elderly were 2.067–4.708 times and 3.093–14.385 times of the values in the young, respectively; the minimum principal strains and mean SEDs of osteocyte in the elderly were 1.497–3.246 times and 3.044–12 times of the values in the young, respectively; the amplification factors of minimum principal strain in the inferior (Inf), anterior (Ant), and posterior (Post) quadrants in the young were 1.241–1.804 times of the values in the elderly, but the amplification factor of minimum principal strain in the superior (Sup) quadrant was 87.4% of the value in the elderly; the amplification factors of mean SED in the young were 1.124–9.637 times of the values in the elderly.Conclusion: The mass and bone mineral density (BMD) of cortical bone in the femoral neck is closely related to the mechanical response of osteocytes, which provides a new idea for improving cortical bone quality. Perhaps cortical bone quality could be improved by stimulating osteocytes. Quadrantal differences of bone quality in the mid-femoral neck should be considered to improve fracture risk prediction in the future.

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Section: Methodsmentioning

confidence: 99%

A Comparative Study on the Multiscale Mechanical Responses of Human Femoral Neck Between the Young and the Elderly Using Finite Element Method

Cen

Gong

Liu

et al. 2022

Front. Bioeng. Biotechnol.

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“…This approach was chosen because displacement boundary conditions cause a stiffer response due to all of the outer surfaces of the unit cell remaining flat [17]. For this reason, PBCs are commonly used for the micromechanical investigation of composite and porous materials [18][19][20][21]. These boundary conditions are achieved by constraining the displacement of opposite nodes of the unit cell:…”

Section: Unit Cellmentioning

confidence: 99%

Pressure and heat treatment of continuous fibre reinforced thermoplastics produced by fused filament fabrication

Handwerker

Wellnitz

Marzbani³

et al. 2022

Prog Addit Manuf

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Fused filament fabrication allows for the additive manufacturing of complex geometries without requiring moulds. However, due to large air voids and poor layer adhesion, the mechanical properties of parts manufactured using fused filament fabrication lag behind those of parts manufactured using conventional techniques. A previous study found that the tensile strength and Young’s modulus of such parts could be increased by a heat-treatment process. However, large air voids were still present after annealing. This study, therefore, investigates the influence of a post-pressure-treatment process on the mechanical performance and the air void ratio of continuous glass fibre-reinforced polyamide 6 in the directions perpendicular to the fibres. Without the treatment, Young’s modulus on the plane parallel to the printing bed is eight times higher than Young’s modulus perpendicular to it. Annealing at 1 MPa homogenises the material and leads to a significant increase of both the tensile strength (55 MPa) and Young’s modulus (5 GPa). Increasing the pressure to 3 MPa only slightly increases the mechanical performance, whereas a further increase to 6 MPa causes no significant changes.

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“…The use of periodic boundary conditions (PBCs) while calculating the mechanical response of damaged composites decreases the computational costs of numerical analysis when the damage patterns are periodic (Garoz et al, 2019;Jahanshahi et al, 2020;Tian et al, 2019). Based on this approach, it is possible to model a large system using data from a much smaller part which is called the representative volume element (RVE).…”

Section: Periodic Boundary Conditionsmentioning

confidence: 99%

A computational study about the effects of ply cracking and delamination on the stiffness reduction of damaged lamina and laminate

Ahmadi

Hajikazemi

Paepegem

2021

International Journal of Damage Mechanics

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Accurate prediction of stiffness degradation in the damaged plies (laminae) is a fundamental requirement for developing damage models for composite materials. In this study, a mesoscale analysis is proposed to predict all the effective thermo-elastic constants of damaged plies containing ply cracks and delaminations based on a numerical homogenization method. To do so, the in-plane and out-of-plane loading conditions are imposed on the three-dimensional representative volume elements (RVEs) using the periodic boundary conditions (PBCs). Considering the stress/strain fields obtained from the numerical simulations, the effective behavior of the damaged plies is evaluated. Moreover, the effects of various damage configurations, material properties, orientations of adjacent plies and ply thicknesses are studied to address the dependency of the effective elastic constants to those parameters. Numerical results reveal that the ply cracking and delaminations significantly reduce the in-plane and out-of-plane properties ([Formula: see text], [Formula: see text],[Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]) of the damaged plies. Furthermore, to demonstrate the accuracy and capability of the developed homogenization method, the homogenized properties of the damaged plies are used in the intact laminates where the stiffness of such laminates are compared with direct FE simulation and available experimental data of the laminates containing ply cracks and local delamination.

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Periodic boundary condition and its numerical implementation algorithm for the evaluation of effective mechanical properties of the composites with complicated micro-structures

Cited by 127 publications

References 26 publications

A Comparative Study on the Multiscale Mechanical Responses of Human Femoral Neck Between the Young and the Elderly Using Finite Element Method

A Comparative Study on the Multiscale Mechanical Responses of Human Femoral Neck Between the Young and the Elderly Using Finite Element Method

Pressure and heat treatment of continuous fibre reinforced thermoplastics produced by fused filament fabrication

A computational study about the effects of ply cracking and delamination on the stiffness reduction of damaged lamina and laminate

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