Identification of couple-stress moduli of vertebral trabecular bone based on the 3D internal architectures

Goda, Ibrahim; Ganghoffer, Jean‐François

doi:10.1016/j.jmbbm.2015.06.036

Cited by 47 publications

(30 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is the necessary condition that the RVE is modeled as the continuum medium, in which the equivalent quantities, such as the equivalent stress, equivalent couple stress, equivalent strain and equivalent torsion defined by Eqs. (25), (26), (27) and (28), respectively, within the framework of present work, must satisfy the equivalence condition of virtual work (36) exactly.…”

Section: Definitions Of Boundary Value For the Equivalent Physical Qumentioning

confidence: 92%

“…(25) and (26). Similar to the geometry equation (1), the definition of equivalent strain is introduced…”

Section: Definitions Of Boundary Value For the Equivalent Physical Qumentioning

confidence: 96%

“…Finally, the equivalent stress and the equivalent couple stress can be calculated with Eqs. (25) and (26). The result can be expressed as follows: pi do not represent the distribution of strain tensor and distortion tensor in representative volume.…”

Section: Decomposition Of Displacement Boundary Value Problemmentioning

confidence: 96%

“…[18,19]. Equivalent physical quantities are employed to establish appropriate equivalent constitutive equations such as modeling the inclusions of composites as the periodic or weak-periodic micro-polar material, analyzing the equivalent elastic constants, and establishing the high-order constitutive equations [20][21][22][23][24][25]. Aiming for lattices endowed with a central symmetry, for which there is no coupling between stress and curvature, Dos Reis1 and Ganghoffer [24] designed and calculated a lattice endowed with a hierarchical double-scale microstructure, leading to a dominant micro-polar effect under bending at the macroscopic scale.…”

Section: Introductionmentioning

confidence: 99%

“…Aiming for lattices endowed with a central symmetry, for which there is no coupling between stress and curvature, Dos Reis1 and Ganghoffer [24] designed and calculated a lattice endowed with a hierarchical double-scale microstructure, leading to a dominant micro-polar effect under bending at the macroscopic scale. Ibrahim Goda et al [25] developed a homogeneous, orthotropic couple-stress continuum model as a substitute of the 3D periodic heterogeneous cellular solid model of vertebral trabecular bone.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

Zhang

Chu

et al. 2015

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

In this paper, the periodic structure material is modeled as the continuum homogeneous micro-polar media subjecting to thermo-mechanical interaction. Meanwhile, a series of equivalent quantities such as the equivalent stress, couple stress, displacement gradient and torsion tensor were defined by the integral forms of the boundary values of the external surface force, moment, displacement and the angular displacement, and were proved to satisfy the equivalence conditions of virtual work. Based on above works, the displacement boundary value problem was established to deduce the equivalent constitutive equation. Assume the representative volume element is composed of the spatial cross-framework, and applying the boundary value problem of displacement on frame structures, the equivalent elastic coefficients, temperature coefficients of equivalent stress and the temperature gradient coefficients of equivalent couple stress are deduced. In addition, the method can also be extended to the stress boundary value problem to deduce the equivalent constitutive equation. The calculations indicate that the equivalent result can be obtained from the two kinds of boundary value problems.

show abstract

Section: Definitions Of Boundary Value For the Equivalent Physical Qumentioning

confidence: 92%

“…(25) and (26). Similar to the geometry equation (1), the definition of equivalent strain is introduced…”

Section: Definitions Of Boundary Value For the Equivalent Physical Qumentioning

confidence: 96%

Section: Decomposition Of Displacement Boundary Value Problemmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

Zhang

Chu

et al. 2015

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

show abstract

Unravelling Size‐Dependent and Coupled Properties in Mechanical Metamaterials: A Couple‐Stress Theory Perspective

Eskandari,

shahryari,

Akbarzadeh

2024

Advanced Science

View full text Add to dashboard Cite

The lack of material characteristic length scale prevents classical continuum theory (CCT) from recognizing size effect. Additionally, the even‐order material property tensors associated with CCT only characterize the materials' centrosymmetric behavior and overlook their intrinsic chirality and polarity. Moreover, CCT is not reducible to 2D and 1D space without adding couples and higher‐order deformation gradients. Despite several generalized continuum theories proposed over the past century to overcome the limitations of CCT, the broad application of these theories in the field of mechanical metamaterials has encountered significant challenges. These obstacles primarily arise from a limited understanding of the material coefficients associated with these theories, impeding their widespread adoption. Implementing a bottom‐up approach based on augmented asymptotic homogenization, a consistent and self‐sufficient effective couple‐stress theory for materials with microstructures in 3D, 2D, and 1D spaces is presented. Utilizing the developed models, material properties associated with axial‐twist, shear‐bending, bending‐twist, and double curvature bending couplings in mechanical metamaterials are characterized. The accuracy of these homogenized models is investigated by comparing them with the detailed finite element models and experiments performed on 3D‐printed samples. The proposed models provide a benchmark for the rational design, classification, and manufacturing of mechanical metamaterials with programmable coupled deformation modes.

show abstract

Prediction of the Effective Mechanical Properties of Regular and Random Fibrous Materials Based on the Mechanics of Generalized Continua

Ganghoffer

Goda

Elnady

et al. 2019

Mechanics of Fibrous Materials and Applications

View full text Add to dashboard Cite

Identification of couple-stress moduli of vertebral trabecular bone based on the 3D internal architectures

Cited by 47 publications

References 21 publications

Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

Unravelling Size‐Dependent and Coupled Properties in Mechanical Metamaterials: A Couple‐Stress Theory Perspective

Prediction of the Effective Mechanical Properties of Regular and Random Fibrous Materials Based on the Mechanics of Generalized Continua

Contact Info

Product

Resources

About