Journal ArticleDOI
An alternative model for anisotropic elasticity based on fabric tensors
Philippe K. Zysset,Alain Curnier +1 more
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TLDR
In this paper, a general approach relating fabric tensors characterizing microstructure to the fourth rank elasticity tensor is proposed using a Fourier expansion in spherical harmonics, the orientation distribution function of a positive, radially symmetric microstructural property is approximated by a scalar and a symmetric, traceless second rank tensor Following this approximation, a general expression of the elastic free energy potential is derived from representation theorems for anisotropic scalar functions.About:
This article is published in Mechanics of Materials.The article was published on 1995-11-01. It has received 185 citations till now. The article focuses on the topics: Cauchy stress tensor & Elasticity (economics).read more
Citations
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Journal ArticleDOI
Biomechanics of trabecular bone.
TL;DR: The state of the art in trabecular bone biomechanics is reviewed, focusing on the mechanical aspects, and attempts to identify important areas of current and future research.
Journal ArticleDOI
Bone Mechanical Properties in Healthy and Diseased States.
TL;DR: The basic tenets of bone mechanics are presented and some of the arcs of research that have brought the field to recent advances are connected to several avenues of future research.
Journal ArticleDOI
Biomechanics and Mechanobiology of Trabecular Bone: A Review
Ramin Oftadeh,Ramin Oftadeh,Miguel Perez-Viloria,Juan C. Villa-Camacho,Ashkan Vaziri,Ara Nazarian +5 more
TL;DR: The aims of the current work are to first review the mechanobiology of trabecular bone and then present classical and new approaches for modeling and analyzing the trabECular bone microstructure and macrost structure and corresponding mechanical properties such as elastic properties and strength.
Journal ArticleDOI
On quantitative characterization of microstructures and effective properties
Mark Kachanov,Igor Sevostianov +1 more
TL;DR: In this article, the authors focus on microstructures that can be characterized as continuous matrices containing isolated inhomogeneities of diverse shapes, properties and orientations, and address their proper quantitative characterization in the context of elastic and conductive properties (transport and fracture related properties are also briefly discussed).
Book
Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability
TL;DR: In this article, the authors apply local and global uniqueness and stability criteria to non-associative elastoplasticity for wave propagation, stability and bifurcation of elastic solids.
References
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Journal ArticleDOI
Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor
Timothy P. Harrigan,R. W. Mann +1 more
TL;DR: In this article, a second rank symmetric tensor which describes the degree of orientation in orthotropic materials is presented and shown to reflect accurately patterns of experimental data, and the use of this tensor to describe microstructural anisotropy is compared to currently accepted methods.
Journal ArticleDOI
Distribution of directional data and fabric tensors
TL;DR: In this paper, the distribution of directional data is characterized by what is termed fabric tensors, and a formal least square approximation is applied, and three kinds of fabric tensor are defined in connection with the choice of a basis of the space of functions on a unit sphere or a unit circle.
Journal ArticleDOI
The relationship between the elasticity tensor and the fabric tensor
TL;DR: This contribution presents a reformulation of the relationship between fabric tensor and anisotropic elastic constants that is approximation free and symmetry-invariant and employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium.
BookDOI
Applications of tensor functions in solid mechanics
TL;DR: A rational formulation of isotropic and anisotropic hardening and results for invariant and tensor representations for classical plastic potential and Tensor function theory and classical Plastic potential are presented.
Journal ArticleDOI
Stereological determination of structural anisotropy
TL;DR: In this paper, a general mathematical formulation is given to the problem of determining the structural anisotropy by means of the stereological principle, and three cases are considered: (i) the number of intersections with a probe line or plane is viewed as a transformation, which is termed the “Buffon transform”, between two distribution densities, and a form of its inverse transform is given.
Related Papers (5)
Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor
Timothy P. Harrigan,R. W. Mann +1 more