ArticleMechanics of materials : an international journal2012
A symmetry invariant formulation of the relationship between the elasticity tensor and the fabric tensor.
Article in Mechanics of materials : an international journal, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 38 papers.
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38 citing papers in PubMed.
- Forward and inverse optimality problems of bone adaptation at the homogenised RVE level.Biomechanics and modeling in mechanobiology · 2026Article
- The microarchitectural variability in the echinoid skeleton: a 3D geometrical and stiffness characterization ofRoyal Society open science · 2025Article
- A data-driven framework for developing a unified density-modulus relationship for the human lumbar vertebral body.Journal of the mechanical behavior of biomedical materials · 2025Article
- Three-dimensional biphase fabric estimation from 2D images by deep learning.Scientific reports · 2024Article
- Biomechanics of the Human Osteochondral Unit: A Systematic Review.Materials (Basel, Switzerland) · 2024Review
- X-ray 3D imaging-based microunderstanding of granular mixtures: Stiffness enhancement by adding small fractions of soft particles.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- The impact of the parameters of the constitutive model on the distribution of strain in the femoral head.Biomechanics and modeling in mechanobiology · 2023Article
- Deformation of Gels with Spherical Auxetic Inclusions.Gels (Basel, Switzerland) · 2022Article
- A Nonparametric Approach for Estimating Three-Dimensional Fiber Orientation Distribution Functions (ODFs) in Fibrous Materials.IEEE transactions on medical imaging · 2022Article
- Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine.Medical & biological engineering & computing · 2022Article
- Three-dimensional computation of fibre orientation, diameter and branching in segmented image stacks of fibrous networks.Journal of the Royal Society, Interface · 2020Article
- Effect of fabric on the accuracy of computed tomography-based finite element analyses of the vertebra.Biomechanics and modeling in mechanobiology · 2020Article
- Exploratory Full-Field Strain Analysis of Regenerated Bone Tissue from Osteoinductive Biomaterials.Materials (Basel, Switzerland) · 2020Article
- Homogenization of cortical bone reveals that the organization and shape of pores marginally affect elasticity.Journal of the Royal Society, Interface · 2019Article
- Bone Mechanical Properties in Healthy and Diseased States.Annual review of biomedical engineering · 2018Review
- Dietary Advanced Glycation End Products Have Sex- and Age-Dependent Effects on Vertebral Bone Microstructure and Mechanical Function in Mice.Journal of bone and mineral research : the official journal of the American Society for Bone and Mineral Research · 2018Article
- Article
- Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone.Biomechanics and modeling in mechanobiology · 2017Article
- Image-based multiscale mechanical modeling shows the importance of structural heterogeneity in the human lumbar facet capsular ligament.Biomechanics and modeling in mechanobiology · 2017Article
- Trabecular bone in the calcaneus of runners.PloS one · 2017Article
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3 authors.
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Abstract
The fabric tensor is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric tensor can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of the relationship between fabric tensor and anisotropic elastic constants that is approximation free and symmetry-invariant. From specific data on the elastic constants and the fabric, the parameters in the reformulated relationship can be evaluated individually and efficiently using a simplified method that works independent of the material symmetry. The well-behavedness of the parameters and the accuracy of the method was analyzed using the Mori-Tanaka model for aligned ellipsoidal inclusions and using Buckminster Fuller's octet-truss lattice. Application of the method to a cancellous bone data set revealed that employing the fabric tensor allowed explaining 75-90% of the total variance. An implementation of the proposed methods was made publicly available.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.