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Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. How-ever, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.
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This content will become publicly available on December 20, 2025
Orientation Piezometry: Methods for Quantifying Stress From the Compositions and Orientations of Multicomponent Minerals
Abstract Mineral chemistry records the pressure and temperature conditions of lithospheric processes. Active tectonic margins, however, are subjected to non‐hydrostatic stresses wherein stress magnitudes vary directionally, and the impact of non‐hydrostatic stress on mineral chemistry is uncertain. The work of materials scientists F. Larché and J. Cahn provides a framework for quantifying how stress affects mineral chemistry. Crystallographically and mechanically anisotropic, multicomponent minerals will have different compositions as a function of their orientation under a fixed stress meaning that grain‐to‐grain compositional variation can be used to estimate stress. We develop two “orientation piezometry” methods that use the chemistry and orientations of multicomponent, anisotropic minerals to estimate stress. The first method uses chemistry and orientation (“coupled orientation piezometry”) whereas the second method uses composition alone (“decoupled orientation piezometry”). We apply the methods to clinopyroxene and feldspar solid solutions using synthetic data sets. The first method determines the full stress tensor whereas the second method can only determine the differential stress magnitude unless additional a priori information is specified. Plausible scenarios for orientation piezometry include minerals undergoing diffusion creep, recrystallized grains formed during dislocation creep, and minerals grown statically under stress. Preliminary application of the decoupled piezometer to the famous eclogite facies shear zones on Holsnøy, Norway, suggests differential stresses in the range of 300–900 MPa, broadly consistent with previous estimates from the area. Thus, orientation piezometry techniques may provide valuable constraints on geodynamic processes and insights into long‐standing geological problems such as the relationship between pressure and depth.
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- Award ID(s):
- 2208229
- PAR ID:
- 10561518
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Solid Earth
- Volume:
- 129
- Issue:
- 12
- ISSN:
- 2169-9313
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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