Related Experiment Video
Updated: Jun 7, 2026

10:36
Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
Published on: May 20, 2018
Internal strain gradients quantified in bone under load using high-energy X-ray scattering
S R Stock1, Fang Yuan, L C Brinson
1Department of Molecular Pharmacology and Biological Chemistry, Feinberg School of Medicine, Northwestern University, 303 E. Chicago Ave., Chicago, IL 60611-3008, USA. s-stock@northwestern.edu
Journal of Biomechanics
|November 6, 2010
Summary
High-energy X-ray scattering quantifies bone
Area of Science:
- Biophysics
- Materials Science
- Orthopedics
Background:
- Bone's mechanical properties are crucial for skeletal health.
- Noninvasive methods are needed to assess internal bone strain.
- Cortical bone's response to stress is complex and not fully understood.
Purpose of the Study:
- To demonstrate high-energy synchrotron X-ray scattering for noninvasive bone strain mapping.
- To validate this technique against traditional strain gauges and finite element models.
- To investigate strain distribution in cortical bone under compression.
Main Methods:
- Utilized wide-angle X-ray scattering (WAXS) with high-energy synchrotron X-rays (>60 keV).
- Analyzed diffraction patterns from carbonated hydroxyapatite mineral phase in bone.
- Converted changes in Debye cone ellipticity to strain measurements.
Main Results:
- Successfully mapped internal strain distribution in murine and bovine cortical bone.
- Experimental strains correlated qualitatively with finite element models and strain gauge data.
- Observed significant strain gradients, residual strains, and stress concentration effects.
Conclusions:
- High-energy WAXS is a viable noninvasive technique for quantifying bone strain.
- The method reveals detailed strain patterns, including stress concentration.
- Findings support improved understanding of bone mechanics and injury mechanisms.
Related Concept Videos
Measurements of Strain
Strain quantifies the deformation of a material under force, typically measured as normal strain, which represents the change in length when compared with the original length. Electrical strain gauges are used for enhanced accuracy. These devices consist of a conductive wire mounted on a paper backing that adheres to the material's surface. These gauges operate on the piezoresistive effect, where the wire's electrical resistance changes in response to mechanical deformation. The strain gauge...
Strain-Energy Density
Understanding the strain energy density in materials under axial load is crucial for evaluating their mechanical behavior and durability. When a rod is subjected to such a load, it elongates and stores energy, known as strain energy, as potential energy within the material. This energy is measured in terms of energy per unit volume.
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
In the elastic region of a material, the relationship between the stress and the strain is linear and follows Hooke's Law. The strain energy density in this region...
Shearing Strain
The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
Normal Strain under Axial Loading
Normal strain under axial loading is an important concept in the field of mechanics of materials. Axial loading implies the application of a force along the axis of a material, like a column or bar. This force can either compress or stretch the material. In the context of axial loading, normal strain is the deformation experienced by the material in the direction of the loading force. It's calculated as the change in length divided by the original length of the material. This unitless ratio...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
Elastic Strain Energy for Shearing Stresses
As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...

