Statistical mechanics of bone damage: a constitutive model

Area of Science:

• Biomechanics
• Materials Science
• Statistical Mechanics

Background:

• Cortical bone exhibits microcracking after exceeding its elastic limit.
• Understanding post-elastic mechanical behavior is crucial for bone health assessment.

Purpose of the Study:

• To develop a thermodynamically consistent, nonlinear constitutive model for cortical bone.
• To predict stress-strain relationships and inter-osteon microcracking progression.
• To quantitatively assess entropy increases during mechanical loading.

Main Methods:

• Development of a statistical mechanics-based constitutive model.
• Uniaxial tensile and bending tests on 51 and 15 cortical bone specimens, respectively.
• Digital image correlation and video analysis for displacement and strain field recording.

Main Results:

• The model accurately fits experimental tensile and bending test data.
• Correlations were found between constitutive parameters and anthropometric variables.
• Entropy calculations revealed microcracking escalates significantly beyond a critical strain threshold.

Conclusions:

• The developed model robustly predicts cortical bone's post-elastic behavior.
• The findings challenge a purely linear stress-strain relationship in bone.
• Quantitative entropy assessment provides insights into bone fracture mechanics.