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The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
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The work-energy theorem for rotational motion is analogous to the work-energy theorem in translational motion. It states that the net work done by an external force to rotate a rigid body equals the change in the object's rotational kinetic energy. The power delivered is simply the time derivative of the work done; therefore, power is the dot product of torque and angular velocity. This relation is analogous to power in translational motion, which is given by the dot product of force and...
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When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...
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Revisiting the Mechanical Work-Energy Framework in Dynamic Biomechanical Systems.

Donglu Shi1

  • 1The Materials Science and Engineering Program, Department of Mechanical and Materials Engineering, Department of Biomedical Engineering, College of Engineering and Applied Science, University of Cincinnati, Cincinnati, OH 45221, USA.

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|September 27, 2025
PubMed
Summary

Loading rate significantly impacts mechanical work and energy dissipation in biological tissues. Neglecting these rate effects leads to underestimation of energy costs and tissue stresses in classical models.

Keywords:
biological tissuesbiomechanicsenergy partitioningmuscle contractionnano deliveryrate of force applicationsoft mattertime-dependent systemswork–energy relationship

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Area of Science:

  • Biomechanics
  • Biomaterials Science
  • Cellular Mechanics

Background:

  • Classical mechanical work definitions (W = F × D) ignore loading rate.
  • Biological tissues (muscles, connective tissues) exhibit inherent rate sensitivity.
  • Rate effects influence force generation, stiffness, and injury thresholds.

Purpose of the Study:

  • Revisit the work-energy framework in biomechanics and biomaterials.
  • Quantify how loading rate modulates energy partitioning (elastic storage vs. viscous dissipation).
  • Develop a rate-matched nano-bio indentation experiment.

Main Methods:

  • Combined theoretical models and simulations.
  • Proposed and utilized a rate-matched nano-bio indentation experiment.
  • Analyzed muscle contraction, viscoelastic tissue mechanics, and nanoparticle-membrane interactions.

Main Results:

  • Rapid loading significantly increases viscous dissipation and total mechanical work.
  • Peak force and displacement can remain constant despite increased work and dissipation.
  • Classical quasi-static models underestimate energy costs and tissue stresses.

Conclusions:

  • Temporal dynamics and nonlinear material responses are crucial for accurate biomechanical analysis.
  • A multi-physics experimental-simulation platform enables controlled investigation of rate-dependent phenomena.
  • Insights inform biomaterials design, experimental biomechanics, and applications in sports science, orthopedics, rehabilitation, and nanomedicine.