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Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear...
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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.
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Muscle Constitutive Model With a Tangent Modulus Approximation: Ansys Implementation and Verification.

Manuel Lucas Sampaio de Oliveira1, Thomas K Uchida1

  • 1Department of Mechanical Engineering, University of Ottawa, 161 Louis-Pasteur, Ottawa, ON K1N 6N5, Canada.

Journal of Biomechanical Engineering
|February 22, 2023
PubMed
Summary

Implementing complex muscle material models in finite element analysis (FEA) software is simplified using an approximated tangent modulus in Ansys. This approach enables accurate soft tissue simulations, overcoming previous implementation challenges.

Keywords:
Ansyselasticity tensorfinite elementhyperelastic materialmuscle modeltangent modulus

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Area of Science:

  • Computational mechanics
  • Biomechanical modeling
  • Finite element analysis

Background:

  • Accurate finite element simulations of soft tissue require sophisticated muscle material models.
  • Current commercial finite element software lacks built-in advanced muscle models.
  • Implementing custom muscle models is complex due to challenging derivations and programming of the tangent modulus tensor.

Purpose of the Study:

  • To implement a user-defined muscle material model in Ansys.
  • To simplify the implementation of complex muscle material models by approximating the tangent modulus tensor.
  • To validate the Ansys implementation against established software (FEBio).

Main Methods:

  • Developed an Ansys implementation of a muscle material model using an approximated tangent modulus.
  • Created three geometric muscle models (rectangle, right trapezoid, obtuse trapezoid) for testing.
  • Performed simulations applying displacement to fixed muscle models.
  • Validated Ansys results against FEBio simulations using the exact tangent modulus.

Main Results:

  • Good agreement was observed between Ansys and FEBio simulations.
  • Root-mean-square-percentage errors in Von Mises stress along the centerline were 0.00% (RR), 3.03% (RTR), and 6.75% (RTO).
  • Similar errors were noted for longitudinal strain, indicating model accuracy.

Conclusions:

  • The approximated tangent modulus approach simplifies muscle material model implementation in Ansys.
  • This method facilitates accurate finite element simulations of soft tissues.
  • The provided Ansys implementation allows for reproducibility and further research.