Presentation on theme: "2D Deformation and Creep Response of Articular Cartilage By: Mikhail Yakhnis & Robert Zhang."— Presentation transcript:
2D Deformation and Creep Response of Articular Cartilage By: Mikhail Yakhnis & Robert Zhang
Motivation Articular cartilage transfers load between bones enables smooth motion along joints Cartilage has limited capacity for self repair Applications: biomaterials, prosthetics, biomedical devices
Problem Description Consider cartilage in an unconfined compression under constant load F Analyze the 2D elastic deformation over time Articular Cartilage F Compression plate Frictionless Supports
Material Background Cartilage often modeled as a viscoelastic material Viscous and elastic by superposition Elasticity and viscosity can be linear or nonlinear Established models: Kelvin-Voigt, Maxwell, Standard-Linear Solid
Mathematical Model for Cartilage Mechanical Analogue of Kelvin-Voigt Model
Assumptions for Model B3 B2 B1 B4 x y F c L
Experimental Data Data Book on Mechanical Properties of Living Cells, Tissues, and Organs /. Tokyo ; New York : Springer, Print.
Derivation of Weak Form
Decoupling a Transient Problem Reddy, J. N.. "Time-Dependent Problems." An introduction to nonlinear finite element analysis. Oxford: Oxford University Press, Print.
Displacement Equation for Creep Response
Modeling Creep in MATLAB Changes in Preprocessor.m Provide initial displacement Define time step Adjust boundary conditions Changes in Assemble.m Assemble the damping matrix [C] Changes in NodalSoln.m Add initial condition, damping, time inputs Modify reaction force and displacement equations
Modeling Creep in MATLAB Discussion: MATLAB result converges toward experimental data farther away from initial time 10% error at 6 seconds MATLAB model reaches equilibrium faster than experimental data
Considerations for ANSYS Model What experimental data is available to us? Can we fit the experimental data to the model? Can we use the built-in Mechanical APDL curve fitting procedure? Is there more emphasis on primary creep or secondary creep? Does the model satisfy our constitutive equation?
Parameters in the ANSYS Model ANSYS Advanced Nonlinear Materials: Lecture 3 – Rate Dependent Creep
ANSYS Results – Creep Response Long Term Response – 3000 Seconds Short Term Response – 30 Seconds
Animation of Deformation in ANSYS
Comparison of ANSYS and Experiment Result: Theoretical Model-Based ANSYS data tends to overshoot experimental data Error is between 30% to 40% per data point Experimental-based model performs better Discussion: Results demonstrate the limitations of ANSYS models A combined primary-secondary model is ideal Long term response in ANSYS is not accurate Function models primary response Primary + Secondary Time Hardening
ANSYS Model: Mesh and Time Refinement Time % Difference w.r.t. Base Case -MeshTimeMesh and Time Mesh [Nodes]Time [s] Base Case805Between 0.1 and 900 Refinement15747Between 1e-4 and 1e-2
Sensitivity Analysis TimeBase CaseCase C1Difference %Case C2Difference %Case C5Difference % 13.60E E E E E E E E E E E E E E E E E E E E E E E E *The simulation did not converge at C2 +50% so C2 +10% was used instead
2D Deformation and Creep Response of Articular Cartilage By: DJ Mikey Mike & Big Rob Zhang Thank you for listening. Questions?