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Updated: Nov 2, 2025
11:28
A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
Published on: May 18, 2015
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An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials
Will Zhang1, Adela Capilnasiu2, Gerhard Sommer3
1Department of Biomedical Engineering, University of Michigan, Ann Arbor, USA.
Computer Methods in Applied Mechanics and Engineering
|June 17, 2021
Summary
This study introduces an efficient numerical method for computational biomechanics, enabling accurate modeling of viscoelastic tissues. The new approach significantly reduces computational cost and storage requirements for simulations.
Area of Science:
- Biomedical Engineering
- Computational Solid Mechanics
- Viscoelasticity
Background:
- Computational biomechanics models often simplify tissue behavior, assuming hyperelasticity instead of viscoelasticity, which is experimentally observed.
- Existing fractional viscoelastic models are computationally expensive and difficult to implement in 3D simulations.
- Current numerical approximations for fractional derivatives lead to high computational (O(N_T^2)) and storage (O(N_T)) costs.
Purpose of the Study:
- To develop a novel, computationally efficient numerical approximation for fractional viscoelastic constitutive models.
- To integrate this method into a finite element solid mechanics framework for biomechanical simulations.
- To demonstrate the accuracy and efficiency of the proposed method for modeling viscoelastic materials.
Main Methods:
- Developed a new numerical approximation for the Caputo derivative using a recurrence relation.
- Achieved computational cost of O(N_T) and fixed storage cost.
- Integrated the approximation into a finite element solid mechanics framework.
- Proved unconditional stability for the linear viscoelastic case.
Main Results:
- The novel approximation reduces computational cost to O(N_T) and storage cost to a fixed amount.
- The method was validated through analytic tests and an analytic fractional differential equation.
- Demonstrated accuracy and computational efficiency in a computational biomechanical model problem.
- The finite element implementation showed unconditional stability in the linear viscoelastic case.
Conclusions:
- The presented numerical method offers a computationally efficient and accurate approach for modeling viscoelastic materials in biomechanics.
- This advancement facilitates the use of more realistic viscoelastic models in computational biomechanical simulations.
- The method has the potential to improve understanding of pathophysiology, treatment, and device design by enabling better simulations.
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