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Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate
1Department of Mechanics, Tianjin University, 92 Weijin Road, Tianjin 300072, China.
Journal of Biomechanical Engineering
|May 25, 2017
Summary
This study introduces an approximation method for calculating the tangent modulus tensor in finite element (FE) analysis. The method simplifies material Jacobian evaluation for complex hyperelastic models, enhancing computational efficiency.
Area of Science:
- Computational mechanics
- Materials science
- Finite element analysis
Background:
- Objective stress rates are common in commercial finite element (FE) programs.
- Deriving tangent modulus tensors for complex material models with objective stress rates is challenging.
- Accurate material Jacobian evaluation is crucial for FE analysis convergence and accuracy.
Purpose of the Study:
- To present an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of Kirchhoff stress.
- To simplify the evaluation process of the material Jacobian in FE analysis.
- To demonstrate the method's effectiveness for complex material models.
Main Methods:
- An approximation method for the tangent modulus tensor was developed.
- The method was applied to two user-defined fiber-reinforced hyperelastic material models.
- Comparisons were made against a closed-form analytical method.
Main Results:
- The approximation method simplifies material Jacobian evaluation with satisfactory accuracy.
- The method retains computational efficiency compared to analytical methods.
- The approach is independent of specific material models.
Conclusions:
- The proposed approximation method offers a computationally efficient and accurate way to evaluate the tangent modulus tensor.
- This method facilitates the implementation of complex material models in FE analysis, particularly for shell/membrane elements in Abaqus.
- The independence from material models broadens its applicability in computational mechanics.
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