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In order to accelerate implementation of hyperelastic materials for finite element analysis, we developed an automatic numerical algorithm that only requires the strain energy function. This saves the effort on analytical derivation and coding of stress and tangent modulus, which is time-consuming and prone to human errors. Using the one-sided Newton difference quotients, the proposed algorithm first perturbs deformation gradients and calculate the difference on strain energy to approximate stress. Then, we perturb again to get difference in stress to approximate tangent modulus. Accuracy of the approximations were evaluated across the perturbation parameter space, where we find the optimal amount of perturbation being $10^{-6}$ to obtain stress and $10^{-4}$ to obtain tangent modulus. Single element verification in ABAQUS with Neo-Hookean material resulted in a small stress error of only $7times10^{-5}$ on average across uniaxial compression and tension, biaxial tension and simple shear situations. A full 3D model with Holzapfel anisotropic material for artery inflation generated a small relative error of $4times10^{-6}$ for inflated radius at $25 kPa$ pressure. Results of the verification tests suggest that the proposed numerical method has good accuracy and convergence performance, therefore a good material implementation algorithm in small scale models and a useful debugging tool for large scale models.
FEpX is a modeling framework for computing the elastoplastic deformations of polycrystalline solids. Using the framework, one can simulate the mechanical behavior of aggregates of crystals, referred to as virtual polycrystals, over large strain defor
We present a novel method for finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resol
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the calculation of de
Capturing the interaction between objects that have an extreme difference in Young s modulus or geometrical scale is a highly challenging topic for numerical simulation. One of the fundamental questions is how to build an accurate multi-scale method
Algorithm NCL is designed for general smooth optimization problems where first and second derivatives are available, including problems whose constraints may not be linearly independent at a solution (i.e., do not satisfy the LICQ). It is equivalent