The first part of this two part presentation, outlined the implementation details for a new method to compute the generalized internal force vector and its Jacobian for continuum mechanics based Absolute Nodal Coordinate Formulation (ANCF) elements using a linear viscoelastic material model. &nbsp;This second part the presentation provides a comparison of the computational efficiency of this new method across five different ANCF elements with respect to other existing computational strategies in the literature.Two different styles of approaches have been used to develop computationally efficient methods for calculating the generalized internal force vector for continuum mechanics based ANCF elements. &nbsp;Gerstmayr and Shabana presented an algorithm using the ``Continual Integration'' approach, where the integration across the volume of the element of the partial derivative of the strain energy density with respect to the nodal coordinates was made as efficient as possible. &nbsp;The performance of this style of strategy depends on both the number of quadrature point used for the numerical integration as well as the number of nodal coordinates. &nbsp;Since the newly proposed method is based on Gerstmayr and Shabana's method, it also uses the ``Continual Integration'' strategy. &nbsp;Additionally, it includes an analytical expression for the Jacobian which is significantly more efficient than using numerical differentiation as shown in the first presentation.In the alternative ``Pre-Integration'' style of strategy, the terms that must be integrated across the volume of the element can be factored out from the nodal coordinates so that this integration only needs to occur once prior to the start of the simulation. &nbsp;The resulting performance of this strategy during the simulation depends on the number of nodal coordinates but not the number of quadrature points used to integrate across the volume of the element. &nbsp;Garcia-Vallejo et. al. presented the first ANCF method using this approach where they showed that a set of constant sparse matrices equal in both number and size of the nodal coordinate could be pulled out of the expression for the generalized internal force vector and its Jacobian which contained all of the terms that required integration across the volume of the element. &nbsp;The authors also listed other characteristics of these matrices, including sparsity and symmetry, that could be leveraged to enhance the efficiency of the calculations. &nbsp;Liu et. al. later showed through tensor notation manipulation that two large constant matrices could be pulled out of the expression for the generalized internal force vector and a third constant matrix for the Jacobian which the authors claimed was even more efficient.

An Efficiency Comparison of Different Ancf Implementations

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.