Share This Article:

Trilinear Hexahedra with Integral-Averaged Volumes for Nearly Incompressible Nonlinear Deformation

Full-Text HTML XML Download Download as PDF (Size:2152KB) PP. 765-788
DOI: 10.4236/eng.2015.711067    4,553 Downloads   5,003 Views Citations


Many materials such as biological tissues, polymers, and metals in plasticity can undergo large deformations with very little change in volume. Low-order finite elements are also preferred for certain applications, but are well known to behave poorly for such nearly incompressible materials. Of the several methods to relieve this volumetric locking, the method remains popular as no extra variables or nodes need to be added, making the implementation relatively straightforward and efficient. In the large deformation regime, the incompressibility is often treated by using a reduced order or averaged value of the volumetric part of the deformation gradient, and hence this technique is often termed an approach. However, there is little in the literature detailing the relationship between the choice of and the resulting and stiffness matrices. In this article, we develop a framework for relating the choice of to the resulting and stiffness matrices. We examine two volume-averaged choices for , one in the reference and one in the current configuration. Volume-averaged formulation has the advantage that no integration points are added. Therefore, there is a modest savings in memory and no integration point quantities needed to be interpolated between different sets of points. Numerical results show that the two formulations developed give similar results to existing methods.

Cite this paper

Foster, C. and Nejad, T. (2015) Trilinear Hexahedra with Integral-Averaged Volumes for Nearly Incompressible Nonlinear Deformation. Engineering, 7, 765-788. doi: 10.4236/eng.2015.711067.

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.