An assessment of the average nodal volume formulation for the analysis of nearly incompressible solids under finite strains.

*(English)*Zbl 1302.74173Summary: This paper provides an assessment of the average nodal volume methodology originally proposed by Bonet and Burton (Commun. Numer. Meth. Engng. 1998; 14:437-449) for the analysis of finitely strained nearly incompressible solids. An implicit version of the average nodal pressure formulation is derived by re-casting the original concept in terms of average nodal volume change ratio within the framework of the F-bar method proposed by de Souza Neto et al. (Int. J. Solids Struct. 1996; 33: 3277-3296). In this context, a linear triangle for implicit plane strain and axisymmetric analysis of nearly incompressible solids under finite strains is obtained. An exact expression for the corresponding element stiffness matrix is presented. This allows the use of the full Newton-Raphson algorithm, ensuring quadratic rates of asymptotic convergence in the global equilibrium iterations. The performance of the procedure is thoroughly assessed by means of numerical examples. The results show that the nodal averaging technique substantially reduces the volumetric locking tendency of the linear triangle and allows an accurate prediction of deformed shapes and reaction forces in situations of practical interest. However, the formulation is found to produce considerable checkerboard-type hydrostatic pressure fluctuations which poses severe limitations on its range of applicability.

##### MSC:

74S10 | Finite volume methods applied to problems in solid mechanics |

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\textit{F. M. Andrade Pires} et al., Commun. Numer. Methods Eng. 20, No. 7, 569--583 (2004; Zbl 1302.74173)

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