Am averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications

This paper presents a new linear tetrahedral element that overcomes the sho rtcomings in bending dominated problems of the average nodal pressure eleme nt presented in Bonet and Burton (Communications in Numerical Methods in En gineering 1998; 14:437-439) Zienkiewicz et al. (International Journal for N umerical Methods in Engineering 1998; 43:565-583) and Bonet et al. (Interna tional Journal for Numerical Methods in Engineering 2001; 50(1):119-133). T his is achieved by extending some of the ideas proposed by Dohrmann et al. (International Journal for Numerical Methods in Engineering 2000; 47:1549-1 568) to the large strain nonlinear kinematics regime. In essence, a nodal d eformation gradient is defined by weighted average of the surrounding eleme nt values. The associated stresses and internal forces are then derived by differentiation of the corresponding simplified strain energy term. The res ulting element is intended for use in explicit dynamic codes (Goudreau and Hallquist, Computer Methods in Applied Mechanics and Engineering 1982; 33) where the use of quadratic tetrahedral elements can present significant dif ficulties. Copyright (C) 2001 John Wiley & Sons, Ltd.