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

This paper presents a new linear tetrahedral element that overcomes the shortcomings in bending dominated problems of the average nodal pressure element presented in Bonet and Burton (Communications in Numerical Methods in Engineering 1998; 14:437–439) Zienkiewicz et al. (Internatinal Journal for Numerical Methods in Engineering 1998; 43:565–583) and Bonet et al. (Internatinal Journal for Numerical Methods in Engineering 2001; 50(1):119–133). This is achieved by extending some of the ideas proposed by Dohrmann et al. (Internatinal Journal for Numerical Methods in Engineering 2000; 47:1549–1568) to the large strain nonlinear kinematics regime. In essence, a nodal deformation gradient is defined by weighted average of the surrounding element values. The associated stresses and internal forces are then derived by differentiation of the corresponding simplified strain energy term. The resulting 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 difficulties.