ERRATUM: Transversal isotropy based on a multiplicative decomposition of the deformation gradient within p‐version finite elements

Abstract

We found out that there is a mistake in the derivative of the strain-energy function ψ ani (C, M 0 ) with respect to the right Cauchy-Green tensor,T = 2∂ψ(C, M 0 )/C. The correct derivative leads, however, to an elasticity tensor, where there is no connection between the shear strains and the shear stresses in the undeformed state. This leads to a singular tangential stiffness matrix in the computations. Thus, a new strain-energy w(I C r ), instead of Eq. (40), has to be found, which yields on the one hand to a stress-free initial configuration, and on the other hand to a reasonable elasticity tensor. We made a few attempts but solved not the problem. In the meanwhile, a similar approach has been published by [1] to which we refer to.This circumstance has to be apologized and we express regret for not working carefully.Acknowledgement We would like to thank Chris Leistner, who found out the inconsistence.