ABSTRACT
Recall that the displacement vector u(X) is assumed to admit a satisfactory approximation at the element level in the form u(X)=φT(X)Φγ(t). Also recall that the deformation-gradient tensor is given by Suppose that the body under study is subjected to a load vector, P, which is applied incrementally via load increments, ∆jP. The load at the nth load step is denoted as Pn. The solution, Pn, is known, and the solution of the increments of the displacements is sought. Let ∆nu=un+1−un, so that ∆nu=φT(X)Φ∆nγ. By suitably arranging the derivatives of ∆nu with respect to X, a matrix, M(X), can easily be determined for which VEC(∆nF)=M(X)∆nγ.
