The deformation gradient F is the fundamental measure ofdeformation in continuum mechanics It is the second order tensorwhich maps line elements in the reference configuration into lineelements consisting of the same material particles in the currentconfiguration Consider a line element dX emanating from position Xin the reference configuration which becomes dx in the currentconfiguration Fig 221 Then usingdx X dX XGrad dXA capital G is used on Grad to emphasise that this is agradient with respect to the material coordinates1 the materialgradientXThe motion vectorfunction is a function of the variable X but it is customary to denotethis simply by x the value of at X ie xxXt so thatF xXGrad x FiJ xiXJwithdx FdX dxi FiJ dXJLower case indices are
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