1. The deformation gradient tensor at current position x and time t is defined as F(x,t)=Xx where X is the corresponding positon vector in the undeformed frame. Now consider an initially undeformed object subject to a uniform velocity gradient v (that is, v is constant and independent of x and t ). a) Show that the evolution of F(x,t) is governed by dtdF=F=LF, where L is defined as L=(v)T. b) Show that F(x,t)=k=0k!1(Lt)k is the solution to F=LF