D With the cylindrical coordinates, the currentspatial coordinates are (r, 0, z) while theinitial material coordinates are (R, 0, Z),which are related to the Cartesian currentspatial coordinates (x, y, z) and the initialCartesian material coordinates (X, Y, Z) byx=r*cos0, y=r*sin0, z = zX=R*cosO, y=R*sinO, Z = Z%3DLet us consider an axisymmetricdeformation of a body with R26>0 (where6 is a given positive constant) given in thecylindrical coordinates asr=R3, z = Z, 0=0, 12=x²+y?, R²=x²+Y1) Write down the deformation in terms ofthe 3 Cartesian current spatial coordinates(x, y, z)as 3 functions of the initial Cartesianmaterial coordinates (X, Y, Z);2) Calculate the deformation gradienttensor F and its determinant det(F) in termsof theinitial Cartesian material coordinates(X, Y, Z);

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With the cylindrical coordinates, the current spatial coordinates are (r, 0, z) while the initial material coordinates are (R, 0, Z), which are related to the Cartesian current spatial coordinates (x, y, z) and the initial Cartesian material coordinates (X, Y, Z) by x=r*cose, y=r*sin0, z = z X=R*cose, y=R*sin0, Z = Z Let us consider an axisymmetric deformation of a body with R≥8>0 (where 6 is a given positive constant) given in the cylindrical coordinates as r=R³, z = Z, 0=0,² = x² + y²₁ R² = x² + y² 1) Write down the deformation in terms of the 3 Cartesian current spatial coordinates (x, y, z)as 3 functions of the initial Cartesian material coordinates (X, Y, Z); 2) Calculate the deformation gradient tensor F and its determinant det(F) in terms of theinitial Cartesian material coordinates (X, Y, Z);