A CAS Approach to Handle the Anisotropic Hooke’s Law for Cancellous Bone and Wood

Algorithm 4

In[10]∶=HookeVto4[  myC_]  ∶=

 Array[  myC[[  {#1,  #2}  /.  indexrule2to1,  {#3,  #4}  /.

   indexrule2to1]]  &,  Array[3  &,  4]]

In[11]∶=(C2  =  MakeTensor["C",  2,  6])  //  MatrixForm

In[12]∶=C2

In[13]∶=(C2to4  =  HookeVto4[C2]  )  //  MatrixForm

In[14]∶=C2to4

In[15]∶=Hooke4toV[  myC_]  ≔

 Apply[  Part[  myC,  ##]  &,

  Array[  Join[  #1  /.  indexrule1to2  ,  #2  /.  indexrule1to2]  &,

   Array[6  &,  2]]  ,  {2}]

In[16]∶=C2back  =  Hooke4toV[C2to4]  )  //  MatrixForm

In[17]∶=(C4to2  =  Hooke4toV[C4]  )  //  MatrixForm

  In[18]∶=(C4back  =  HookeVto4[C4to2])  //  MatrixForm

In[19]∶=Hooke2toV[myc2_]  ∶=  Table[

  Which[

   i  <=  3  &&  j  <=  3  ,  myc2[[i,  j]],

   4  <=  i  &&  j  <=  3  ,  myc2[[i,  j]]  /  𝟸^∧(1/2),

   i  <=  3  &&  4  <=  j  ,  myc2[[i,  j]]/  𝟸^∧(1/2),

   4  <=  i  &&  4  <=  j  ,  myc2[[i,  j]]/  2

      ],  {i,  6},  {j,  6}]

HookeVto2[mycV_]  ≔  Table[

   Which[

   i  <=  3  &&  j  <=  3  ,  mycV[[i,  j]],

   4  <=  i  &&  j  <=  3  ,  mycV[[i,  j]]  *  𝟸^∧(1/2),

   i  <=  3  &&  4  <=  j  ,  mycV[[i,  j]]  *  𝟸^∧(1/2),

   4  <=  i  &&  4  <=  j  ,  mycV[[i,  j]]  *  2

        ],  {i,  6},  {j,  6}]

Hooke4to2[myC_]  ∶=  HookeVto2[Hooke4toV[  myC  ]]

  Hooke2to4[myC_]  ∶=  HookeVto4[Hooke2toV[  myC  ]]

  In[20]∶=(CV  =  Hooke2toV[  C2  ]  )  //  MatrixForm

  In[21]∶=(C2back  =  HookeVto2[  CV  ]  )  //  MatrixForm

In[22]∶=(CV  =  Hooke4to2[C4])  //  MatrixForm

In[23]∶=C4back  =  Hooke2to4[CV])  //  MatrixForm