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# Using Submodels to Give Adam a Leg to Stand On

December 5, 2014 By: Patrick Cunningham

For all those engineers out there who also happen to be Renaissance art aficionados this is the blog post for you!  CAE Associates recently completed a project with The Metropolitan Museum of Art that involved finite element modeling of the 15th-century statue of Adam by the Italian sculptor Tullio Lombardo. In 2002, the statue was severely damaged when the pedestal it was displayed on collapsed. What followed was a twelve-year effort by the museum that became a cohesion of art conservation and computer modeling techniques.

 Tullio Lombardo (Italian, ca. 1455-1532)AdamCa. 1490-95MarbleThe Metropolitan Museum of Art, Fletcher Fund, 1936Photo: The Metropolitan Museum of Art, Photograph Studio/Joseph Coscia, Jr.

CAE Associates was enlisted by the Met conservation team to calculate the stress distribution in Adam's left leg for several restoration techniques. By laser scanning the fragments of the statue, the conservation team was able to construct a 3D solid geometry that CAE Associates used to create the finite element model of Adam. The finite element results helped the Met conservators make the difficult decision on the use of pins versus adhesive-only in critical "joins" in the statue.

From a loading standpoint, Adam simply needed to support his own weight, a task he had excelled at for over five centuries prior to the accident.  Although the focus was the stress distribution in the left leg, we needed to model the entire statue to determine the force distribution. After calculating the force distribution and deformation of the full statue, we ran several sensitivity studies looking at the use of single versus multiple pins, pin diameter and location in the left leg. We could have used the entire model of Adam to evaluate each case, but this was a good opportunity to apply submodeling techniques.

Submodeling is an application of Saint-Venant’s principle which states that if two different load distributions are statically equivalent, the effects on a location a sufficient distance away will be the same. When a global model of the displacement field is used to define boundary conditions on a detailed submodel with a refined mesh, the submodel will provide a more accurate representation of the local region.

In Adam's case we only needed to generate the global displacement field one time and re-use it at the cut boundary regions as the loading of the submodel for each pin configuration investigated. Since the submodel contained only a portion of the statue, we could increase the mesh refinement to the required level while maintaining a reasonable solution time. Shorter solution times that did not compromise the fidelity of the result gave us the flexibility to analyze many more design ideas and "what if" type scenarios within the timeframe of the restoration schedule.

If you are interested in more information or would like to see a demonstration of submodeling, check out CAE Associates' e-Learning seminar.