A New Methodology for the Structural Analysis of 3D Digitized Cultural Heritage through FEA

Finite Elements Analysis (FEA) is widely used for modelling stress behaviour in any mechanical system. The processing workflow starts from CAD 3D models representing the ideal shape of the object to be simulated. Such models are typically made of mathematical elements defining its geometrical components. Those are pre-processed before the simulation for creating a volumetric mesh out of the CAD model. Recently the use of FEA has also been extended to the simulation of ancient structures and artefacts, revealing significant potentialities for the conservation of Cultural Heritage. Unlike modern mechanical systems, heritage objects are usually altered by the time passed since their original creation, and the representation with a schematic CAD model may introduce an excessive level of approximation leading to wrong simulation results. In the last two decades, 3D documentation of CH has been developed through reality-based approaches. However, the related mesh models of the exterior surfaces are not proper for direct use in FEA. Such high-resolution surface meshes has to be converted to volumetric meshes made of tetrahedral or hexahedral elementary volumes and a limited number of external and internal nodes. The focus of this paper is on a new method aiming at generating the best possible 3D solid representation of a real artefact from its accurate reality-based surface model by reducing its number of nodes of several orders of magnitude while maintaining a geometrical coherence in the order of the measurement uncertainty of the 3D capturing technique used. The approach proposed is based on wise use of retopology procedures and a transformation of this retopologized model to a mathematical one made by NURBS surfaces, suitable for being processed by a volumetric mesh generator typically embedded in any standard FEM package. The resulting volumetric mesh allows obtaining FEA of ancient structures, providing a far better accurate simulation than those attainable by a rough CAD redrawing of the heritage asset of interest.