Computational solid and structural mechanics; Engineering practices in Classical Antiquity
My research and teaching interests are in computational solid and structural mechanics and in the development of engineering practices in Classical Antiquity. My current research areas are in (a) biomechanics: computational modeling of soft and cardiac tissue structures undergoing developmental processes, and (b) structural and solid mechanics: computational modeling of the mechanics of monumental concrete domes and vaults from Roman Imperial architecture. Both areas are highly interdisciplinary: my students and I work on the one hand with colleagues in archeology, classics, and architecture, and curators of monuments, and on the other with colleagues in developmental biology, anatomy, and cardiology. Central to both research areas is the development and application of finite element methods (FEM) from linear to highly nonlinear. Working on biomechanical problems we have developed a FEM formulation for hyperelastic incompressible materials, based on large strains and capable of modeling muscle contraction and growth mechanisms. Based on this formulation, we have created a 2- and 3-D FEM code capable of analyzing geometrically complex domains (for example, the complete heart in the chick embryo as well as densely trabeculated cardiac walls.) We have recently added a fully nonlinear visco-elastic formulation and we are working on the implementation of nonlinear damage models to be applicable both to soft tissue and concrete. My current work also builds on past research on 3D solid modeling and automatic/adaptive meshing and parallel processing FEM procedures. My research projects on Roman structures are also connected with my teaching in Roman Engineering (visit my courses web pages here)
Structural Design of Roman Concrete Domes at Hadrian's Villa
Collaboration with C. F. Giuliani, Archaeology and Ancient Topography, La Sapienza, Roma and A. Becene, University of Rochester. The long term objective is to determine the structural behavior and the inherent structural design philosophy for pozzolanic concrete domes at Hadrian's Villa at Tivoli, Italy. These include the Vestibule of Piazza d'Oro, the octagonal room in the Small Baths, the semidome of the Canopo, and the Eliocamino. The investigation is based on systematic computational modeling and analysis involving detailed solid modeling reconstruction, linear static and dynamic FEM analysis, nonlinear FEM analysis including fracture mechanics and nonlinear material characterization. For each selected dome we have three specific aims: (1) Determine the static conditions of the structure as originally built (structure in its original service conditions.) (2) Determine the design process (or processes) that likely led to the particular structural-architectural solution. (3) Determine the process (or processes) of structural decay and partial collapse that transformed the structure from the original service conditions to the present degraded state. The preliminary study on the structural design of the Vestibule is nearly completed and is in the process of being published. For an introductory presentation with FEM results on the Vestibolo, see here Le Cupole Cementizie (in Italian.)
The Grande Aula (Great Hall) of Trajan's Markets
Collaboration with L. Ungaro and M. Vitti, Sovraintendenza ai Beni Culturali di Roma, and C. F. Giuliani, Archaeology and Ancient Topography, La Sapienza, Roma. The long term objective is to establish the role of the Great Hall in the evolution of monumental concrete vault design. Of particular interest is the structural function of the lateral supporting arches and kinematic behavior of the supportive travertine blocks. As for the study at Hadrian's Villa, the investigation is based on systematic computational modeling and analysis involving detailed solid modeling reconstruction, linear static and dynamic FEM analysis, nonlinear FEM analysis including contact analysis, fracture mechanics and nonlinear material characterization. To address structural issues that arise during construction and before concrete setting, we plan to develop a nonlinear material formulation for pozzolanic concrete with large aggregate, typical of Trajanic and Hadrianic construction. To date, 3D linear and nonlinear (contact only) FEM analyses has shown that the arches do not fulfill a structural function. We are in the process of publishing the initial results. graduate research assistant: Philip Brune, undergraduate research project Sarilyn Swayngim. For 3D linear results, see here Structural Analysis of the Grande Aula.
Computational Modeling of Developmental Processes
Collaboration with L. A. Taber, Washington U., St. Louis. Building on our prior work, we propose to write a general computational code that can be used to model the biomechanics of developing soft tissue structures. This project includes six specific aims. The first three aims deal with software development, and the last three aims test the utility of the code for representative applications. Work at Rochester is primarily on FEM code development. Aims: (1) Extend our FEM code to include remodeling of individual tissue constituents. (2) Extend the code to include mechanical feedback as a regulator of developmental processes. Feedback, which enables self assembly of tissues, will be implemented mathematically through user-specified tissue construction rules. (3) Develop an algorithm to automatically update the geometrical description and the mesh of finite element models undergoing geometrical transformations due to large deformations. Dynamic updating of the geometrical representation will allow, for example, regional addition or subtraction of tissue (e.g., added cell layers or cell death) and the fusion of epithelial sheets (e.g., wound healing). (4) Construct a finite element model for early brain development, including growth regulated by mechanical feedback. (5) Construct a finite element model for functional adaptation of arteries, including cell growth, matrix remodeling, and smooth muscle tone, all regulated by mechanical feedback. (6) Construct a finite element model for cardiac looping morphogenesis, including cell growth and cytoskeletal contraction regulated by mechanical feedback. Graduate research assistant: Jonathan Young.
Mechanics of Looping in the Embryonic HeartL. A. TaberChristopher Buttaccio
- R. Perucchio, "Self-adaptive FEM procedures based on Hierarchical Substructuring and Multigrid Analysis,” in S. Kodiyalam and M. Saxena, Editors, Geometry and Optimization Techniques for Structural Design, Southampton, UK: Computational Mechanics Publications & London, UK: Elsevier Publishing Company, pp. 141-175, 1994.
- R. Srinivasan and R. Perucchio, "Finite element analysis of anisotropic nonlinear incompressible elastic solids by a mixed model,” International Journal for Numerical Methods in Engineering, vol.37, pp. 3075-3092, 1994.
- L. A. Taber and R. Perucchio, “Modeling heart development,” Journal of Elasticity, vol.61, pp. 165-197, 2000; reprinted in S. C. Cowin and J. D. Humphrey, Eds., Cardiovascular Soft Tissue Mechanics, Dordrecht, The Netherlands : Kluvier, pp. 165-197, 2002.
- Xie W. and R. Perucchio, “Multiscale finite element modeling of the trabeculated embryonic Heart: Numerical Evaluation of the Constitutive Relations for the Trabeculated Myocardium,” Computer Methods in Biomechanics and Biomedical Engineering, vol. 4, pp. 231-248, 2001.
- Xie W. , R. Thompson, and R. Perucchio, “A topology-preserving parallel 3D thinning algorithm for extracting the curve skeleton,” Pattern Recognition, vol. 36, pp. 1529-1544, 2003.
- Xie W. and R. Perucchio, "Nonlinear 3D FE Biomechanical Analysis of the Trabeculated Embryonic Heart Under Cardiac Cycle Loading," ASME-BED Proceedings of the 2003 Summer Bioengineering Conference, pp. 425-426, Key Biscayne, FL, June 25-29, 2003.
- Taber L.A., J. Zhang, and R. Perucchio, “Computational Model for the Transition from Peristaltic to Pulsatile Flow in the Embryonic Heart Tube,” Journal of Biomechanical Engineering, Vol. 129, June 2007, pp. 441-449, 2007. Awarded the 2007 Richard Skalak ASME Journal of Biomechanical Engineering Best Paper.
- Young J.M., E. M. Beecher, B.A. Filas, L.A. Taber, and R. Perucchio, “FEM Voxel Modeling of the Tubular Embryonic Chick Heart for Finite Strain Analysis,” ASME-BED 2008 Summer Bioengineering Conference, June 25-29, Marco Island, FL.
- Yao J. , V.D. Varner, R. Perucchio, and L.A. Taber, “Viscoelastic Material Properties of the Hamburger-Hamilton Stage 12 Chick Heart,” ASME-BED 2008 Summer Bioengineering Conference, June 25-29, Marco Island, FL.
- R. Perucchio and P. Brune, “The Structural Design of the Great Hall of Trajan’s Markets,” Bullettino della Commissione Archeologica Comunale di Roma, invited paper, to appear in 2009.