Narasimhan's researches have been focused on the theoretical, computational and applied aspects of Solid Mechanics, Fracture Mechanics and Mechanics of Materials.[7] During his post-doctoral days at Caltech, he worked with Rosakis on elastic-plastic solids with regard to crack initiation and growth and their studies on three-dimensional effects on elastic-plastic crack tip fields demonstrated the dominance of the effect at a distance of half the specimen thickness from the crack front.[4] He has also worked on the deformation and fracture behaviour of bulk metallic glasses and is credited with the development of a method for quantifying the micro-mechanics of mixed mode ductile fracture involving microvoid coalescence and shear band.[9] Collaborating with Upadrasta Ramamurty, his colleague at IISc, he worked on fracture mechanics of bulk metallic glasses and these studies enabled them to identify the time scale of fracture as well as to propose an explanation for the nano-trenches.[10] He has documented his researches in several articles;[11][note 2]ResearchGate and Google Scholar, online repositories of scientific articles, have listed 103[12] and 141 of them respectively.[13]
Narasimhan is a former member of the Science and Engineering Research Board of the Department of Science and Technology.[4] He sits in the editorial boards of journals including Engineering Fracture Mechanics[14] and Journal of Mechanics and Physics of Solids of Elsevier,[15] and the International Journal of Fracture of Springer.[16] Besides, he is a former member of the editorial board of Current Science journal of the Indian Academy of Sciences.[8] He has mentored a number of master's and doctoral scholars in their studies and has delivered several keynote or invited speeches including at the Complex Geometry and Operator Theory conference jointly organized by the Indian Statistical Institute and Institute of Mathematical Sciences in December 2015.[17]
His work alongside Ares Rosakis at Caltech earned Narasimhan the Rudolph Kingslake Medal of the SPIE, an honor he shared with Rosakis and Alan Taylor Zehnder in 1988.[18] The Council of Scientific and Industrial Research awarded him the Shanti Swarup Bhatnagar Prize, one of the highest Indian science awards in 1999.[19] The Indian Academy of Sciences elected him as a fellow in 2000[3] and he became an elected fellow of the Indian National Science Academy in 2002.[20] A year later, the Indian Institute of Science awarded him the 2003 Prof. Rustom Choksi Award for Excellence in Research[21] and he received the Distinguished Alumnus Award of the Indian Institute of Technology, Madras in 2016.[7] Narasimhan, who has been holding the J. C. Bose National Fellowship of the Department of Science and Technology of India since 2010, is also an elected fellow of the Indian National Academy of Engineering.[5]
Ghosal, A. K.; Narasimhan, R. (1997). "A finite element study of the effect of void initiation and growth on mixed-mode ductile fracture". Mechanics of Materials. 25 (2): 113–127. doi:10.1016/S0167-6636(96)00047-6.
Roy, Y. Arun; Narasimhan, R.; Arora, P. R. (1999). "An experimental investigation of constraint effects on mixed mode fracture initiation in a ductile aluminium alloy". Acta Metallurgica Sinica. 47 (5): 1587–1596. Bibcode:1999AcMat..47.1587A. doi:10.1016/S1359-6454(99)00015-4.
Basu, Sumit; Narasimhan, R. (2000). "A numerical investigation of loss of crack tip constraint in a dynamically loaded ductile specimen". Mechanics and Physics of Solids. 48 (9): 1967–1985. Bibcode:2000JMPSo..48.1967B. doi:10.1016/S0022-5096(99)00078-2.
Jayadevan, K. R.; Narasimhan, R.; Ramamurthy, T. S.; Dattaguru, B. (2001). "A numerical study of T-stress in dynamically loaded fracture specimens". International Journal of Solids and Structures. 38 (28–29): 4987–5005. doi:10.1016/S0020-7683(00)00323-1.
Biswas, P.; Narasimhan, R. (2002). "A numerical study of constraint effects on dynamic ductile crack initiation". Mechanics of Materials. 34 (9): 577–592. doi:10.1016/S0167-6636(02)00154-0.
Narasimhan, R. (2004). "Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model". Mechanics of Materials. 36 (7): 633–645. doi:10.1016/S0167-6636(03)00075-9.
^ ab"Faculty profile". Department of Mechanical Engineering, Indian Institute of Science. 2017. Archived from the original on 13 January 2018. Retrieved 28 January 2017.