Virtual monitoring of self-sensing CNT-reinforced polymer nanocomposite plates experiencing crack growth


The production and application of carbon nanotubes (CNTs) in different fields have increased exponentially in the last decades. CNT reinforced composites (CNTRC) materials exhibit exceptional strength and stiffness properties as well as improved fatigue performance and fracture toughness. In addition, CNTs are electrically conductive fillers and can form conductive networks in CNTRCs. The electrical conductivity and associated piezoresistive behaviors can, therefore, endow polymeric CNTRCs with strain self-sensing capabilities, making them ideal candidates for structural health monitoring (SHM) and related applications.

The electro-mechanical properties of CNTRCs are influenced by different factors, such as CNT type, alignment, volume fraction and aspect ratio. To evaluate such factors and enable material optimization, recent research efforts have focused on developing robust numerical techniques to predict the sensing capabilities of these materials. Notably, the performance and service life of CNTRC components are highly susceptible to crack growth. Therefore, it is important that numerical tools used to simulate crack-type defects in these composites be able to predict the influence of crack growth on the structural integrity and sensing capabilities of CNTRC components.

Herein, Professor Luis Rodríguez-Tembleque, Mr. J. Vargas, Dr. Enrique García-Macías, Professor Federico C. Buroni and Professor Andrés Sáez from Universidad de Sevilla developed an eXtended Finite Element Method (XFEM)-based computational framework for simulating the crack growth in CNTRC nanocomposite plates. The developed framework, was implemented in the commercial software ANSYS, was applied to conduct virtual monitoring of the effect of crack growth on the mechanical response, electrical conductivity and sensing performance of self-sensing CNTRC polymer plates. The work is currently published in the journal, Composite Structures.

In brief, the proposed framework follows a two-step scheme. In the first step, the mechanical properties were homogenized using the proposed framework to establish the strain responses of the cracked composites. In the second step, the electrical conductivity and piezoresistive properties of the elements within the composite domains were homogenized as per the strain state to compute the electrical resistance between the electrodes. These steps provided a clear definition of the non-homogenous electrical conductivity problem that was later solved using coupled-field elements provided by the ANSYS software. This framework was validated for stationary cracks and applied to a series of crack-growth configurations.

The authors have shown that the cracks and their growth significantly modified the electrical properties and self-sensing performance of the CNTRC. A better sensor efficiency was observed at lower crack permittivity. However, the piezoresistive effect under electrically impermeable crack-face conditions was generally negligible. This suggested that the crack-growth-induced discontinuity in the electrical field was relatively higher that piezoresistivity effects triggered by the strain field modification. Furthermore, the measured electrical resistances were highly sensitive to changes in the orientation and the size of the cracks.

In summary, the effects of crack growth on the electricalmechanical properties of CNTRC materials were successfully simulated and virtually monitored using the proposed numerical XFEM scheme. The changes in the electrical resistance between the electrodes, as well as changes in piezoresistivity, were correlated with the presence of cracks in the domains of the CNTRC plates, allowing prompt detection of the growth and severity of the cracks. The effectiveness and applicability of the proposed framework was successfully validated. In a statement to Advances in Engineering, Professor Luis Rodríguez-Tembleque, first and corresponding author stated that the study provided useful insights that would advance the application of CNTRC materials in virtual and on-site SHM.

Virtual monitoring of self-sensing CNT-reinforced polymer nanocomposite plates experiencing crack growth - Advances in Engineering

About the author

Dr. Luis Rodríguez-Tembleque is an Associate Professor in the Department of Continuum Mechanics and Theory of Structures at the Universidad de Sevilla, Spain. He received his BEng degree in Mechanical Engineering from the Universidad de Mlaga in 2003, M. S., his MSc degree (1st class with distinction) from the Universidad de Sevilla in 2007 and his PhD degree from Universidad de Sevilla in 2009. He is founder member of the Spanish Society of Theoretical and Applied Mechanics (SEMTA), a member of the European Mechanics Society (EUROMECH) and of the Spanish Society of Numerical Methods in Engineering (SEMNI).

His main research interests are focused on computational mechanics with emphasis on computational contact mechanics, substructure coupling techniques, fracture and damage mechanics problems and multiscale modelling in advanced (multifield and multifunctional) materials systems, i.e., piezoelectric and piezocomposites (Lead-free piezoelectrics) and nanocomposites (carbon nanotube-reinforced composites). He has led several research projects on these topics and co-organized several international conferences on fracture and damage mechanics. He has edited several books, journal special issues and conference proceedings, and he has published several chapters and papers in scientific journals.


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Andres Saez is Professor at the Department of Continuum Mechanics and Structural Analysis of Universidad de Sevilla (Seville, Spain). He received his BEng degree in Mechanical Engineering from the School of Engineering at Universidad de Sevilla in 1992, his MSc degree from the Civil Engineering Department at Northwestern University (Evanston, Illinois, USA) in 1994 and his PhD degree from Universidad de Sevilla in 1997.

His scientific contributions have mainly focused on characterizing the dynamic behavior of structures and on applications related to structural integrity. His seminal contributions focused on the development of models and numerical tools (based on the Boundary Element Method and, to a lesser extent, on the Extended Finite Element Method) for the simulation of damage in structural components built with advanced materials. The analyzed material models encompass from composites to functional materials, which present a multi-field coupling between their elastic and electric/magnetic properties (for instance piezoelectric or magnetoelectroelastic materials). More recently, his research has extended to the field of experimental identification of the dynamic properties of structures, with application to aeronautical and, fundamentally, civil engineering structures (monitoring of structural integrity, rehabilitation of masonry constructions, behavior of pedestrian footbridges); as well as to the design and development of sensors based on carbon nanotube-reinforced elements (CNT) and lead-free piezoelectrics, aimed at their subsequent use in damage detection applications.

He has co-authored more than 250 publications, including research papers in scientific journals, books, book chapters and conference proceedings and he has led several research projects on damage mechanics and structural integrity.

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Dr. Enrique García-Macías is an Assistant Professor in the Department of Structural Mechanics and Hydraulic Engineering at the University of Granada (Spain). He graduated with valedictorian honours in Civil Engineering in 2011 and in MSc. of Structures in 2012 at University of Granada (Spain). He received his PhD in Mechanical Engineering and Industrial Organization from University of Seville in 2018. His Ph.D. thesis, entitled “Carbon NanoTubes (CNTs) for the development of high-performance and smart composites” received the distinction of “Best Thesis Award” by the Royal Academy of Doctors of Spain in 2018, and the “Extraordinary Thesis Award” by the University of Seville in 2022. He completed a postdoc position at the University of Perugia in Italy (2018-2019) and worked as a Teaching Fellow at Imperial College London (UK) (2019-2020) until getting his current position in 2020.

His scientific interests are organized along two main lines, including (i) smart multifunctional materials, and (ii) Structural Health Monitoring (SHM). The latter particularly focuses on vibration-based SHM, machine learning techniques, and the development of new damage identification approaches exploiting continuous monitoring data.

About the author

Dr. Federico C. Buroni is an Associate Professor in the Department of Mechanical Engineering & Manufacturing at the University of Seville (Spain). He has completed a Mechanical Engineering (5-years) degree from the Universidad Nacional de Mar del Plata in Argentina, and a M.Sc. (2-years) degree from the Universidade Federal do Rio Grande do Sul in Brazil. In 2012 he completed his Ph.D thesis entitled “Three-dimensional Green functions for anisotropic and multifield materials” at the University of Seville, obtaining the (highest) ‘cum laude’ designation. His thesis led him to receive the distinction of receiving the ‘Premio Extraordinario de Doctorado’ award. After that he got a position as an Assistant Professor at the University of Seville.  During his postdoctoral stage, he had the opportunity to complete research stays at Rutgers University (USA), the Universidad Nacional de Mar del Plata (Argentina), and the University of Bristol (UK) as Research Fellow.  He has also been awarded a postdoctoral scholarship to visit the University of Oxford under the ”José Castillejo” program for young doctors sponsored by the Ministerio de Educación, Cultura y Deporte of Spain. He has participated as scientific committee in several international congresses, and he is cofounder of the SEMTA (Sociedad Española de Mecánica Teórica y Aplicada) association. He is Principal Investigator of two research projects founded by the Spanish government.

His main research interests are related to the micromechanics, computational modelling, and theory of multifunctional composites and materials. Through his research, he has presented several contributions related to anisotropic elasticity, Green’s functions, and the boundary element method for coupled problems. Currently, his research has focused on the modelling and design of three-dimensional printable lead-free piezocomposites, which offer scalable and environmentally friendly solutions in many engineering applications. The aim of this investigation is to identify and understand the underlying micromechanisms for the amplification of the piezoelectric and piezoresistive responses via analytical and numerical methods. The final goal is to propose competitive alternatives to well-established lead-based piezocomposites.


Rodríguez-Tembleque, L., Vargas, J., García-Macías, E., Buroni, F.C., & Sáez, A. (2022). XFEM crack growth virtual monitoring in self-sensing CNT reinforced polymer nanocomposite plates using ANSYSComposite Structures, 284, 115137.

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