Roger A. Bustamante Plaza



                                                                                                              Roger Bustamante                                  


Full Professor


Contact Information
     Mail Address:  Departamento de Ingeniería Mecánica, Universidad de Chile, Torre Poniente, Piso 4, Beauchef 851, Santiago Centro,         Santiago, Chile

Office phone number:         (56)-2-29784543


Research Interests

My main areas of research are Nonlinear Elasticity and Magneto-Electro-Elasticity. At the present I am working on the following topics:

·        Study of some new classes of constitutive relations for elastic bodies:

Recently some new classes of constitutive relations have been proposed, where the Cauchy stress tensor T and left Cauchy-Green strain tensor B are assumed to be obtained from in general implicit relations of the for f(T,B)=0. Several interesting cases can be derived from such a general constitutive relation, for example, if the strains (the gradient of the displacement field) are assumed to be small, such that B=2e+I (where e is the linearized strain tensor), then for the case we have arbitrarily large stresses, but strains are small, it can be proved that the type of constitutive equation that we must use in such a  case would be of the form e=g(T), and not of the form T=h(e), which is the incorrect expression used by many researchers for such classes of problems. The equation e=g(T) is interesting on its own right, since we can study problems where the strains can be small but the behaviour may be nonlinear. Such problems appear for example, in fracture mechanics of brittle bodies, in rock mechanics (if in a first approximation we consider rock as elastic materials), and in the study of some metal alloys, among many other possible applications. At the present, I am working on different topics, such as to solve some simple boundary value problems considering e=g(T) and some other more general expressions that can be derived from f(T,B)=0. As well as this, I am studying some restrictions on these functions to actually have elastic bodies, and also the way constraints for the deformations can be incorporated for these new theories

·        Research on some topics on magneto- and electro-elasticity:

There is type of elastomer, where the rubber-like matrix is filled with electro-magneto active particles during the curing process, i.e. when the rubber-like material is in a liquid state. When the material solidifies, the particles remain locked inside the matrix, and if an external electric or magnetic field is applied, the material can show relatively large deformations. It is possible to control the amount of deformation of a body made from such material with that external magnetic or electric field, and therefore these elastomers have attracted the attention of the researchers, in particular in the design of vibration control devices and in the design of robot parts. I am interested in some theoretical and numerical aspects regarding the mathematical modelling of such materials. From the point of view of modelling, it is necessary to consider two coupled systems of equations; one is the equation of motion, and the other being the Maxwell equations. At the present, I am interested in studying the case when the magneto- or electro-active particles have an initial preferred alignment, and so when a field is applied, the material behaves as an orthotropic body. I am interested in finding some expressions for the constitutive equations for that case and also in solving some boundary value problems analytically and numerically.

Other Research Projects

·        Mathematical modelling of rock mechanics: I have been one of the participants of a series of projects for one of the leading mining companies of Chile. In such projects we have been interested in modelling the mechanical behaviour of rock, with applications to:

§  The modelling of propagations of cracks induced by liquid injection: In underground mining, in order to help the natural fracture of rock due to caving, in previous step artificial cracks are created inside the mountain, using the injection of high pressure fluid (such as in fracking). The modelling of the behaviour of such cracks, i.e. how such cracks grow and behaves, and the interaction with the fluid inside, is a challenging topic from the point of view of mathematical modelling

§  Modelling of the caving: In underground mining, the caving is a process in which an initial gallery is created underground, where at some moment some pillars are dynamited, generating an initial cave, which starts growing upward naturally. The reason is that inside the mountain there are stresses, which are approximately uniform, but when that initial gallery is created, around it the stresses behave in a non-uniform way, where it is possible to show some concentration of stresses in some parts of the surface of the initial cave. Such concentration of stresses causes the rock to fail, and it is possible then to extract the minerals using such natural forces, minimizing the use of explosives. In that project I studied that process considering a plane strain model, using the finite element method, and assuming the rock as an inhomogeneous material with different failure mechanisms in traction and in compression. 

§  Modelling of the caving in or collapse: The caving process mentioned in the previous paragraph, sometimes does not work because a whole section of the mountain collapse on the galleries. Such process is called caving in. At the moment I am working in the mathematical modelling of that phenomenon, considering different advances nonlinear constitutive equation for the rock.


·        Modelling of the micro-movement in dental implants: With the help of some final year students, and in collaboration with colleagues from the Faculty of Odontology of Universidad de Chile, we have been working on the problem of modelling the behaviour of dental implants, for completely toothless people (who have lost the teeth a long time ago), when 4 o 6 implants are used in order to support the artificial teeth. When a long time has passed since a person loses the teeth, the bone on the jaw may be lost, therefore two of such implants are located on the zygomatic bone. We have been interested in studying the relative movement between the surface of the implants, and the surrounding bone, for the period of time immediately after the implants are put on the patient. It has been indicated in the literature that such relative movement (micro-movement) may be very important in order to assess if the implants will fail or not. The study has been carried using the finite element method, considering a nonlinear model for the friction between the surfaces of the implants and the bone.

Publications Click here


·        Fondecyt number 1160030

o   ‘On the use of implicit constitutive relations to model the behaviour of elastic and inelastic deformations in continua: Applications to the mathematical modelling of rock’.

o   Dates: April 2016 to the present.

·        Fondecyt number 1120011

o   ‘Study of some new constitutive laws for elastic bodies’

o   Dates: March 2012 to March 2016

·        Fondecyt number 11085024

o   ‘Mathematical modelling of non-linear magneto-sensitive elastomers’.

o   Dates: November 2008 to October 2011


  1. R. Bustamante, Some topics on some new classes of constitutive relations for elastic bodies, Department of Mechanical Engineering, University of Texas A&M, College Station, Texas, USA, 19th of January 2017.
  2. R. Bustamante, Implicit constitutive relations for thermoelastic bodies. 40th Solid Mechanics Conference, Warsaw, Poland, 28th of August- 2nd  September 2016.
  3. R. Bustamante, Constraints for some new classes of constitutive relations for elastic bodies, 9th European Solid Mechanics Conference ESMC 2015, Madrid, Spain, 6-10 July 2015.
  4. R. Bustamante, M.H.B.M. Shariff, New sets of invariants for an electro-elastic body with one and two families of fibres, Encuentro de Elasticidad No-lineal, Homogenización y Fractura, Facultad de Matematicas, Pontificia Universidad Católica de Chile, 24-24 June 2015.
  5. R. Bustamante, Some topics on some new classes of constitutive relations for elastic bodies, XXI Congreso sobre Métodos Numéricos y sus Aplicaciones ENIEF 2014, Bariloche, Argentina, 23-26 September 2014.
  6. Ortiz-Bernardin, R. Bustamante, K. R. Rajagopal, Estudio numérico de cuerpos elásticos que están descritos por ecuaciones constitutivas que exhiben deformaciones limitadas, Jornadas de Mecánica Computacional, Santiago, Chile, 3-4 October 2013.
  7. R. Bustamante, New classes of constitutive relations for electro-elastic materials, International Workshop on New Trends in Solid Mechanics: Coupled Fields and Multi-scale Modelling, Castro Urdiales, Cantabria, Spain, 24-28 June 2013.
  8. R. Bustamante, Implicit constitutive relations for electro-elastic bodies, Chinese-Italian Bilateral Meeting on Mechanics and International Workshop on Mathematical and Mechanical Modelling for Materials, City University of Hong Kong, Hong Kong, China 28-31 August 2012
  9. R. Bustamante, K. R. Rajagopal, On a new class of elastic bodies: Some theoretical issues and applications, 8th European Solid Mechanics Conference, Graz, Austria 9-13 July 2012
  10. R. Bustamante, Un nuevo tipo de ecuación constitutiva para cuerpos elásticos: Desafíos para la modelación numérica, X Jornadas de Mecánica Computacional, Departamento de Ingeniería Estructural, Pontificia Universidad Católica de Chile, Santiago, 13-14 Octubre 2011.
  11. R. Bustamante, Some topics on a new class of elastic bodies, Perambulation in Continuum Mechanics: A Meeting in Celebration of the 60th Birthday of Professor K. R. Rajagopal, Texas A&M University, College Station, Texas, USA 11-13 November 2010
  12. R. Bustamante and G. Holzapfel, The problem of computing 3D residual stresses distributions in a neo-Hookean tube, Symposium in honor of the contribution of Ray Ogden, the recipient of the Prager Medal, 47th Annual Technical Meeting of the Society of Engineering Science, Iowa State University, Ames, Iowa, USA 4-6 October 2010
  13. R. Bustamante, Mathematical modelling of a new class of elastic bodies, Symposium on Nonlinear Mechanics in Celebration of the 60th Birthday of K. R. Rajagopal, 47th Annual Technical Meeting of the Society of Engineering Science, Iowa State University, Ames, Iowa, USA 4-6 October 2010
  14. R. Bustamante, Finite element modelling of magneto-sensitive elastomers, 9th World Congress on Computational Mechanics and 4th Asian Pacific Congress on Computational Mechanics (WCCM/APCOM 2010), Sydney, Australia 19-23 Julio 2010
  15. R. Bustamante, A variational formulation for a magneto sensitive body interacting with a rigid semi-infinite body, and some restrictions for the total energy function, Kolloquium für Mechanik, Universität Erlangen Nünberg, Erlangen, Germany, 19 January 2010
  16. R. Bustamante, R. W. Ogden, Transversely isotropic electro-sensitive rubber-like materials, 3rd Canadian Conference on Nonlinear Solid Mechanics, University of Toronto, Toronto, Ontario, Canada 25-29 Julio 2008
  17. R. Bustamante, A. Dorfmann and R. W. Ogden, A variational formulation for magneto-active elastomers based on the total energy approach, International Conference on Industrial and Applied Mathematics, Federal Institute of Technology, Zurich, Switzerland 16-20 July 2007
  18. R. Bustamante, Transversely isotropic non-linear magneto-sensitive rubber-like materials, Kolloquium für Mechanik, Technische Universität Kaiserslautern, Kaiserslautern, Germany, 27 February 2007
  19. R. Bustamante, R. W. Ogden, Some boundary value problems for non-linear transversely isotropic electro-active elastomers, International Symposium on Trends in Applications of Mathematics to Mechanics (STAMM), Vienna University of Technology, Vienna, Austria, 10-14 Julio 2006
  20. R. Bustamante, R. W. Ogden, A numerical model of the electric field for an electro-active rubber like cylinder under traction, British Applied Mathematics Colloquium (BAMC), Keele University, 24-27, United Kingdom, April 2006



·        Resistencia de Materiales ME46-A, ME3202 (Strength of Materials)

·        Mecánica de Medios Continuos ME701 (Continuum Mechanics)

·        Elementos Finitos ME 564 (Finite Element Method)


Short Courses

·        Electro-elasticidad no-lineal: teoría y desafíos en modelación numérica (Nonlinear electroelasticity: Theory and challenges to numerical modelling). Universidad Politécnica de Madrid 14-28 Mayo 2011.


·        Formulaciones variacionales en mecánica de sólidos (Variational formulations in solid mechanics). Universidad Politécnica de Madrid 17-25 Mayo 2012.


·        Member of the scientific committee of the journal Ingenius

·        I was co-organizer of the Minisymposium on Nonlinear Elasticity for the Euromech 2015 Congress

·        I was one of the co-editors for a Special Volume for the IMA Journal of Applied Mathematics in honour of Ray Ogden.

·        I was the main organizer and chair for the XIV Pan American Congress of Applied Mechanics PACAMXIV, which was held from the 24th to the 28th of March of 2014.

At the present, I am the editor of a special volume for Acta Mechanica, where some of the works presented in the conference will be published.

·        I was co-organizer of the Minisymposium on Nonlinear Elasticity for the Euromech 2012 Congress

·        I have been peer to peer reviewer for some articles submitted to the following journals:

§  Journal of Elasticity

§  International Journal of Solids and Structures

§  Journal of Electrostatics

§  Acta Mechanica

§  Mathematics and Mechanics of Solids

§  Proceedings of the Royal Society A

§  International Journal of Damage Mechanics

§  Computer Methods in Applied Mechanics and Engineering

§  Mechanics Research Communications

§  International Journal of Engineering Sciences

§  International Journal of Non-linear Mechanics

§  International Journal of Advances in Engineering Sciences and Applied Mathematics

§  The European Physical Journal E: Soft Matter and Biological Physics

§  Indian Journal of Engineering & Materials Sciences

§  Rubber Chemistry and Technology

§  The Quarterly Journal of Mechanics and Applied Mathematics

§  Meccanica

§  Journal of the Mechanics and Physics of Solids

§  Journal of Applied Physics

§  International Journal of Engineering Technologies, IJET

§  International Journal for Numerical Methods in Engineering

§  BioMedical Engineering OnLine

§  Mathematical Reviews

§  Mathematical Problems in Engineering

·        Member of the European Mechanics Society

·        Member of the Society for Natural Philosophy