**Full Professor**

**Contact**** ****Information**

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

Email: rogbusta@ing.uchile.cl

Office phone number:
(56)-2-29784543

**Education**

- PhD (Mathematics),
University of Glasgow, 2007

- Thesis title: ‘Mathematical modelling of
non-linear magneto- and electro-active rubber-like materials’
- PhD supervisor: Ray Ogden
- Master´s Degree Mechanical Engineering, Universidad Técnica Federico Santa María,
Valparaíso, Chile, 2000

- Thesis title: ‘Aplicación de la mecánica
de fractura con dos parámetros para un recipiente a presión con una
grieta elíptica 3D’ (Application of two parameters in fracture mechanics to study a 3D elliptic crack
in a pressure vessel).
- Supervisors: Fernando Labbe,
Juan Donoso
- Ingeniero Civil Mecánico (Mechanical Engineer), Universidad Técnica Federico Santa
María, 2000

- Final project: ‘Modelación con elementos finitos de los esfuerzos residuales en
uniones soldadas’ (Finite element
modelling of residual stresses
in welded unions)
- Supervisors: Fernando Labbe,
Juan Donoso

**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**=2**e**+**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__

**Projects**

·
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

**Presentations**

- 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, 19
^{th}of January 2017. - R. Bustamante, Implicit
constitutive relations for thermoelastic bodies.
40
^{th}Solid Mechanics Conference, Warsaw, Poland, 28^{th}of August- 2^{nd}September 2016. - R. Bustamante,
Constraints for some new classes of constitutive relations for elastic
bodies, 9
^{th}European Solid Mechanics Conference ESMC 2015, Madrid, Spain, 6-10 July 2015. - 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.
- 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.
- 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.
- 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.
- 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
- R. Bustamante, K. R. Rajagopal, On a new class of elastic bodies: Some
theoretical issues and applications, 8
^{th}European Solid Mechanics Conference, Graz, Austria 9-13 July 2012 - 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.
- R. Bustamante, Some
topics on a new class of elastic bodies,
*Perambulation in Continuum Mechanics: A Meeting in Celebration of the 60*, Texas A&M University, College Station, Texas, USA 11-13 November 2010^{th}Birthday of Professor K. R. Rajagopal - 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, 47*, Iowa State University, Ames, Iowa, USA 4-6 October 2010^{th}Annual Technical Meeting of the Society of Engineering Science - R. Bustamante,
Mathematical modelling of a new class of elastic bodies,
*Symposium on Nonlinear Mechanics in Celebration of the 60*, Iowa State University, Ames, Iowa, USA 4-6 October 2010^{th}Birthday of K. R. Rajagopal, 47^{th}Annual Technical Meeting of the Society of Engineering Science - R. Bustamante, Finite
element modelling of magneto-sensitive elastomers,
*9*, Sydney, Australia 19-23 Julio 2010^{th}World Congress on Computational Mechanics and 4^{th}Asian Pacific Congress on Computational Mechanics (WCCM/APCOM 2010) - 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 - R. Bustamante, R. W. Ogden, Transversely isotropic
electro-sensitive rubber-like materials,
*3*University of Toronto, Toronto, Ontario, Canada 25-29 Julio 2008^{rd}Canadian Conference on Nonlinear Solid Mechanics, - 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 - R. Bustamante,
Transversely isotropic non-linear magneto-sensitive rubber-like materials,
*Kolloquium**für Mechanik,*Technische Universität Kaiserslautern, Kaiserslautern, Germany, 27 February 2007 - 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 - 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

**Teaching**

·
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.

**Other**

·
Member of the scientific committee of the journal Ingenius http://revistas.ups.edu.ec/index.php/ingenius/index

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

http://www.esmc2015.org/_medien/_content/pdf/RogerBustamante_LuisDorfmann.pdf

·
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 24^{th}
to the 28^{th} of March of 2014.

http://pacamxiv.org/

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

http://www.esmc2012.tugraz.at/conference-format.html#mini_symposia

·
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
http://www.ms.uky.edu/~snp/