Papers
1. M.H.B.M. Shariff, R. Bustamante, M. Hossain, A generalised
time-dependent mathematical formulation for magnetoelectrically
coupled soft solids at finite strains. Symmetry,
15 (2023) 628.
2. R. Bustamante,
Incremental equations and propagation of small amplitude waves for isotropic
incompressible elastic bodies. The case the Hencky
strain tensor is a function of the Cauchy stress tensor. International Journal of Engineering Science, 183 (2023) 103808.
3. R. Bustamante, K.R.
Rajagopal, Applications of implicit constitutive
theory for describing the elastic response of rocks and concrete. Archive of Mechanics, 74 (2022) 513--547.
4. A. Melnikov, J. Merodio, R.
Bustamante, J. Merodio, Bifurcation analysis of
residually stressed neo-Hookean and Ogden electroelastic tubes. Philosophical
Transactions of the Royal Society A, 380
(2022) 20210331.
5. M.H.B.M. Shariff, J. Merodio, R.
Bustamante, Nonlinear elastic constitutive relations of residually stressed
composites with stiff curved fibres. Applied Mathematics and Mechanics, 43 (2022) 1515--1530.
6. R. Ibarra, R.
Bustamante, Analysis of the propagation of small-amplitude waves in nonlinear
elastic solids for problems with infinitesimal strains. Wave Motion, 113 (2022)
102985
7. R. Bustamante, K.R.
Rajagopal, A three-dimensional implicit constitutive
relation for a body exhibiting stress softening. Part II: Analysis of some
boundary value problems. Acta Mechanica, 233 (2022) 3319--3335.
8. R. Bustamante, K.R.
Rajagopal, A three-dimensional implicit constitutive
relation for a body exhibiting stress softening. Part I: Theoretical
underpinning. Acta Mechanica, 233 (2022) 2541-2559.
9. R. Bustamante, K.R.
Rajagopal, On the response
of anisotropic elastic bodies described by implicit constitutive relations. Zeitschrift fur angewandte Mathematik und Mechanik, 102 (2022) e202200029
10. M.H.B.M. Shariff, M. Hossain, R. Bustamante, J. Merodio,
Modelling the residually stressed magneto-electrically coupled soft elastic
materials. International Journal of
Nonlinear Mechanics, 137 (2021)
103802.
11. R. Bustamante, A
note on a new constitutive model for rubber-like solids. Mechanics Research Communications, 117 (2021) 103775.
12. R. Bustamante, K.
R. Rajagopal, A new type of constitutive equation for
nonlinear elastic bodies. Fitting with experimental data for rubber-like
materials. Proceedings of the Royal
Society of London A, 477 (2021)
13. R. Bustamante, K.R.
Rajagopal, The circumferential shearing of a
cylindrical annulus of viscoelastic solids described by implicit constitutive
relations. Acta Mechanica, 232 (2021) 2679-2694.
14. J. Tobar, L. Andueza, A. Jimenez, R.
Bustamante, J. Carvajal, Micromotion
analysis of immediately loaded implants with titanium and cobalt-chrome
superstructures. 3D finite element analysis. Clinical and Experimental Dental Research, 7 (2021) 581--590.
15. R. Bustamante, K.R.
Rajagopal, A class of transversely isotropic
non-linear elastic bodies that is not Green elastic. Journal of Engineering Mathematics, 127 (2021) 2.
16. R. Bustamante, M.
Hossain, M.H.B.M. Shariff, A generalized mathematical
formulation for magneto-electrically coupled soft materials at finite strains. International Journal of Engineering Science
159 (2021) 103429.
17. M.H.B.M. Shariff, R. Bustamante, A spectral approach for nonlinear
transversely isotropic elastic bodies, for a new class of constitutive
equation. Applications to rock mechanics. Acta Mechanica 231 (2020) 4803-4818.
18. R. Bustamante, K.R.
Rajagopal, R. Meneses, O.
Orellana, Implicit constitutive relations for visco-elastic
solids: Part II. Non-homogeneous deformations. International Journal of Nonlinear Mechanics 126 (2020) 103560.
19. R. Bustamante, K.R.
Rajagopal, R. Meneses, O.
Orellana, Implicit constitutive relations for describing the response of visco-elastic bodies. International
Journal of Nonlinear Mechanics 126
(2020) 103526.
20. M.H.B.M. Shariff, R. Bustamante, J. Merodio,
A nonlinear spectral rate-dependent constitutive equation for
electro-viscoelastic solids. Zeitschrift fur angewandte Mathematik und Physik 71
(2020) 126.
21. R. Bustamante, Some
universal solutions for a class of incompressible elastic body that is not
Green elastic. The case of large elastic deformations. The Quarterly
Journal of Mechanics and Applied Mathematics 73 (2020) 177-199.
22. R. Bustamante, New
classes of electro-elastic and thermo-electro-elastic bodies that are not Green
elastic. International Journal of
Engineering Science 152 (2020)
103308.
23. M.H.B.M. Shariff, R. Bustamante, J. Merodio,
A nonlinear constitutive model for a two preferred direction electro-elastic
body with residual stresses. International Journal of Nonlinear Mechanics 119 (2020) 103352.
24. M.H.B.M. Shariff, R. Bustamante, J. Merodio,
A nonlinear electro-elastic model with residual stresses and a preferred
direction Mathematics and Mechanics of
Solids 25 (2020) 838-865
25. R. Bustamante, Some
universal solutions for incompressible elastic bodies that are not Green
elastic. International Journal of
Engineering Science 149 (2020)
103223.
26. R. Bustamante,
Corrigendum: Direct determination of stresses from the stress equations of
motion and wave propagation for a new class of elastic bodies. Mathematics and Mechanics of Solids 25 (2020) 866-868.
27. M.H.B.M. Shariff,
R. Bustamante, J. Merodio, Nonlinear electro-elastic bodies with residual
stresses: Spectral formulation. The
Quarterly Journal of Mechanics and Applied Mathematics 71 (2018) 485-504
28. R. Bustamante, K.R.
Rajagopal, Modeling residual stresses in elastic
bodies described by implicit constitutive relations. International Journal of Nonlinear Mechanics, 105 (2018) 113-129.
29. R. Bustamante, K.R.
Rajagopal, Correction to: On
a new class of electroelastic bodies. I. Proceedings of the
Royal Society of London, 473 (2018)
20170523
30. R. Bustamante, K.R.
Rajagopal, A nonlinear model for describing the
mechanical behaviour of rock. Acta Mechanica 229 (2018) 251-272
31. R. Meneses, O. Orellana, R. Bustamante, A note on the wave
equation for a new class of constitutive relation for nonlinear elastic bodies.
Mathematics and Mechanics of Solids 23 (2018)148-158
32. M.H.B.M. Shariff, R. Bustamante, J. Merodio,
Rate type constitutive equations for fiber reinforced nonlinearly vicoelastic solids using spectral invariants. Mechanics Research Communications 84 (2017) 60-64
33. M.H.B.M. Shariff, R. Bustamante, J. Merodio,
On the spectral analysis of residual stress in finite
elasticity. IMA Journal of Applied
Mathematics 82 (2017) 656-680.
34. R. Bustamante, K.R.
Rajagopal, Implicit equations for thermoelastic
bodies. International Journal of Non-linear
Mechanics 92 (2017) 144-152
35. M.H.B.M Shariff, R. Bustamante, M. Hossain and P. Steinmann, A
novel spectral formulation for nonlinear transversely magnetoelastic deformations. Mathematics and Mechanics of Solids 22 (2017) 1158-1176.
36. R. Bustamante, Solutions
of some boundary value problems for a class of constitutive relation for
nonlinear elastic bodies that is not Green elastic. The Quarterly
Journal of Mechanics and Applied Mathematics, 69 (2016)
257-279.
37. M.H.B.M. Shariff, R. Bustamante, An anisotropic model for the
Mullins effect in magneto-active rubber-like materials. Journal of Mechanics of Materials and Structures, 11 (2016)
559-582.
38. P. Arrue, R. Bustamante, D. Sfyris, A
note on incremental equations for a new class of constitutive relation for
elastic bodies. Wave Motion
65 (2016) 44-54
39. D. Sfyris, G.I.
Sfyris and R. Bustamante, Nonlinear electro-magneto-mechanical
constitutive modeling of monolayer graphene. Proceedings of the
Royal Society of London A 472 (2016) 20150750
40. R. Bustamante, O.
Orellana, R. Meneses and K.R. Rajagopal,
Large deformations of a new class of incompressible elastic bodies. Zeitschrift fur angewandte
Mathematik und Physik 67 (2016) 47
41. R. Bustamante,
M.H.B.M. Shariff, New set of invariants for an electro-elastic
body with one and two families of fibres. European
Journal of Mechanics A 58 (2016)
42-53.
42. S. Montero, R.
Bustamante, A. Ortiz, Numerical study of some plane stress problems for a new
class of constitutive relation for elastic bodies. Acta Mechanica, 227 (2016) 601-615.
43. R. Bustamante, K.
R. Rajagopal, On the consequences of the
constraint of incompressibility with regard to a new class of constitutive
relations for elastic bodies. Small displacement gradient approximation. Continuum Mechanics and Thermodynamics 28 (2016) 293-303.
44. R. Bustamante, K.
R. Rajagopal, Study of a new class of non-linear inextensible
elastic bodies. Zeitschrift fur angewandte Mathematik und Physik 66
(2015) 3663-3677.
45. R. Bustamante, K.
R. Rajagopal, A note on some new classes of
constitutive relations for elastic bodies, IMA
Journal of Applied Mathematics, 80
(2015) 1287-1299.
46. R. Bustamante, K.
R. Rajagopal, Implicit constitutive relations in
nonlinear magneto-elasticity. Proceedings
of the Royal Society of London A, 471
(2015) 20140959
47. M.H.B.M. Shariff, R. Bustamante, On the
strain invariants for a body with two preferred directions in nonlinear
elasticity. International Journal of
Engineering Science 97 (2015)
18-25
48. D. Sfyris, R. Bustamante, On the treatment of non-solvable
implicit constitutive relations in solid mechanics, Zeitschrift
fur angewandte Mathematik
und Physik, 66
(2015) 1165-1774
49. R. Bustamante, K.
R. Rajagopal, Solutions of some boundary value problems for a new
class of elastic bodies. Comparison with the classical theory of linear
elasticity: Part I Problems with cylindrical symmetry. Acta Mechanica, 226 (2015) 1815-1838
50. R. Bustamante, K.
R. Rajagopal, Solutions of some boundary value
problems for a new class of elastic bodies. Comparison with the classical
theory of linear elasticity: Part II A problem with spherical symmetry. Acta Mechanica, 226 (2015) 1807-1813
51. E. Salas, R.
Bustamante, Numerical solution of some boundary value problems in nonlinear magnetoelasticity, Journal
of Intelligent Material Systems and Structures, 26 (2015) 156-171.
52. R. Bustamante,
M.H.B.M. Shariff, A principal axis formulation for
nonlinear magnetoelastic deformations: Isotropic
bodies, European Journal of Mechanics,
50 (2015) 17-27
53. R. Bustamante, D. Sfyris, Direct determination of stresses from the stress
equations of motion and wave propagation for a new class of elastic bodies, Mathematics and Mechanics of Solids, 20 (2015) 80-91
54. A. Ortiz-Bernardin, R. Bustamante, K. R. Rajagopal,
A numerical study of elastic bodies that are described by constitutive
equations that exhibit limited strains, International
Journal of Solids and Structures, 51
(2014) 875-885
55. D. Sfyris, R. Bustamante, Use of some theorems related with the
tensor equation AX+XA=H for some classes of implicit constitutive relations, The Quarterly Journal of Mechanics and
Applied Mathematics, 66 (2013)
157-163
56. R. Bustamante, R.
W. Ogden, Nonlinear
magnetoelastostatics: energy functional and their second
variations, Mathematics and Mechanics of
Solids, 18 (2013) 760-772.
57. R. Bustamante, K.
R. Rajagopal, On a new class of electroelastic
bodies. II. Boundary value problems, Proceedings
of the Royal Society of London A, 469
(2013) 20130106.
58. R. Bustamante, K.
R. Rajagopal, On a new class
of electroelastic bodies: Part I, Proceedings of the Royal Society of London A,
469 (2013) 20120521.
59. F. Vogel, R.
Bustamante, P. Steinmann, On some mixed variational
principles in magneto elastostatics. International Journal of Nonlinear Mechanics,
51 (2013) 157-169
60. G. deBotton, R. Bustamante, A.
Dorfmann, Axisymmetric bifurcations of thick
spherical shells under inflation and compression, International Journal of Solids and Structures, 50 (2013) 403-413
61. R. Bustamante, J.
Merodio, On weak formulations and their second variation in nonlinear electroelasticity, Mechanics
Research Communications, 46
(2012) 15-19
62. R. Bustamante, K.
R. Rajagopal, On the
inhomogeneous shearing of a new class of elastic bodies, Mathematics and Mechanics of Solids, 17 (2012) 762-778
63. A. Ortiz, R.
Bustamante, K. R. Rajagopal, A numerical study of a
plate with a hole for a new class of elastic bodies, Acta Mechanica, 223 (2012) 1971-1981
64. F. Vogel, R. Bustamante, P. Steinmann, On mixed variational principles in electro-elastostatics,
International Journal of Nonlinear
Mechanics, 47 (2012) 341-354
65.
R. Bustamante, K. R. Rajagopal, Solutions of some simple boundary value
problems within the context of a new class of elastic bodies, International Journal of Nonlinear
Mechanics, 46 (2011) 376-386
66.
R. Bustamante, J.
Merodio, Constitutive structure in coupled non-linear electro-elasticity:
Invariant descriptions and constitutive restrictions, International Journal of Nonlinear Mechanics, 46 (2011) 1315-1323
67.
R. Bustamante, A. Dorfmann and R. W. Ogden,
Numerical solution of finite geometry boundary-value problems in nonlinear magnetoelasticity, International
Journal of Solids and Structures, 48
(2011) 874-883
68.
R. Bustamante, G. Holzapfel, Methods to compute 3D residual stress
distributions in hyperelastic tubes with application
to arterial walls, International Journal
of Engineering Science, 48
(2010) 1066-1082
69. R. Bustamante, J.
Merodio, On some simple constitutive restrictions for transversely isotropic
nonlinearly elastic materials and isotropic magneto-sensitive elastomers, Journal of Engineering Mathematics, 68 (2010), 15-26
70. R. Bustamante, K.
R. Rajagopal, A note on plane
strain and plane stress problems for a new class of elastic bodies, Mathematics and Mechanics of Solids, 15 (2010), 229-238
71. R. Bustamante,
Transversely isotropic nonlinearly magnetoelastic
solids, Acta Mechanica, 210 (2010), 183-214
72. R. Bustamante, A variational formulation for a boundary value problem
considering an electro-sensitive elastomer interacting with two bodies, Mechanics Research Communications, 36 (2009), 791-795
73. R. Bustamante, A. Dorfmann and R. W. Ogden,
On electric body forces and Maxwell stresses in an electroelastic
solid, International Journal of
Engineering Science, 47 (2009)
1131-1141
74. R. Bustamante, Some
topics on a new class of elastic bodies, Proceedings
of the Royal Society of London, Series A, 465 (2009) 1377-1392
75. R. Bustamante,
Mathematical modelling of boundary conditions for magneto -sensitive
elastomers: variational formulations, Journal of
Engineering Mathematics, 64 (2009) 285-301
76. R. Bustamante,
Transversely isotropic non-linear electro-active elastomer, Acta Mechanica, 206 (2009) 237-259
77. R. Bustamante, A. Dorfmann and R. W. Ogden, Nonlinear electroelastostatics:
a variational framework, Zeitschrift
fur angewandte Mathematik
und Physik 60 (2009) 154-177
78. R. Bustamante, A. Dorfmann and R. W. Ogden, On variational
formulations in nonlinear magneto-elastostatics, Mathematics
and Mechanics of Solids 13 (2008)
435-450
79. R. Bustamante, A. Dorfmann and R. W. Ogden, A nonlinear magnetoelastic
tube under extension and inflation in an axial magnetic field: numerical
solution, Journal of Engineering Mathematics 59 (2007) 139-153
80. R. Bustamante, A. Dorfmann and R. W. Ogden, Universal relations in isotropic
nonlinear magnetoelasticity, The Quarterly Journal of Mechanics and Applied Mathematics 59
(2006) 435-450
81. R. Bustamante, R.
W. Ogden, On nonlinear universal relations in nonlinear elasticity, Zeitschrift fur angewandte
Mathematik und Physik 57 (2006) 708-721
82. R. Bustamante, R.
W. Ogden, Universal relations for nonlinear electroelastic
solids, Acta Mechanica
182 (2006) 125-140
Papers in preparation or submitted
1.
R. Bustamante, A beam theory for a new class of
constitutive relation for elastic bodies. Mathematics
and Mechanics of Solids, (in press).
2.
R. Bustamante, Approximate determination of shear
stresses for a 2D beam made of a non-Green elastic solid. (Submitted).
3.
B. Wang, R. Bustamante, L. Kari, X. Gong, Magnetic and
nonlinear dependence of viscoelasticity in modelling the rate-dependent
magneto-mechanical coupled response of magneto-rheological elastomers:
experiments, constitutive modelling and finite element implementation.
(Submitted).
4.
R. Bustamante, A string theory considering a new class
of constitutive relations for elastic bodies. (In Preparation).
5.
R. Bustamante, K. R. Rajagopal,
Nonlinear implicit magneto-visco-elasticity. (In
Preparation).
6.
R. Bustamante, On a class of
non-linear thermo-elastic that is non Green elastic. Large elastic deformations
and analysis of the propagation of small amplitude waves. (In Preparation).
7.
R. Bustamante, K.R. Rajagopal,
Nonlinear implicit visco-elastic bodies. (In
Preparation).
8.
R. Bustamante, Implicit relations for compressible
nonlinear elastic solids. (In Preparation).
9.
R. Bustamante, J. Gomez, K.R. Rajagopal,
A bimodular model for strain limiting. (In
Preparation).
Chapters of Books
1.
R. Bustamante, K.R. Rajagopal,
A Review of Implicit Constitutive Theories to Describe
the Response of Elastic Bodies. (Accepted) in Constitutive Modelling of Solid
Continua, Eds. J. Merodio and R.W. Ogden. Springer
International Publishing (2019) 187-230.
Proceedings papers and papers in non-ISI journals
5.
M.H.B.M. Shariff, R.
Bustamante, A consistent isotropic spectral constitutive equation: The
infinitesimal strain depends nonlinearly on the stress. Applications in
Engineering Science 1 (2020) 100007.
Presentations