Papers
1. R. Bustamante, O. Orellana, Some new methods of solving boundary value
problems in linearized elasticity and for a class of nonlinear elastic body. Journal of Elasticity, 158 (2026) 11
2. R. Bustamante, K.R. Rajagopal, Correction: A
new type of constitutive equation for nonlinear elastic bodies. Fitting with
experimental data for rubber-like materials (2021), by Bustamante et al. Proceedings of the Royal Society A, 482 (2026) 20210330
3. R. Bustamante, A constitutive equation for nonlinear elastic solids,
which is based on the use of the Gibbs potential and the nominal stress tensor.
European Journal of Mechanics-A/Solids,
116 (2026) 105870
4. R. Bustamante, C. Rodriguez, K.R. Rajagopal,
Piecewise linear constitutive relations for stretch-limited elastic strings. IMA Journal of Applied Mathematics 90 (2025) 99-114
5. R. Bustamante, O. Orellana, A note on the inhomogeneous shear for a
class of visco-electro-elastic slab. A parametric
study. Applications in Engineering
Science, 24 (2025) 100276
6. M.H.B.M. Shariff, R. Bustamante, J. Merodio, Rate-dependent transversely isotropic
magneto-viscoelastic solids. Mathematics
and Mechanics of Solids, 30
(2025) 2224-2242
7. R. Bustamante, R. Ibarra, K.R. Rajagopal,
Response of a sandwich composite beam comprised of a layer of an elastic solid
described by an implicit constitutive relation, Zeitschrift fur Angewandte Mathematik
und Mechanik, 105 (2025) e70044
8. R. Bustamante, P. Arrue, On a new class of
implicit constitutive relation for quasi-incompressible and compressible
isotropic nonlinear elastic solids, International
Journal of Non-Linear Mechanics, 175
(2025) 105084
9. M.H.B.M. Shariff, R. Bustamante, J. Merodio, Spectral formulations in nonlinear solids: A brief
summary, Mathematics and Mechanics of
Solids, 30 (2025) 267-322
10. R. Bustamante, K.R. Rajagopal, O. Orellana,
Circumferential shear for an incompressible non-Green elastic cylindrical
annulus, Mathematics and Mechanics of
Solids, 30 (2025) 340-355
11. R. Bustamante, P. Arrue, O. Orellana, R. Meneses, An iteration method to study nonlinear wave
propagation for a non-Green elastic 1D bar, IMA
Journal of Applied Mathematics, 89
(2024) 426-440
12. D. Sfyris, R. Bustamante, K.R. Rajagopal, On the hyperbolicity
of the governing equations for the linearization of a class of implicit
constitutive relations, Mechanics
Research Communications, 138
(2024) 104291
13. M.H.B.M. Shariff, R. Bustamante, On a class of
implicit constitutive relations for nonlinear elastic bodies, International Journal of Engineering Science,
200 (2024) 104089
14. M.H.B.M. Shariff, R. Bustamante, J. Merodio, Basic errors in couple-stress hyperelasticity
articles, Mathematics and Mechanics of
Solids, 29 (2024) 1729-1738
15. R. Bustamante, K.R. Rajagopal, A. Wineman, Residual stresses for a new class of transversely
isotropic nonlinear elastic solid. Mathematics
and Mechanics of Solid, 29
(2024), 2164-2172
16. M.H.B.M. Shariff, R. Bustamante, J. Merodio, A generalized strain model for spectral
rate-dependent constitutive equation of transversely isotropic
electro-viscoelastic solids, Journal of
the Mechanics and Physics of Solids, 192
(2024) 105838
17. A. Wineman, R. Bustamante, K.R. Rajagopal, The Treloar-Kearsley
bifurcation problem using a new class of constitutive equations, Zeitschrift fur angewandte Mathematik und Mechanik, 75 (2024) 206
18. R. Bustamante, K.R. Rajagopal, A note on
constitutive relationships for viscoelastic bodies with density-dependent
material properties. Mechanics of
Time-Dependent Materials, 28
(2024) 639-652
19. R. Bustamante, Approximate determination of shear stresses for a 2D beam
made of a non-Green elastic solid. Mathematics
and Mechanics of Solids, 29
(2024) 421-435
20. M.H.B.M. Shariff, R. Bustamante, On a class of implicit constitutive relations for nonlinear
elastic bodies. International Journal of
Engineering Science, 200 (2024)
104089
21. M.H.B.M. Shariff, R. Bustamante, J. Merodio, A generalized strain model for nonlinear
residually stressed magneto-electrically coupled viscoelastic solids, International Journal of Solids and
Structures, 289 (2024) 112659
22. D. Sfyris, R. Bustamante, K.R. Rajagopal, On the hyperbolicity
of the governing equations for the linearization of a class of implicit
constitutive relations, Mechanics
Research Communications, 138 (2024)
104291
23. K.R. Rajagopal, R. Bustamante, Constitutive
relations for anisotropic porous solids undergoing small strains whose material
moduli depend on the density and the pressure. International Journal of Engineering Science, 195 (2024) 104005
24. R. Bustamante, Corrigendum: New classes of electro-elastic and
thermo-electro-elastic bodies that are not Green elastic. International Journal of Engineering Science, 195 (2024) 103967
25. R. Bustamante, M.H.B.M. Shariff, On a class of
nonlinear isotropic thermo-elastic body that is non-Green elastic: Applications
to large elastic deformations, The
Quarterly Journal of Mechanics and Applied Mathematics, 76 (2023) 435-470
26. R. Bustamante, A beam theory for a new class of constitutive relation
for elastic bodies. Mathematics and
Mechanics of Solids, 28 (2023)
1545-1575
27. M.H.B.M. Shariff, J. Merodio,
R. Bustamante, A. Laadhari, A
Non-second-gradient model for nonlinear electroelastic
bodies with fibre stiffness. Symmetry, 15 (2023) 1065
28. M.H.B.M. Shariff, J. Merodio,
R. Bustamante, A non-second-gradient model for nonlinear elastic bodies with fibre stiffness. Scientific
Reports, 13 (2023) 6562
29. B. Wang, R. Bustamante, L. Kari, X. Gong, Modelling the influence of
magnetic fields to the viscoelastic behaviour of soft
magnetorheological elastomers under finite strains. International Journal of Plasticity, 164 (2023) 103578
30. 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
31. 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
32. 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
33. A. Melnikov, J. Merodio,
R. Bustamante, L. Dorfmann, Bifurcation analysis of
residually stressed neo-Hookean and Ogden electroelastic tubes. Philosophical
Transactions of the Royal Society A, 380
(2022) 20210331
34. 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
35. 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
36. 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
37. 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
38. 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
39. N. Yevenes, R. Bustamante, A nonlinear
constitutive model for some hard electro-elastic solids. Solutions of some
boundary value problems. Applications in
Engineering Science, 11 (2022)
100109
40. M.H.B.M. Shariff, J. Merodio,
R. Bustamante, Finite deformations of fibre-reinforced
elastic solids with fibre bending stiffness: A spectral
approach. Journal of Applied and
Computational Mechanics, 8
(2022) 1332-1342
41. 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
42. R. Bustamante, A note on a new constitutive model for rubber-like
solids. Mechanics Research Communications,
117 (2021) 103775
43. 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) 20210330
44. 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
45. 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
46. 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
47. 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
48. R. Bustamante, C. Ortiz, A bimodular nonlinear
constitutive equation for rock. Applications
in Engineering Science, 8 (2021)
100067
49. 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
50. 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
51. 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
52. 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
53. 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
54. 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
55. 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
56. 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
57. R. Bustamante, Some universal solutions for incompressible elastic
bodies that are not Green elastic. International
Journal of Engineering Science 149 (2020)
103223
58. 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
59. R. Bustamante, S. Montero, A. Ortiz-Bernardin,
A novel nonlinear constitutive model for rock: numerical assessment and
benchmarking. Applications in Engineering
Science 3 (2020) 100012
60. 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
61. 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
62. 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
63. 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
64. R. Bustamante, K.R. Rajagopal, A nonlinear
model for describing the mechanical behaviour of
rock. Acta Mechanica 229 (2018) 251-272
65. 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
66. 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
67. 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
68. R. Bustamante, K.R. Rajagopal, Implicit
equations for thermoelastic bodies. International Journal of Non-linear
Mechanics 92 (2017) 144-152
69. 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
70. 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
71. 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
72. 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
73. 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
74. 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
75. 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
76. 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
77.
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
78. 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
79. 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
80. R. Bustamante, K. R. Rajagopal, Implicit
constitutive relations in nonlinear magneto-elasticity. Proceedings of the Royal Society of London A, 471 (2015) 20140959
81. 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
82.
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
83. 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
84. 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
85. 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
86. 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
87. 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
88. 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
89. 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
90. R. Bustamante, R. W. Ogden, Nonlinear magnetoelastostatics: energy functional and their second
variations, Mathematics and Mechanics of
Solids, 18 (2013) 760-772
91. 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
92. 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
93. F. Vogel, R. Bustamante, P. Steinmann, On some mixed variational
principles in magneto elastostatics. International Journal of Nonlinear Mechanics,
51 (2013) 157-169
94. 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
95. R. Bustamante, J. Merodio, On weak formulations and their second
variation in nonlinear electroelasticity, Mechanics Research Communications, 46 (2012) 15-19
96. 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
97. 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
98. F. Vogel, R. Bustamante, P.
Steinmann, On mixed variational
principles in electro-elastostatics, International Journal of Nonlinear
Mechanics, 47 (2012) 341-354
99.
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
100.
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
101.
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
102.
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
103.
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
104.
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
105.
R. Bustamante, Transversely isotropic
nonlinearly magnetoelastic solids, Acta Mechanica, 210 (2010), 183-214
106.
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
107.
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
108.
R. Bustamante, Some topics on a new class
of elastic bodies, Proceedings of the
Royal Society of London, Series A, 465
(2009) 1377-1392
109.
R. Bustamante, Mathematical modelling of
boundary conditions for magneto -sensitive elastomers: variational
formulations, Journal of Engineering Mathematics, 64 (2009) 285-301
110.
R. Bustamante, Transversely isotropic
non-linear electro-active elastomer, Acta
Mechanica, 206 (2009) 237-259
111.
R. Bustamante, A. Dorfmann and R. W. Ogden, Nonlinear electroelastostatics: a variational
framework, Zeitschrift fur angewandte
Mathematik und Physik 60 (2009) 154-177
112.
R. Bustamante, A. Dorfmann
and R. W. Ogden, On variational formulations in
nonlinear magneto-elastostatics, Mathematics and
Mechanics of Solids 13 (2008)
435-450
113.
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
114.
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
115.
R. Bustamante, R. W. Ogden, On nonlinear
universal relations in nonlinear elasticity, Zeitschrift
fur angewandte Mathematik
und Physik 57 (2006) 708-721
116.
R. Bustamante, R. W. Ogden, Universal
relations for nonlinear electroelastic solids, Acta Mechanica 182
(2006) 125-140
Papers in preparation, submitted or accepted
1.
R. Bustamante, A comprehensive review of
implicit constitutive theories and their subclasses for elastic and inelastic
solids. Vol. 62 (In Press) Advances in
Applied Mechanics. review_article_3_advances_APPL_Mech.pdf
2.
R. Bustamante, Nonlinear implicit magneto-visco-elasticity. (In Preparation)
3.
R. Bustamante, J. Gomez, 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. 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
Presentations