Papers
1. 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.
2. R. Bustamante, A beam theory for a new class of constitutive relation
for elastic bodies. Mathematics and
Mechanics of Solids, 28 (2023)
1545-1575.
3. 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.
4. 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.
5. 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
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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
12. 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.
13. 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.
14. 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
15. 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.
16. 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.
17. 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.
18. R. Bustamante, A note on a new constitutive model for rubber-like
solids. Mechanics Research Communications,
117 (2021) 103775.
19. 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)
20. 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.
21. 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.
22. 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.
23. 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.
24. R. Bustamante, C. Ortiz, A bimodular nonlinear
constitutive equation for rock. Applications
in Engineering Science, 8 (2021)
100067.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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.
30. 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.
31. 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.
32. 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
33. R. Bustamante, Some universal solutions for incompressible elastic
bodies that are not Green elastic. International
Journal of Engineering Science 149 (2020)
103223.
34. 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.
35. 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.
36. 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.
37. 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
38. 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.
39. 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
40. R. Bustamante, K.R. Rajagopal, A nonlinear
model for describing the mechanical behaviour of
rock. Acta Mechanica 229 (2018) 251-272
41. 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
42. 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
43. 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.
44. R. Bustamante, K.R. Rajagopal, Implicit
equations for thermoelastic bodies. International Journal of Non-linear
Mechanics 92 (2017) 144-152
45. 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.
46. 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.
47. 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.
48. 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
49. 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
50. 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
51. 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.
52. 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.
53.
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.
54. 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.
55. 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.
56. R. Bustamante, K. R. Rajagopal, Implicit constitutive
relations in nonlinear magneto-elasticity. Proceedings
of the Royal Society of London A, 471
(2015) 20140959
57. 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
58.
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
59. 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
60. 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
61. 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.
62. 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
63. 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
64. 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
65. 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
66. R. Bustamante, R. W. Ogden, Nonlinear magnetoelastostatics: energy functional and their second
variations, Mathematics and Mechanics of
Solids, 18 (2013) 760-772.
67. 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.
68. 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.
69. F. Vogel, R. Bustamante, P. Steinmann, On some mixed variational
principles in magneto elastostatics. International Journal of Nonlinear
Mechanics, 51 (2013) 157-169
70. 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
71. R. Bustamante, J. Merodio, On weak formulations and their second
variation in nonlinear electroelasticity, Mechanics Research Communications, 46 (2012) 15-19
72. 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
73. 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
74. F. Vogel, R. Bustamante, P.
Steinmann, On mixed variational
principles in electro-elastostatics, International Journal of Nonlinear
Mechanics, 47 (2012) 341-354
75.
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
76.
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
77. 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
78.
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
79. 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
80. 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
81. R. Bustamante, Transversely isotropic nonlinearly magnetoelastic
solids, Acta Mechanica, 210 (2010), 183-214
82. 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
83. 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
84. R. Bustamante, Some topics on a new class of elastic bodies, Proceedings of the Royal Society of London,
Series A, 465 (2009) 1377-1392
85. R. Bustamante, Mathematical modelling of boundary conditions for magneto
-sensitive elastomers: variational formulations, Journal
of Engineering Mathematics, 64 (2009) 285-301
86. R. Bustamante, Transversely isotropic non-linear electro-active
elastomer, Acta Mechanica, 206 (2009) 237-259
87. R. Bustamante, A. Dorfmann and R. W. Ogden, Nonlinear electroelastostatics: a variational
framework, Zeitschrift fur angewandte
Mathematik und Physik 60 (2009) 154-177
88. R. Bustamante, A. Dorfmann and R. W. Ogden, On
variational formulations in nonlinear magneto-elastostatics, Mathematics and Mechanics of Solids 13 (2008) 435-450
89. 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
90. 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
91. R. Bustamante, R. W. Ogden, On nonlinear universal relations in
nonlinear elasticity, Zeitschrift fur angewandte Mathematik und Physik 57
(2006) 708-721
92. 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, 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, (In Press), https://doi.org/10.1093/qjmam/hbae001
2.
R. Bustamante, K.R. Rajagopal,
O. Orellana, Circumferential shear for an incompressible non-Green elastic
cylindrical annulus. Mathematics and
Mechanics of Solid, (In Press), https://doi.org/10.1177/10812865231207401
3.
M. H. B. M., Shariff,
R. Bustamante, J. Merodio, Spectral formulations in
nonlinear solids: A brief summary. Mathematics
and Mechanics of Solid, (In Press),
https://doi.org/10.1177/10812865231204366
4.
R. Bustamante, K.R. Rajagopal,
A note on constitutive relationships for viscoelastic bodies with
density-dependent material properties. Mechanics
of Time-Dependent Materials, (In Press).
https://doi.org/10.1007/s11043-023-09599-8
5.
R. Bustamante, Approximate determination
of shear stresses for a 2D beam made of a non-Green elastic solid. Mathematics and Mechanics of Solids, (In
Press), https://doi.org/10.1177/10812865231201623
6.
R. Bustamante, K.R. Rajagopal,
A. Wineman, Residual stresses for a new class of
transversely isotropic nonlinear elastic solid. Mathematics and Mechanics of Solids, (Accepted).
7.
R. Bustamante, R. Ibarra, K.R. Rajagopal, The response of a sandwich composite beam
comprised of a layer of an elastic solid described by an implicit constitutive
relation. (In Preparation).
8.
R. Bustamante, P. Arrue,
O. Orellana, An iteration method to study nonlinear wave propagation for a
non-Green elastic 1D bar. (Submitted).
9.
R. Bustamante, A string theory considering
a new class of constitutive relations for elastic bodies. (In Preparation).
10. R. Bustamante, K. R. Rajagopal, Nonlinear
implicit magneto-visco-elasticity. (In Preparation).
11. R. Bustamante, Implicit relations for compressible nonlinear elastic
solids. (In Preparation).
12. 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. 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