MSc, PhD (Leningrad), DSc (Cracow)
Room Number..........:  4.06
Building....................:  Physical Sciences
Phone.......................:   +44 (0)1970 622753
Home Page...............:   Personal
Gennady Mishuris is Professor of Mathematical Modelling at the Institute of Mathematics and Physics of Aberystwyth University. This position has been recently established by the Wales Institute for Mathematical and Computational Sciences in 2007. He works in the area of Applied Mathematics and Computational Modelling.
- My Interests are:
- Singular integral equations, functional equations of the Wiener-Hopf type.
- Asymptotic methods.
- Mathematical modelling of problems of solid mechanics: BVPs with irregular boundaries, singular fields, composites with imperfect interfaces.
- Waves and dynamic fracture in complex and discrete structures.
- Mathematical and numerical modelling of hydraulic fracture.
- Mathematical modelling in rheology: plastic and visco-plastic materials.
- Engineering applications: crack propagation, metal forming, material testing.
Awards and Research Fellowships
- Wolfson Research Merit Award, Royal Society, 2016
- Marie Curie Fellowship, University of Liverpool, UK, 2005
- Liverhulme Trust Visiting Research Fellowship, LSBU, UK, 2004
- Prize of Polish Ministry of Education for Scientific Research, Poland, 2000
- Alexander von Humboldt Fellowship, Erlangen-Nuremberg University, Germany, 1999
- Research Fellowship, Warsaw University, Poland, 1991
Recent Research Grants
Three-dimensional contact of transversely isotropic transversely homogeneous cartilage layers: A closed-form solution. European Journal of Mechanics - A/Solids 65 pp. 195-204. Cadair2017.
On the concept of "far points" in Hertz contact problems. International Journal of Engineering Science 113 pp. 20-36. Cadair2017.
Cylindrical lateral depth-sensing indentation of anisotropic elastic tissues: Effects of adhesion and incompressibility. Journal of Adhesion Cadair2017.
Energy release rate in hydraulic fracture: Can we neglect an impact of the hydraulically induced shear stress? International Journal of Engineering Science 111 pp. 28-51. Cadair2017.
Transient wave in a transformable periodic flexural structure. International Journal of Solids and Structures Cadair2016.
Articular Contact Mechanics From an Asymptotic Modeling Perspective: a Review. Frontiers in Bioengineering and Biotechnology 4 83 Cadair2016.
Analysis of dynamic damage propagation in discrete beam structures. International Journal of Solids and Structures 97-98 pp. 699-713. Cadair2016.
Resolution of the threshold fracture energy paradox for solid particle erosion. Philosophical Magazine Cadair2016.
An approximate JKR model of elliptical contact between thin incompressible elastic coatings covering rigid cylinders. Tribology Letters 64 12 Cadair2016.
Analysis of the Unilateral Contact Problem for Biphasic Cartilage Layers with an Elliptic Contact Zone and Accounting for Tangential Displacements. Mathematical Modelling and Analysis 21 (5) pp. 585-609. Cadair2016.
Factorization of a class of matrix-functions with stable partial indices. Mathematical Methods in the Applied Sciences 39 (13) pp. 3791–3807. Cadair2016.
Dynamic crack propagation along the interface with non-local interactions. Journal of the European Ceramic Society 36 (9) CERMODEL 2015: Modelling and Simulation Meet Innovation in Ceramics Technology. pp. 2241-2244. Cadair2016.
Analysis of residual stresses in thermoelastic multilayer cylinders. Journal of the European Ceramic Society 36 (9) pp. 2411-2417. Cadair2016.
Asymptotic modelling of the JKR adhesion contact for a thin elastic layer. Quarterly Journal of Mechanics and Applied Mathematics 69 (2) pp. 161-179. Cadair2016.
Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles. Meccanica 51 (5) pp. 1041-1055. Cadair2016.
Impact problem for the quasi-linear viscoelastic standard solid model. Journal of Strain Analysis for Engineering Design 51 (4) pp. 294-303. Cadair2016.
Constructive methods for factorization of matrix-functions. IMA Journal of Applied Mathematics 81 (2) pp. 365-391. Cadair2016.
An asymptotic model for a thin bonded elastic layer coated with an elastic membrane. Applied Mathematical Modelling 40 (4) pp. 2541-2548. Cadair2016.
Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation. Computers and Geotechnics 71 pp. 310-337. Cadair2016.
Existence results for a nonlinear transmission problem. Journal of Mathematical Analysis and Applications 430 (2) pp. 718-741. Cadair2015.
A phenomenological model of damage in articular cartilage under impact loading. Mechanics Research Communications 69 pp. 87-90. Cadair2015.
Hydraulic fracture revisited: Particle velocity based simulation. International Journal of Engineering Science 94 pp. 23-58. Cadair2015.
An asymptotic model for a thin biphasic poroviscoelastic layer. Quarterly Journal of Mechanics and Applied Mathematics 68 (3) pp. 289-297. Cadair2015.
Contact Mechanics of Articular Cartilage Layers. Advanced Structured Materials Springer Nature Cadair2015.
On application of Fung's quasi-linear viscoelastic model to modeling of impact experiment for articular cartilage. Mechanics Research Communications 67 pp. 24-60. Cadair2015.
General transmission conditions for thin elasto-plastic pressure-dependent interphase between dissimilar materials. International Journal of Solids and Structures 64-65 pp. 9-21. Cadair2015.
Simulating the Hele-Shaw flow in the presence of various obstacles and moving particles. Mathematika 61 (2) pp. 457-474. Cadair2015.
Improved algorithm for analytical solution of the heat conduction problem in doubly periodic 2D composite materials. Complex Variables and Elliptic Equations 60 (1) pp. 1-23. Cadair2015.
Cylindrical lateral depth-sensing indentation testing of thin anisotropic elastic films. European Journal of Mechanics - A/Solids 49 pp. 299-307. Cadair2015.
Exact solution of a nonlinear heat conduction problem in a doubly periodic 2D composite material. Archives of Mechanics 67 (2) pp. 157-178. Cadair2015.
Longitudinal shear of a composite with elliptic nanofibers: Local stresses and effective stiffness. International Journal of Engineering Science 84 pp. 79-94. Cadair2014.
Hele-Shaw flow with a small obstacle. Meccanica 49 (9) pp. 2037-2047. Cadair2014.
Remarks on the energy release rate for an antiplane moving crack in couple stress elasticity. International Journal of Solids and Structures 51 (18) pp. 3087-3100. Cadair2014.
Boundary integral formulation for cracks at imperfect interfaces. Quarterly Journal of Mechanics and Applied Mathematics 67 (3) pp. 363-387. Cadair2014.
Brittle fracture in a periodic structure with internal potential energy. Spontaneous crack propagation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470 (2167) 20140121 Cadair2014.
Effective thermal conductivity of a composite with thermo-sensitive constituents and related problems. International Journal of Engineering Science 80 pp. 124-135. Cadair2014.
An asymptotic method of factorization of a class of matrix-functions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470 (2166) 20140109 Cadair2014.
Brittle fracture in a periodic structure with internal potential energy. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470 (2165) 20130821 Cadair2014.
Efficient pseudo-spectral solvers for the PKN model of hydrofracturing. International Journal of Fracture 184 (1-2) pp. 151-170. Cadair2013.
Perturbation analysis for an imperfect interface crack problem using weight function techniques. International Journal of Solids and Structures 50 (24) pp. 4098-4107. Cadair2013.
On fracture criteria for dynamic crack propagation in elastic materials with couple stresses. International Journal of Engineering Science 71 pp. 45-61. Cadair2013.
Dislocations and inclusions in prestressed metals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469 (2154) 20120752 Cadair2013.
Propagation of Slepyan's crack in a non-uniform elastic lattice. Journal of the Mechanics and Physics of Solids 61 (6) pp. 1464-1488. Cadair2013.
Integral identities for a semi-infinite interfacial crack in anisotropic elastic bimaterials. International Journal of Solids and Structures 50 (9) pp. 1437-1448. Cadair2013.
Threshold fracture energy in solid particle erosion. Philosophical Magazine 93 (19) pp. 2485-2496. Cadair2013.
Integral Identities for a Semi-infinite Interfacial Crack in 2D and 3D Elasticity. Journal of Elasticity 110 (2) pp. 117-140. Cadair2013.
Accounting for the thickness effect in dynamic spherical indentation of a viscoelastic layer: Application to non-destructive testing of articular cartilage. European Journal of Mechanics - A/Solids 37 pp. 304-317. Cadair2013.
Remarks on application of different variables for the PKN model of hydrofracturing: various fluid-flow regimes. International Journal of Fracture Cadair2013.
Weight Function Approach to a Crack Propagating along a Bimaterial Interface Under Arbitrar Loading in an Anisotropic Solid. Journal of Mechanics of Materials and Structures 8 (8-10) pp. 479-500. Cadair2013.
Dynamic energy release rate in couple-stress elasticity. International Symposium on Dynamic Deformation and Fracture of Advanced Materials (D2FAM 2013). Journal of Physics Conference Series, vol. 451 International Symposium on Dynamic Deformation and Fracture of Advanced Materials (D2FAM). IOP Publishing, Bristol Cadair2013.
Analysis of interfacial crack propagation under asymmetric loading in anisotropic materials. International Symposium on Dynamic Deformation and Fracture of Advanced Materials (D2FAM 2013). Journal of Physics Conference Series, vol. 451 International Symposium on Dynamic Deformation and Fracture of Advanced Materials (D2FAM). IOP Publishing, Bristol Cadair2013.
Application of imperfect interface weight function techniques for modelling of glued structures containing cracks and small defects. INTERNATIONAL SYMPOSIUM ON DYNAMIC DEFORMATION AND FRACTURE OF ADVANCED MATERIALS (D2FAM 2013). Journal of Physics Conference Series, vol. 451 International Symposium on Dynamic Deformation and Fracture of Advanced Materials (D2FAM). IOP Publishing, BRISTOL Cadair2013.
An analytical solution for a linear viscoelastic layer loaded with a cylindrical punch: Evaluation of the rebound indentation test with application for assessing viability of articular cartilage. Mechanics Research Communications 38 (8) pp. 565-568.2012.
Contact Problem For Thin Biphasic Cartilage Layers: Perturbation Solution. Quarterly Journal of Mechanics and Applied Mathematics 64 (3) pp. 297-318.2012.
Interaction of an interfacial crack with linear small defects under out-of-plane shear loading. Computational Materials Science 52 (1) pp. 226-230.2012.
Mode III interfacial crack in the presence of couple stress elastic materials. Engineering Fracture Mechanics 80 pp. 60-71.2012.
Perturbation analysis of Mode III interfacial cracks advancing in a dilute heterogeneous material. International Journal of Solids and Structures 49 (1) pp. 244-255.2012.
Eigenfrequency correction of Bloch-Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces. Wave Motion 49 (2) pp. 258-270.2012.
DYNAMICS OF A FAULT STEADILY PROPAGATING WITHIN A STRUCTURAL INTERFACE. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 10 (3) pp. 936-953. Cadair2012.
Steady-state propagation of a Mode III crack in couple stress elastic materials. International Journal of Engineering Science 61 pp. 112-128.2012.
On modeling hydraulic fracture in proper variables: Stiffness, accuracy, sensitivity. International Journal of Engineering Science 61 pp. 10-23. Cadair2012.
Mode III crack propagation in a bimaterial plane driven by a channel of small line defects. Computational Materials Science 64 pp. 239-243.2012.
Weight function in a bimaterial strip containing an interfacial crack and an imperfect interface. application to Bloch-Floquet analysis in a thin inhomogeneous structure with cracks. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 9 (4) pp. 1327-1349.2012.
Frictionless elliptical contact of thin viscoelastic layers bonded to rigid substrates. Applied Mathematical Modelling 35 (7) pp. 3201-3212.2011.
Elliptical contact of thin biphasic cartilage layers: Exact solution for monotonic loading. Journal of Biomechanics pp. 759-761.2011.
Dynamic mode-III interface crack in a bi-material strip. International Journal of Fracture 166 (1-2) pp. 1-2.2011.
Perturbation of mode III interfacial cracks. International Journal of Fracture 166 (1-2) pp. 1-2.2011.
On the evaluation of mechanical properties from the axisymmetric tensile test. Archives of Metallurgy and Materials 55 (2) pp. 325-330.2011.
Axisymmetric contact problem for a biphasic cartilage layer with allowance for tangential displacements on the contact surface. European Journal of Mechanics - A/Solids 29 (6) pp. 1051-1064.2010.
Bloch–Floquet waves and localisation within a heterogeneous waveguide with long cracks. Continuum Mechanics and Thermodynamics 22 (6-8) pp. 545-553.2010.
Crack in a lattice waveguide. International Journal of Fracture 162 (1-2) pp. 91-106.2010.
Localised knife waves in a structured interface. Journal of the Mechanics and Physics of Solids 57 (12) pp. 1958-1979.2009.
Coupled FEM-BEM approach for axisymetrical heat transfer problems. Defect and Diffusion Forum 273-276 pp. 740-745.2009.
Qualitative behaviour of viscoplastic solutions in the vicinity of maximum-friction surfaces. Journal of Engineering Mathematics 65 (2) pp. 143-156.2009.
Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks. Journal of the Mechanics and Physics of Solids 57 (9) pp. 1657-1682.2009.
The Viscous Froth Model: steady states and the high-velocity limit. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465 (2108) pp. 2391-2405.2009.
Asymptotic modelling of an elastic roller crossing a scratch. European Journal of Mechanics - A/Solids 28 (4) pp. 858-867.2009.
Numerical method for solving joint thermo-diffusive problems in an infinite combined domain with thin resistant interphase. International Journal of Multiphysics 3 (2) pp. 111-128.2009.
Exact solution to a refined contact problem for biphasic cartilage layers. In (eds) Computational and Mathematical Biomedical Engineering. Minuteman Press pp. 151 - 154.2009.
Transmission Conditions for Thin Reactive Heat-Conducting Interphases: General Case. Defect and Diffusion Forum 283 - 286 pp. 283-286.2009.
Numerical Modelling of Mass Transfer Problems in Combined Domains with Non-linear Imperfect Transmission Conditions. Defect and Diffusion Forum 283-286 pp. 527-532.2009.
Modelling of the multiaxial elasto-plastic behaviour of porous metals with internal gas pressure. Finite Elements in Analysis and Design 45 (2) pp. 104-112.2009.
Perturbing Paths of Slow Cracks in PMMA by Local Heating.2009.
Mathematics, it is easy. Mnemozina Publisher2009.
Magnus effect and dynamics of a spinning disc in a rarefied medium. Archives of Mechanics 61 (5) pp. 391-406.2009.
Localisation and dynamic defects in lattice structures. In (ed) Computational and Experimental Mechanics of Advanced Materials. CISM International Centre for Mechanical Sciences Springer Nature pp. 51-82.2009.
Compression of a viscoelastic layer between rough parallel plates. Mechanics of Solids 43 (6) pp. 863-869.2008.
Flow of viscoplastic materials through converging channels. Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting.2008.
Dynamics of a bridged crack in a discrete lattice. Quarterly Journal of Mechanics and Applied Mathematics 61 (2) pp. 151-160.2008.
Evaluation of Transmission Conditions for Thin Reactive Heat-Conducting Interphases. Defect and Diffusion Forum 273-276 pp. 394-399.2008.
Dynamical extraction of a single chain from a discrete lattice. Journal of the Mechanics and Physics of Solids 56 (2) pp. 487-495.2008.
A New Finite Element Formulation for Thin Non-Homogeneous Heat-Conducting Adhesive Layers. Journal of Adhesion Science and Technology 22 (13) pp. 1365-1378.2008.
Solution asymptotics near maximum friction surfaces in plane strain block compression: various viscoplastic laws with a saturation stress.2008.
Remarks on the accuracy of algorithms for motion by mean curvature in bounded domains. Journal of Mechanics of Materials and Structures 4 (9) pp. 1555–1572.2008.
Solution asymptotics near meximum friction surfaces in the plane strain b lock compression : various viscoplastic laws with saturation stress. In (eds) Continuum Models and Discrete Systems CMDS 11: Proceedings of the International Symposium held in Paris, July 30th- August 2nd 2007. Presses des Mines pp. 225 - 231. Cadair2008.
Delamination of a bi-material strip by a steady-state interfacial crack. In Proc. International Symposium, CMDS-11, Continuum Models and Discrete Systems. International Symposium CMDS11. pp. 231-242.2008.
A new evaluation procedure for the butt-joint test of adhesive technology: Determination of the complete set of linear elastic constants. International Journal of Adhesion and Adhesives 27 (8) pp. 703-711.2007.
2D modelling of a thin elasto-plastic interphase between two different materials: Plane strain case. Composite Structures 80 (3) pp. 361-372.2007.
Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack. Journal of the Mechanics and Physics of Solids 55 (8) pp. 1575-1600.2007.
Crack redirection with thermal secondary loading. Engineering Fracture Mechanics 74 (11) pp. 1719-1726.2007.
Viscoplasticity with a saturation stress: distinguishing features of the model. Archive of Applied Mechanics 77 (1) pp. 35-47.2007.
Necking in the tensile test. Correction formulae and related error estimation. Archives of Metallurgy and Materials pp. 231-238.2007.
An attempt to improve the evaluation of mechanical material properties from the axisymmetric tensile test.2007.
Waves and fracture in an inhomogeneous lattice structure. Waves in Random and Complex Media 17 (4) pp. 409-428.2007.
Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks. Waves in Random and Complex Media 17 (4) pp. 511-533.2007.
Evaluation of transmission conditions for a thin heat-resistant inhomogeneous interphase in dissimilar material. Material Science Forum 553 pp. 87-92.2007.
Finite element verification of transmission conditions for 2D heat conduction problems. Material Science Forum 553 pp. 93-99.2007.
Vibrations of damaged 1D-3D multi-structures.2007.
Steady-state motion of a Mode-III crack on imperfect interfaces. Quarterly Journal of Mechanics and Applied Mathematics 59 (4) pp. 487-516.2006.
Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 81 (12) pp. 811-826.2001.