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Mathematics Subject Classification – MSC2020

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to mechanics of deformable solids 317

74-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids 1234

74-02

Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids 2570

74-03

History of mechanics of deformable solids [Consider also classification numbers pertaining to Section 01-XX] 354

74-04

Software, source code, etc. for problems pertaining to mechanics of deformable solids 1367

74-05

Experimental work for problems pertaining to mechanics of deformable solids 2625

74-06

Proceedings, conferences, collections, etc. pertaining to mechanics of deformable solids 2239

74-10

Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids 45

74-11

Research data for problems pertaining to mechanics of deformable solids 0

74Axx

Generalities, axiomatics, foundations of continuum mechanics of solids 22857

74A05

Kinematics of deformation 633

74A10

Stress 1376

74A15

Thermodynamics in solid mechanics 6209

74A20

Theory of constitutive functions in solid mechanics 3093

74A25

Molecular, statistical, and kinetic theories in solid mechanics 662

74A30

Nonsimple materials 269

74A35

Polar materials 1259

74A40

Random materials and composite materials 1932

74A45

Theories of fracture and damage 1420

74A50

Structured surfaces and interfaces, coexistent phases 576

74A55

Theories of friction (tribology) 3528

74A60

Micromechanical theories 2853

74A65

Reactive materials 39

74A70

Peridynamics 0

74A99

None of the above, but in this section 2068

74Bxx

Elastic materials 23152

74B05

Classical linear elasticity 6278

74B10

Linear elasticity with initial stresses 1933

74B15

Equations linearized about a deformed state (small deformations superposed on large) 258

74B20

Nonlinear elasticity 8622

74B99

None of the above, but in this section 6628

74Cxx

Plastic materials, materials of stress-rate and internal-variable type 13733

74C05

Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 2725

74C10

Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) 1544

74C15

Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) 2291

74C20

Large-strain, rate-dependent theories of plasticity 1719

74C99

None of the above, but in this section 7227

74Dxx

Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) 6271

74D05

Linear constitutive equations for materials with memory 2387

74D10

Nonlinear constitutive equations for materials with memory 2007

74D99

None of the above, but in this section 2740

74Exx

Material properties given special treatment 23674

74E05

Inhomogeneity in solid mechanics 4453

74E10

Anisotropy in solid mechanics 6328

74E15

Crystalline structure 1928

74E20

Granularity 1257

74E25

Texture in solid mechanics 135

74E30

Composite and mixture properties 11148

74E35

Random structure in solid mechanics 430

74E40

Chemical structure in solid mechanics 107

74E99

None of the above, but in this section 132

74Fxx

Coupling of solid mechanics with other effects 25720

74F05

Thermal effects in solid mechanics 8563

74F10

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 10813

74F15

Electromagnetic effects in solid mechanics 7050

74F20

Mixture effects in solid mechanics 172

74F25

Chemical and reactive effects in solid mechanics 239

74F99

None of the above, but in this section 60

74Gxx

Equilibrium (steady-state) problems in solid mechanics 17526

74G05

Explicit solutions of equilibrium problems in solid mechanics 952

74G10

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics 1542

74G15

Numerical approximation of solutions of equilibrium problems in solid mechanics 442

74G22

Existence of solutions of equilibrium problems in solid mechanics 2

74G30

Uniqueness of solutions of equilibrium problems in solid mechanics 1276

74G35

Multiplicity of solutions of equilibrium problems in solid mechanics 85

74G40

Regularity of solutions of equilibrium problems in solid mechanics 123

74G45

Bounds for solutions of equilibrium problems in solid mechanics 39

74G50

Saint-Venant’s principle 561

74G55

Qualitative behavior of solutions of equilibrium problems in solid mechanics 90

74G60

Bifurcation and buckling 6505

74G65

Energy minimization in equilibrium problems in solid mechanics 1372

74G70

Stress concentrations, singularities in solid mechanics 3776

74G75

Inverse problems in equilibrium solid mechanics 705

74G99

None of the above, but in this section 754

74Hxx

Dynamical problems in solid mechanics 29650

74H05

Explicit solutions of dynamical problems in solid mechanics 370

74H10

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics 1147

74H15

Numerical approximation of solutions of dynamical problems in solid mechanics 1816

74H20

Existence of solutions of dynamical problems in solid mechanics 773

74H25

Uniqueness of solutions of dynamical problems in solid mechanics 1328

74H30

Regularity of solutions of dynamical problems in solid mechanics 84

74H35

Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics 617

74H40

Long-time behavior of solutions for dynamical problems in solid mechanics 341

74H45

Vibrations in dynamical problems in solid mechanics 16476

74H50

Random vibrations in dynamical problems in solid mechanics 1429

74H55

Stability of dynamical problems in solid mechanics 2995

74H60

Dynamical bifurcation of solutions to dynamical problems in solid mechanics 442

74H65

Chaotic behavior of solutions to dynamical problems in solid mechanics 271

74H75

Inverse problems in dynamical solid mechanics 2

74H80

Energy minimization in dynamical problems in solid mechanics 0

74H99

None of the above, but in this section 4314

74Jxx

Waves in solid mechanics 13031

74J05

Linear waves in solid mechanics 755

74J10

Bulk waves in solid mechanics 3425

74J15

Surface waves in solid mechanics 1909

74J20

Wave scattering in solid mechanics 3203

74J25

Inverse problems for waves in solid mechanics 1001

74J30

Nonlinear waves in solid mechanics 693

74J35

Solitary waves in solid mechanics 286

74J40

Shocks and related discontinuities in solid mechanics 434

74J99

None of the above, but in this section 2747

74Kxx

Thin bodies, structures 49497

74K05

Strings 1415

74K10

Rods (beams, columns, shafts, arches, rings, etc.) 15680

Membranes 7877

Plates 16995

Shells 7039

Junctions 318

Thin films 774

None of the above, but in this section 2882

74Lxx

Special subfields of solid mechanics 7325

74L05

Geophysical solid mechanics [See also 86-XX] 1556

74L10

Soil and rock mechanics 3763

74L15

Biomechanical solid mechanics [See also 92C10] 2160

74L99

None of the above, but in this section 24

74Mxx

Special kinds of problems in solid mechanics 16905

74M05

Control, switches and devices (“smart materials”) in solid mechanics [See also 93Cxx] 2600

74M10

Friction in solid mechanics 1968

74M15

Contact in solid mechanics 7936

74M20

Impact in solid mechanics 2326

74M25

Micromechanics of solids 3626

74M99

None of the above, but in this section 43

74Nxx

Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] 2224

74N05

Crystals in solids 772

74N10

Displacive transformations in solids 69

74N15

Analysis of microstructure in solids 386

74N20

Dynamics of phase boundaries in solids 447

74N25

Transformations involving diffusion in solids 175

74N30

Problems involving hysteresis in solids 258

74N99

None of the above, but in this section 245

74Pxx

Optimization problems in solid mechanics [See also 49Qxx] 7632

74P05

Compliance or weight optimization in solid mechanics 541

74P10

Optimization of other properties in solid mechanics 3254

74P15

Topological methods for optimization problems in solid mechanics 1062

74P20

Geometrical methods for optimization problems in solid mechanics 83

74P99

None of the above, but in this section 2989

74Qxx

Homogenization, determination of effective properties in solid mechanics 3304

74Q05

Homogenization in equilibrium problems of solid mechanics 1382

74Q10

Homogenization and oscillations in dynamical problems of solid mechanics 416

74Q15

Effective constitutive equations in solid mechanics 1372

74Q20

Bounds on effective properties in solid mechanics 320

74Q99

None of the above, but in this section 111

74Rxx

Fracture and damage 17580

74R05

Brittle damage 3570

74R10

Brittle fracture 5077

74R15

High-velocity fracture 228

74R20

Anelastic fracture and damage 3088

74R99

None of the above, but in this section 5910

74Sxx

Numerical and other methods in solid mechanics [See also 65-XX, 74G15, 74H15] 49176

74S05

Finite element methods applied to problems in solid mechanics 26937

74S10

Finite volume methods applied to problems in solid mechanics 343

74S15

Boundary element methods applied to problems in solid mechanics 4564

74S20

Finite difference methods applied to problems in solid mechanics 1789

74S22

Isogeometric methods applied to problems in solid mechanics 1

74S25

Spectral and related methods applied to problems in solid mechanics 523

74S40

Applications of fractional calculus in solid mechanics 1

74S50

Applications of graph theory in solid mechanics 0

74S60

Stochastic and other probabilistic methods applied to problems in solid mechanics 529

74S70

Complex-variable methods applied to problems in solid mechanics 252

74S99

None of the above, but in this section 2493

Overview

General and overarching topics; collections

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

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Field theory and polynomials

Commutative algebra

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Linear and multilinear algebra; matrix theory

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Nonassociative rings and algebras

Category theory; homological algebra

\(K\)-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximations and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

Functional analysis

Operator theory

Calculus of variations and optimal control; optimization

Geometry

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Differential geometry

General topology

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Manifolds and cell complexes

Global analysis, analysis on manifolds

Probability theory and stochastic processes

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Computer science

Mechanics of particles and systems

Mechanics of deformable solids

Fluid mechanics

Optics, electromagnetic theory

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Mathematics education

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Mathematics Subject Classification – MSC2020

Overview