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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 74: Mechanics of deformable solids

Introduction

Mechanics of deformable solids: questions of elasticity and plasticity, wave propagation, engineering, and topics in specific solids such as soils.

History

Applications and related fields

This image slightly hand-edited for clarity.

WARNING: This map actually carries the data for a now-defunct predecessor area 73.

Subfields

• 74A: Generalities, axiomatics, foundations of continuum mechanics of solids
• 74B: Elastic materials
• 74C: Plastic materials, materials of stress-rate and internal-variable type
• 74D: Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
• 74E: Material properties given special treatment
• 74F: Coupling of solid mechanics with other effects
• 74G: Equilibrium (steady-state) problems
• 74H: Dynamical problems
• 74J: Waves
• 74K: Thin bodies, structures
• 74L: Special subfields of solid mechanics
• 74M: Special kinds of problems
• 74N: Phase transformations in solids [See also 74A50, 80AXX, 82B26, 82C26]
• 74P: Optimization [See also 49QXX]
• 74Q: Homogenization, determination of effective properties
• 74R: Fracture and damage
• 74S: Numerical methods [See also 65-XX, 74G15, 74H15]

This area is a reorganization (new in 2000) of the former area 73

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Dikmen, M.: "Theory of thin elastic shells", Surveys and Reference Works in Mathematics, 8. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. 364 pp. ISBN 0-273-08431-3 MR84h:73035

Jenkins, Chris H.; Leonard, John W.: "Nonlinear dynamic response of membranes: state of the art", AMR 44 (1991), no. 7, 319--328. CMP1112398

Green, A. E.; Naghdi, P. M.: "A unified procedure for construction of theories of deformable media", Proc. Roy. Soc. London Ser. A 448 (1995), no. 1934, 335--388. MR96f:73004 I. Classical continuum physics. II. Generalized continua. III. Mixtures of interacting continua.

dell'Isola, F.; Rosa, L. "Outlooks in Saint Venant theory. II. Torsional rigidity, shear-stress 'and all that' in the torsion of cylinders with section of variable thickness", Arch. Mech. (Arch. Mech. Stos.) 48 (1996), no. 4, 753--763. MR97i:73020

Software and tables

Other web sites with this focus

• Here are the AMS and Goettingen resource pages for area 74.
• The Net Advance of Physics

Selected topics at this site

• What happened to the Tacoma bridge?
• Numerical calculation of Cauchy stresses
• Bending of a cantilever beam