Numerical analysis of viscoelastic problems. (English) Zbl 0718.73091

Le Tallec, P.

Recherches en Mathématiques Appliquées, 15. Paris etc.: Masson; Berlin etc.: Springer-Verlag. 136 p. FF 160.00 (1990).

The book aims at the numerical and mathematical analysis of viscous solid mechanics problems; including viscoelastic and viscoplastic problems (pure elastoplasticity is also considered), within the framework of small strains and differential constitutive laws. The text starts from the mechanical model, followed by the mathematical analysis and different formulations, and ends with the numerical solution (mixed finite element) to the associated problems.
The book covers classical notions of functional and numerical analysis (convex analysis, maximal monotone operators, alternating direction schemes, conjugate gradient algorithms and Newton’s methods) and presents then in a unified manner, with possible applications to frozen soils, concrete and metal forming.

Reviewer: J.C.F.Telles (Rio de Janeiro)

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74Hxx	Dynamical problems in solid mechanics
74-02	Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74C10	Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)

Keywords:

viscous solid mechanics; small strains; differential constitutive laws; convex analysis; maximal monotone operators; alternating direction schemes; conjugate gradient algorithms; Newton’s methods; frozen soils; concrete; metal forming