zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion. (English) Zbl 1075.74061
Summary: A model for the adhesive, quasistatic and frictionless contact between a viscoelastic body and a deformable foundation is described. The adhesion process is modelled by a bonding field on the contact surface, and contact is described by a modified normal compliance condition. The problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field. The existence of a unique weak solution for the problem and its continuous dependence on the adhesion parameters are established. Then, the numerical analysis of the problem is conducted for the fully discrete approximation. The convergence of the scheme is established and error estimates derived. Finally, representative numerical simulations are presented, depicting the evolution of the state of the system and, in particular, the evolution of the bonding field.
74M15Contact (solid mechanics)
74D10Nonlinear constitutive equations (materials with memory)
74H15Numerical approximation of solutions for dynamical problems in solid mechanics
74H20Existence of solutions for dynamical problems in solid mechanics