Homogénéisation de frontières par épi-convergence en élasticité linéaire. (Homogenization of boundaries by epi- convergence in linear elasticity). (French) Zbl 0691.73013

In an earlier paper the last two of the authors [ibid. 22, No.4, 609-624 (1988; Zbl 0659.73006)], have discussed the asymptotic behaviour of an elastic body with a surface having small sticked regions. The present paper deals with the study of the asymptotic behaviour of a homogeneous elastic body with boundary \(\partial \Omega\) of which a part \(\Sigma\) is stuck on identical zones of side \(r_{\epsilon}\) that are distributed \(\epsilon\)-periodically. A variational problem arising from the boundary value problem is examined and the asymptotic behaviour of the body when \(\epsilon\) \(\to 0\) is described using epi-convergence methods. It is shown that if a certain parameter c equals zero the limit behaviour along \(\Sigma\) is one of total freedom and that if \(c=\infty\) it is a case of complete stickness. If \(0<c<\infty\) there is variation between total freedom and complete stickness. The paper concludes with the study of the limit of the solution of Signorini’s problem for the present case.
Reviewer: S.K.Lakshmana Rao


74S30 Other numerical methods in solid mechanics (MSC2010)
74E05 Inhomogeneity in solid mechanics
35B40 Asymptotic behavior of solutions to PDEs
49J45 Methods involving semicontinuity and convergence; relaxation
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics


Zbl 0659.73006
Full Text: DOI EuDML


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