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

MSC:

 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
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References:

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