A convergence result in the study of bone remodeling contact problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:343

Article

Fernandez, J. R.¹  Figueiredo, I. N.²  Martinez, R.¹ 

[1] Univ Santiago de Compostela, Fac Matemat, Dept Matemat Applicada, Santiago De Compostela 15782, Spain

[2] Univ Coimbra, CMUC, Dept Math, P-3001454 Coimbra, Portugal

关键词: bone remodeling;    Signorini conditions;    normal compliance;    weak solutions;    convergence;    numerical simulations;   

DOI  :  10.1016/j.jmaa.2008.01.084

来源: Elsevier

【 摘 要 】

We consider the approximation of a bone remodeling model with the Signorini contact conditions by a contact problem with normal compliant obstacle, when the obstacle's deformability coefficient converges to zero (that is, the obstacle's stiffness tends to infinity). The variational problem is a coupled system composed of a nonlinear variational equation (in the case of normal compliance contact conditions) or a variational inequality (for the case of Signorini's contact conditions), for the mechanical displacement field, and a first-order ordinary differential equation for the bone remodeling function. A theoretical result, which states the convergence of the contact problem with normal compliance contact law to the Signorini problem, is then proved. Finally, some numerical simulations, involving examples in one and two dimensions, are reported to show this convergence behaviour. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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