A convergence result in the study of bone remodeling contact problems

• Autor(a) principal: Fernández, J. R.
• Data de Publicação: 2008
• Outros Autores: Figueiredo, I. N., Martínez, R.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/4580; https://doi.org/10.1016/j.jmaa.2008.01.084
• topic: Bone remodeling; Signorini conditions; Normal compliance; Weak solutions; Convergence; Numerical simulations

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.