A continuum damage model for alveolar bone remodeling

Several authors ([1, 2] among others) have proposed mechanical models to predict long term tooth movement considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to an “adaptative elasticity” behavior [3, 4]. However, tooth movements obtained through orthodontic appliances result from a complex biochemical process of bone structure and density adaptation to its mechanical environment, called bone remodeling. This process is far from linear elasticity. It leads to permanent deformation due to biochemical actions. The proposed biomechanical constitutive law (inspired from Doblaré’s model [5]) is based on a Continuum Damage Mechanics material coupled to an elasto-visco-plastic law and considering a damage variable not as actual damage but as a measure of bone density. It is formulated as to be used explicitly for alveolar bone, whose remodeling cells, opposite to most bones, are triggered by the pressure state applied to the bone matrix.