A generic anisotropic continuum damage model integration scheme adaptable to both ductile damage and biological damage-like situations

Abstract

This paper aims at presenting a general versatile time integration scheme applicable to anisotropic damage coupled to elastoplasticity, considering any damage rate and isotropic hardening formulations. For this purpose a staggered time integration scheme in a finite strain framework is presented, together with an analytical consistent tangent operator. The only restrictive hypothesis is to work with an undamaged isotropic material, assumed here to follow a J 2 plasticity model. The only anisotropy considered is thus a damage-induced anisotropy.The possibility to couple any damage rate law with the present algorithm is illustrated with a classical ductile damage model for aluminium, and a biological damage-like application. The later proposes an original bone remodelling law coupled to trabecular bone plasticity for the simulation of orthodontic tooth movements. All the developments have been considered in the framework of the implicit non-linear finite element code Metafor (developed at the LTAS/MN 2 L, University of Liège, Belgium -www.metafor.ltas.ulg.ac.be).

Prediction of the mechanical response of canine humerus to three-point bending using subject-specific finite element modelling

“…The computational representation of those blocks is thus a good approximation of the block behaviour and interaction with the bone. Using the verified and validated non-linear FE software Metafor [36][37][38][39] to analyse long-bone three-point bending tests permits high automation of the model pre-and post-processing steps. This reduces user variability to the image segmentation step only.…”

“…Including progressive damage in the model may lead to better results as the physical phenomenon leading to bone non-linear behaviour is most probably related to damage rather than plasticity. 21,34,38,44 No distinction was made between cortical and trabecular tissues in the bone material properties characterizing the non-linear behaviour, although the microstructures of these tissues are clearly different. It is likely that here the trabecular tissue do not participate substantially to the bone bending response.…”

Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review

“…As a first approximation, it was suggested (Argatov and Mishuris, 2015a) that the asymptotic model [equations (3)–(6)] can predict the deformation of articular cartilage and the damage accumulation process until the fracture moment. Of course, the further development of mathematical models for impact-induced fissuring (Atkinson et al, 1998; Kafka, 2002) will require a more sophisticated mathematical modeling framework [see, e.g., Peña (2011) and Mengoni and Ponthot (2015)]. Nevertheless, this simple model reveals the key model parameters, which should be reported in the experimental studies in order to facilitate the comparison between different experiments.…”

Anisotropic constitutive model incorporating multiple damage mechanisms for multiscale simulation of dental enamel

“…In the past decades, a large number of phenomenological hyperelastic models have been proposed (Ogden, 1972;Yeoh, 1993;Ehret and Itskov, 2009) In order to simulate the damage behavior of fiberreinforced composites, continuum damage mechanics has widely been applied to describe the damage accumulation process in different damage modes (Chaboche et al, 1995;Lapczyk and Hurtado, 2007;Maimí et al, 2007;Peña, 2011;Mengoni and Ponthot, 2015;Vasiukov et al, 2015 Anisotropic hyperelastic damage model of dental enamel As outlined in the introduction, dental enamel possesses a fibrous microstructure with several hierarchy levels. In order to predict the mechanical response, a homogenized constitutive model based on the microstructure at a lower hierarchical level is required to capture the anisotropic response of the material at higher hierarchical levels.…”