title: A non-linear homogeneous model for bone-like materials under compressive load.
abstract: Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which currently is only feasible at the expense of extremely high computational costs, coarser models can be used if the local morphology has been linked to the apparent mechanical behavior. The aim of this paper is to implement and validate such a constitutive law. This law is able to capture the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using an elastoplastic material model incorporating hardening. These features are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strain framework. This material model was implemented into metafor (LTAS-MNNL, University of Liège, Belgium), a non-linear FE software. The implementation was validated against experimental data of cylindrical samples subjected to compression. Three materials with bone-like microstructure were tested: aluminum foams of variable density (ERG, Oakland, CA, USA), polylactic acid foam (CERM, University of Liège, Liège, Belgium), and cancellous bone tissue of a deer antler (Faculty of Veterinary Medicine, University of Liège, Liège, Belgium).
authors.affiliation: Department of Aerospaceand Mechanics, LTAS-Non Linear Computational Mechanics, University of Liège, Liège, Belgium. mmengoni@ulg.ac.be.
authors.forename: M
authors.initials: M
authors.lastname: Mengoni
authors.forename: R
authors.initials: R
authors.lastname: Voide
authors.forename: C
authors.initials: C
authors.lastname: de Bien
authors.forename: H
authors.initials: H
authors.lastname: Freichels
authors.forename: C
authors.initials: C
authors.lastname: Jérôme
authors.forename: A
authors.initials: A
authors.lastname: Léonard
authors.forename: D
authors.initials: D
authors.lastname: Toye
authors.forename: R
authors.initials: R
authors.lastname: Müller
authors.forename: G H
authors.initials: GH
authors.lastname: van Lenthe
authors.forename: J P
authors.initials: JP
authors.lastname: Ponthot
mesh_terms: D000535:Aluminum / Q000737:chemistry; D000818:Animals; D016880:Anisotropy; D000999:Antlers / Q000502:physiology; D001842:Bone and Bones / Q000502:physiology*; D019245:Compressive Strength / Q000502:physiology*; D003670:Deer; D020342:Finite Element Analysis; D019344:Lactic Acid / Q000737:chemistry; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011091:Polyesters; D011108:Polymers / Q000737:chemistry; D015203:Reproducibility of Results
chemical_list: D011091:Polyesters; D011108:Polymers; D019344:Lactic Acid; C033616:poly(lactide); D000535:Aluminum
keywords: anisotropy; bone; constitutive law; fabric; large deformation finite element; plasticity