A novel algorithm to resolve lack of convergence and checkerboard instability in bone adaptation simulations using non-local averaging

Calvo-Gallego, J.L. ; Pivonka, P. ; Garcia-Aznar, J.M. (Universidad de Zaragoza) ; Martinez-Reina, J.

Resumen: Checkerboard is a typical instability in finite element (FE) simulations of bone adaptation and topology optimization in general. It consists in a patchwork pattern with elements of alternating stiffness, producing lack of convergence and instabilities in the predicted bone density. Averaging techniques have been proposed to solve this problem. One of the most acknowledged techniques (node based formulation) has severe drawbacks such as: high sensitivity to mesh density and type of element integration (full vs reduced) and, more importantly, oscillatory solutions also leading to lack of convergence. We propose a new solution consisting in a non-local smoothing technique. It defines, as the mechanical stimulus governing bone adaptation in a certain integration point of the mesh, the average of the stimuli obtained in the neighbour integration points. That average is weighted with a decay function of the distance to the centre of the neighbourhood. The new technique has been shown to overcome all the referred problems and perform in a robust way. It was tested on a hollow cylinder, resembling the diaphysis of a long bone, subjected to bending or torsion. Checkerboard instability was eliminated and local convergence of bone adaptation was achieved rapidly, in contrast to the other averaging technique and to the model without control of checkerboard instability. The new algorithm was also tested with good results on the same geometry but in a model containing a void, which produces a stress concentration that usually leads to checkerboard instability, like in other applications such as simulations of bone-implant interfaces.

Idioma: Inglés

DOI: 10.1002/cnm.3419

Año: 2020

Publicado en: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING (2020), e3419 [22 pp]
ISSN: 2040-7939

Factor impacto JCR: 2.747 (2020)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 34 / 108 = 0.315 (2020) - Q2 - T1
Categ. JCR: MATHEMATICAL & COMPUTATIONAL BIOLOGY rank: 19 / 58 = 0.328 (2020) - Q2 - T1
Categ. JCR: ENGINEERING, BIOMEDICAL rank: 56 / 90 = 0.622 (2020) - Q3 - T2

Factor impacto SCIMAGO: 0.74 - Applied Mathematics (Q1) - Biomedical Engineering (Q1) - Software (Q1) - Modeling and Simulation (Q1) - Molecular Biology (Q1) - Computational Theory and Mathematics (Q1)

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Mec.Med.Cont. y Teor.Est. (Dpto. Ingeniería Mecánica)