000108495 001__ 108495
000108495 005__ 20211122153225.0
000108495 0247_ $$2doi$$a10.1002/cnm.3419
000108495 0248_ $$2sideral$$a121617
000108495 037__ $$aART-2020-121617
000108495 041__ $$aeng
000108495 100__ $$aCalvo-Gallego, J.L.
000108495 245__ $$aA novel algorithm to resolve lack of convergence and checkerboard instability in bone adaptation simulations using non-local averaging
000108495 260__ $$c2020
000108495 5060_ $$aAccess copy available to the general public$$fUnrestricted
000108495 5203_ $$aCheckerboard 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.
000108495 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000108495 590__ $$a2.747$$b2020
000108495 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b34 / 108 = 0.315$$c2020$$dQ2$$eT1
000108495 591__ $$aMATHEMATICAL & COMPUTATIONAL BIOLOGY$$b19 / 58 = 0.328$$c2020$$dQ2$$eT1
000108495 591__ $$aENGINEERING, BIOMEDICAL$$b56 / 90 = 0.622$$c2020$$dQ3$$eT2
000108495 592__ $$a0.74$$b2020
000108495 593__ $$aApplied Mathematics$$c2020$$dQ1
000108495 593__ $$aBiomedical Engineering$$c2020$$dQ1
000108495 593__ $$aSoftware$$c2020$$dQ1
000108495 593__ $$aModeling and Simulation$$c2020$$dQ1
000108495 593__ $$aMolecular Biology$$c2020$$dQ1
000108495 593__ $$aComputational Theory and Mathematics$$c2020$$dQ1
000108495 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000108495 700__ $$aPivonka, P.
000108495 700__ $$0(orcid)0000-0002-9864-7683$$aGarcia-Aznar, J.M.$$uUniversidad de Zaragoza
000108495 700__ $$aMartinez-Reina, J.
000108495 7102_ $$15004$$2605$$aUniversidad de Zaragoza$$bDpto. Ingeniería Mecánica$$cÁrea Mec.Med.Cont. y Teor.Est.
000108495 773__ $$g(2020), e3419 [22 pp]$$tINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING$$x2040-7939
000108495 8564_ $$s1856429$$uhttps://zaguan.unizar.es/record/108495/files/texto_completo.pdf$$yPostprint
000108495 8564_ $$s1918557$$uhttps://zaguan.unizar.es/record/108495/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000108495 909CO $$ooai:zaguan.unizar.es:108495$$particulos$$pdriver
000108495 951__ $$a2021-11-22-13:59:45
000108495 980__ $$aARTICLE