PURPOSE: Investigation of trabecular bone strength and compaction is important for fracture risk prediction. At 1-2% compressive strain, trabecular bone undergoes strain softening, which may lead to numerical instabilities and mesh dependency in classical local damage-plastic models. The aim of this work is to improve our continuum damage-plastic model of bone by reducing the influence of finite element mesh size under large compression. METHODOLOGY: This spurious numerical phenomenon may be circumvented by incorporating the nonlocal effect of cumulated plastic strain into the constitutive law. To this end, an over-nonlocal implicit gradient model of bone is developed and implemented into the finite element software ABAQUS using a user element subroutine. The ability of the model to detect the regions of bone failure is tested against experimental stepwise loading data of 16 human trabecular bone biopsies. FINDINGS: The numerical outcomes of the nonlocal model revealed reduction of finite element mesh dependency compared with the local damage-plastic model. Furthermore, it helped reduce the computational costs of large-strain compression simulations. ORIGINALITY: To the best of our knowledge, the proposed model is the first to predict the failure and densification of trabecular bone up to large compression independently of finite element mesh size. The current development enables the analysis of trabecular bone compaction as in osteoporotic fractures and implant migration, where large deformation of bone plays a key role.

Department of Mechanics Faculty of Civil Engineering Czech Technical University Prague Zikova 1903 4 Praha 6 166 36 Czech Republic

Faculty of Medicine Institute for Surgical Technology and Biomechanics University of Bern Stauffacherstr 78 Bern CH 3014 Switzerland

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