A new constitutive model for simulation of softening, plateau, and densification phenomena for trabecular bone under compression.
A new type of constitutive model and its computational implementation procedure for the simulation of a trabecular bone are proposed in the present study. A yield surface-independent Frank-Brockman elasto-viscoplastic model is introduced to express the nonlinear material behavior such as softening beyond yield point, plateau, and densification under compressive loads. In particular, the hardening- and softening-dominant material functions are introduced and adopted in the plastic multiplier to describe each nonlinear material behavior separately. In addition, the elasto-viscoplastic model is transformed into an implicit type discrete model, and is programmed as a user-defined material subroutine in commercial finite element analysis code. In particular, the consistent tangent modulus method is proposed to improve the computational convergence and to save computational time during finite element analysis. Through the developed material library, the nonlinear stress-strain relationship is analyzed qualitatively and quantitatively, and the simulation results are compared with the results of compression test on the trabecular bone to validate the proposed constitutive model, computational method, and material library.
Biomedical Research Institute, Pusan National University Hospital, Busan 49241, Republic of Korea; School of Medicine, Pusan National University, Busan 49241, Republic of Korea.
Chi-Seung
CS
Lee
Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan 46241, Republic of Korea. Electronic address: jaemlee@pusan.ac.kr.
Jae-Myung
JM
Lee
Department of Biological Sciences, Pusan National University, Busan 46241, Republic of Korea.
BuHyun
B
Youn
Biomedical Research Institute, Pusan National University Hospital, Busan 49241, Republic of Korea; School of Medicine, Pusan National University, Busan 49241, Republic of Korea.
Hyung-Sik
HS
Kim
Department of Orthopaedic Surgery, Medical Research Institute, Pusan National University Hospital, Busan 49241, Republic of Korea.
Jong Ki
JK
Shin
Department of Orthopaedic Surgery, Medical Research Institute, Pusan National University Hospital, Busan 49241, Republic of Korea.
Tae Sik
TS
Goh
Department of Orthopaedic Surgery, Medical Research Institute, Pusan National University Hospital, Busan 49241, Republic of Korea. Electronic address: jungsublee@pusan.ac.kr.
Jung Sub
JS
Lee
D001696:Biomechanical Phenomena; D000071556:Cancellous Bone / Q000502:physiology*; D003198:Computer Simulation; D020342:Finite Element Analysis; D006801:Humans; D008954:Models, Biological; D011312:Pressure; D013314:Stress, Mechanical
ABAQUS user-defined subroutine UMAT; Computational inelasticity; Constitutive model; Finite element analysis; Material nonlinearity; Trabecular bone