Length scale parameter of single trabecula in cancellous bone
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ORIGINAL PAPER
Length scale parameter of single trabecula in cancellous bone Majid Akbarzadeh Khorshidi1 Received: 12 November 2019 / Accepted: 18 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, the material length scale parameter of the modified couple stress theory for trabecular bones is studied. For this reason, experimental data for the buckling of single wet and dry trabeculae from the subchondral region of the human medial tibial plateau are used from the literature. A material length scale parameter is extracted using the modified couple stress theory-based buckling relation and the experimental results. This parameter can capture the size-dependent behavior of trabeculae and can be beneficial for micro-mechanical investigation of trabecular bones. In addition, this paper proposes a size-dependent length scale parameter for trabeculae to estimate the buckling behaviors of dry and wet trabeculae, more accurately. Therefore, this paper confirms that the softening (weakening) effects of the modified couple stress theory and size-dependent behavior of the material length scale parameter can be considered for some special cases, and additionally, a correct value for the length scale parameter of the trabecula is revealed. Keywords Modified couple stress theory · Length scale parameter · Cancellous bone · Biomechanics · Micromechanics
1 Introduction Bone is an important organ which has a complex structure with a mixture of protein and mineral. In scrutiny, it is a protein–mineral nanocomposite structure (Ji and Gao 2004) which can expose different behaviors compared with the individual materials. There are five types of bones in the human body on the basis of shape: long, short, flat, irregular and sesamoid (“types of bone” mananatomy.com. Retrieved on Feb 6, 2016). Long bones are characterized by a shaft (diaphysis) and a semi-rounded head at both ends of the shaft (epiphysis). There are two types of bone tissue in the human body. The walls of the diaphysis composed of dense and hard tissue are called compact or cortical bone, and cancellous bone (spongy or trabecular bone) is mostly found at the ends of long bones [see Fig. 1 (Marieb and Hoehn 2007)]. Cancellous bone is a porous, heterogeneous and anisotropic structure combining hard and soft tissues to control the sudden impacts in addition to having enough strength. The mechanical properties of cancellous bone tissue can be determined using a compromise between mineral * Majid Akbarzadeh Khorshidi [email protected] 1
and collagen (Bayraktar et al. 2004). The microstructure of cancellous bone can be defined as plate-like and rod-like trabecula architectures. It is important to improve our knowledge about the micro- or nanoscale characteristics and the mechanical behaviors of bone. Therefore, each research that presents a novel contribution to bone’s structure can be advantageous for this field of biomechanics. Oftadeh et al. (2015) presented a review of the mechanobiology of trabecular bone
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