Parameter identification of hyperelastic material properties of the heel pad based on an analytical contact mechanics model of a spherical indentation

Suzuki, Ritsuro; Ito, Kohta; Lee, Taeyong; Ogihara, Naomichi

doi:10.1016/j.jmbbm.2016.09.027

Cited by 19 publications

(7 citation statements)

References 59 publications

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“…The cartilage is often modeled as a thin cartilaginous layer of 1.0–1.5 mm thickness on the articular surfaces ( Shepherd and Seedhom, 1999 ), but here the bone elements corresponding to articular surfaces were manually selected and assigned as articular cartilage, and the Young’s modulus, Poisson’s ratio, and density were set to 10 MPa, 0.4, and 0.002 g/mm 3 , respectively, based on previous studies ( Gefen, 2003 ; Qian et al, 2013 ). The encapsulated soft tissue was defined as a hyperelastic Ogden material, whose strain energy potential function U can be expressed as

where λ is the deviatoric principal stretch; C and α are coefficients, whose values were determined to be 0.0102 MPa and 8.04, respectively, based on in vivo parameter identification using a spherical indentation and an analytical contact mechanics model ( Suzuki et al, 2017 ). The density was determined to be 0.937 × 10 −3 g/mm 3 ( Qian et al, 2013 ).…”

Section: Methodsmentioning

confidence: 99%

“…where λ is the deviatoric principal stretch; C and α are coefficients, whose values were determined to be 0.0102 MPa and 8.04, respectively, based on in vivo parameter identification using a spherical indentation and an analytical contact mechanics model (Suzuki et al, 2017). The density was determined to be 0.937 × 10 −3 g/mm 3 (Qian et al, 2013).…”

Section: Human Foot Modelmentioning

confidence: 99%

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Comparative Functional Morphology of Human and Chimpanzee Feet Based on Three-Dimensional Finite Element Analysis

Ito

Nakamura

Suzuki

et al. 2022

Front. Bioeng. Biotechnol.

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To comparatively investigate the morphological adaptation of the human foot for achieving robust and efficient bipedal locomotion, we develop three-dimensional finite element models of the human and chimpanzee feet. Foot bones and the outer surface of the foot are extracted from computer tomography images and meshed with tetrahedral elements. The ligaments and plantar fascia are represented by tension-only spring elements. The contacts between the bones and between the foot and ground are solved using frictionless and Coulomb friction contact algorithms, respectively. Physiologically realistic loading conditions of the feet during quiet bipedal standing are simulated. Our results indicate that the center of pressure (COP) is located more anteriorly in the human foot than in the chimpanzee foot, indicating a larger stability margin in bipedal posture in humans. Furthermore, the vertical free moment generated by the coupling motion of the calcaneus and tibia during axial loading is larger in the human foot, which can facilitate the compensation of the net yaw moment of the body around the COP during bipedal locomotion. Furthermore, the human foot can store elastic energy more effectively during axial loading for the effective generation of propulsive force in the late stance phase. This computational framework for a comparative investigation of the causal relationship among the morphology, kinematics, and kinetics of the foot may provide a better understanding regarding the functional significance of the morphological features of the human foot.

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Section: Methodsmentioning

confidence: 99%

Section: Human Foot Modelmentioning

confidence: 99%

Comparative Functional Morphology of Human and Chimpanzee Feet Based on Three-Dimensional Finite Element Analysis

Ito

Nakamura

Suzuki

et al. 2022

Front. Bioeng. Biotechnol.

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“…For the indentation tests, a 3-mm diameter cylindrical flat-ended indenter tip was used [ 54 , 55 ]. The tests were conducted at two different frequencies 0.2Hz and 20Hz to 50% of the participant’s soft tissue thickness in order to identify the viscoelastic properties of the tissue [ 30 ].…”

Section: Methodsmentioning

confidence: 99%

In vivo soft tissue compressive properties of the human hand

et al. 2021

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Background/Purpose Falls onto outstretched hands are the second most common sports injury and one of the leading causes of upper extremity injury. Injury risk and severity depends on forces being transmitted through the palmar surface to the upper extremity. Although the magnitude and distribution of forces depend on the soft tissue response of the palm, the in vivo properties of palmar tissue have not been characterized. The purpose of this study was to characterize the large deformation palmar soft tissue properties. Methods In vivo dynamic indentations were conducted on 15 young adults (21–29 years) to quantify the soft tissue characteristics of over the trapezium. The effects of loading rate, joint position, tissue thickness and sex on soft tissue responses were assessed. Results Energy absorbed by the soft tissue and peak force were affected by loading rate and joint angle. Energy absorbed was 1.7–2.8 times higher and the peak force was 2–2.75 times higher at high rate loading than quasistatic rates. Males had greater energy absorbed than females but not at all wrist positions. Damping characteristics were the highest in the group with the thickest soft tissue while damping characteristics were the lowest in group with the thinnest soft tissues. Conclusion Palmar tissue response changes with joint position, loading rate, sex, and tissue thickness. Accurately capturing these tissue responses is important for developing effective simulations of fall and injury biomechanics and assessing the effectiveness of injury prevention strategies.

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“…The biomechanical properties of the heel pad have been characterized in the relevant literature, and it was found that the heel pad exhibited hyperelastic mechanical characteristics during compression and that materials with this mechanical characteristic undergo a large deformation under compressive loading (Miller-Young et al, 2002;Grigoriadis et al, 2017), allowing the foot to decelerate over a certain distance and achieve effective cushioning. The stress relaxation and creep of the heel pad reflect the viscoelastic material properties (Behforootan et al, 2017;Suzuki et al, 2017;Tecse et al, 2023). Under viscous action, the impact energy absorbed by the heel pad is dissipated in the form of viscoelastic creep and heat (De Clercq et al, 1994), and the energy dissipated by the heel pad can reach approximately 35% during compression (Ledoux and Blevins, 2007), this is important for cushioning performance.…”

Section: Introductionmentioning

confidence: 99%

Effects of extreme cyclic loading on the cushioning performance of human heel pads under engineering test condition

Qian,

Zhuang,

Liu

et al. 2023

Front. Bioeng. Biotechnol.

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Human heel pads commonly undergo cyclic loading during daily activities. Low cyclic loadings such as daily human walking tend to have less effect on the mechanical properties of heel pads. However, the impact of cyclic loading on cushion performance, a vital biomechanical property of heel pads, under engineering test condition remains unexplored. Herein, dynamic mechanical measurements and finite element (FE) simulations were employed to explore this phenomenon. It was found that the wavy collagen fibers in the heel pad will be straightened under cycle compression loading, which resulted in increased stiffness of the heel pad. The stiffness of the heel pads demonstrated an inclination to escalate over a span of 50,000 loading cycles, consequently resulting in a corresponding increase in peak impact force over the same loading cycles. Sustained cyclic loading has the potential to result in the fracturing of the straightened collagen fibers, this collagen breakage may diminish the stiffness of the heel pad, leading to a reduction in peak impact force. This work enhances understanding of the biomechanical functions of human heel pad and may provide potential inspirations for the innovative development of healthcare devices for foot complex.

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Parameter identification of hyperelastic material properties of the heel pad based on an analytical contact mechanics model of a spherical indentation

Cited by 19 publications

References 59 publications

Comparative Functional Morphology of Human and Chimpanzee Feet Based on Three-Dimensional Finite Element Analysis

Comparative Functional Morphology of Human and Chimpanzee Feet Based on Three-Dimensional Finite Element Analysis

In vivo soft tissue compressive properties of the human hand

Effects of extreme cyclic loading on the cushioning performance of human heel pads under engineering test condition

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