Cortical Bone Adaptation to Mechanical Environment: Strain Energy Density Versus Fluid Motion

2019 ◽  
pp. 241-271
Author(s):  
Abhishek Kumar Tiwari ◽  
Jitendra Prasad
Keyword(s):  
Energy Density ◽  
Cortical Bone ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Fluid Motion ◽  
Bone Adaptation ◽  
Mechanical Environment

Analogy of Strain Energy Density Based Bone-Remodeling Algorithm and Structural Topology Optimization

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
In Gwun Jang ◽  
Il Yong Kim ◽  
Byung Man Kwak
Keyword(s):  
Topology Optimization ◽  
Energy Density ◽  
Bone Remodeling ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Optimization Method ◽  
Bone Adaptation ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Topology Optimization Method

In bone-remodeling studies, it is believed that the morphology of bone is affected by its internal mechanical loads. From the 1970s, high computing power enabled quantitative studies in the simulation of bone remodeling or bone adaptation. Among them, Huiskes et al. (1987, “Adaptive Bone Remodeling Theory Applied to Prosthetic Design Analysis,” J. Biomech. Eng., 20, pp. 1135–1150) proposed a strain energy density based approach to bone remodeling and used the apparent density for the characterization of internal bone morphology. The fundamental idea was that bone density would increase when strain (or strain energy density) is higher than a certain value and bone resorption would occur when the strain (or strain energy density) quantities are lower than the threshold. Several advanced algorithms were developed based on these studies in an attempt to more accurately simulate physiological bone-remodeling processes. As another approach, topology optimization originally devised in structural optimization has been also used in the computational simulation of the bone-remodeling process. The topology optimization method systematically and iteratively distributes material in a design domain, determining an optimal structure that minimizes an objective function. In this paper, we compared two seemingly different approaches in different fields—the strain energy density based bone-remodeling algorithm (biomechanical approach) and the compliance based structural topology optimization method (mechanical approach)—in terms of mathematical formulations, numerical difficulties, and behavior of their numerical solutions. Two numerical case studies were conducted to demonstrate their similarity and difference, and then the solution convergences were discussed quantitatively.

In silico modeling of bone adaptation to rest-inserted loading: Strain energy density versus fluid flow as stimulus

2018 ◽  
Vol 446 ◽  
pp. 110-127 ◽  
Author(s):  
Abhishek Kumar Tiwari ◽  
Rakesh Kumar ◽  
Dharmendra Tripathi ◽  
Subham Badhyal
Keyword(s):  
Fluid Flow ◽  
Energy Density ◽  
In Silico ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Bone Adaptation ◽  
In Silico Modeling

scholarly journals Volume free strain energy density method for applications to blunt V-notches

2020 ◽  
Vol 28 ◽  
pp. 734-742
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals On the application of the volume free strain energy density method to blunt V-notches under mixed mode condition

2021 ◽  
Vol 230 ◽  
pp. 111716
Author(s):  
Pietro Foti ◽  
Seyed Mohammad Javad Razavi ◽  
Majid Reza Ayatollahi ◽  
Liviu Marsavina ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Mixed Mode ◽  
Strain Energy ◽  
Density Method ◽  
Free Strain

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Storing Energy in the Mechanical Domain

2014 ◽  
Vol 1679 ◽  
Author(s):  
O.G. Súchil ◽  
G. Abadal ◽  
F. Torres
Keyword(s):  
Energy Source ◽  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Critical Strain ◽  
Substrate Surface ◽  
Maximum Load ◽  
Linear Buckling ◽  
Initial Ph ◽  
Self Powered

ABSTRACTSelf-powered microsystems as an alternative to standard systems powered by electrochemical batteries are taking a growing interest. In this work, we propose a different method to store the energy harvested from the ambient which is performed in the mechanical domain. Our mechanical storage concept is based on a spring which is loaded by the force associated to the energy source to be harvested [1]. The approach is based on pressing an array of fine wires (fws) grown vertically on a substrate surface. For the fine wires based battery, we have chosen ZnO fine wires due the fact that they could be grown using a simple and cheap process named hydrothermal method [2]. We have reported previous experiments changing temperature and initial pH of the solution in order to determine the best growth [3]. From new experiments done varying the compounds concentration the best results of fine wires were obtained. To characterize these fine wires we have considered that the maximum load we can apply to the system is limited by the linear buckling of the fine wires. From the best results we obtained a critical strain of εc = 3.72 % and a strain energy density of U = 11.26 MJ/m3, for a pinned-fixed configuration [4].

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