<i>r</i>‐Adaptation algorithm guided by gradients of strain energy density

Luo, Yunhua

doi:10.1002/cnm.1209

Cited by 5 publications

(5 citation statements)

References 24 publications

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“…19,20 Interior adjustments were made based on a spring smoothing method 58 and maintained the original radial spacing ratios of nodes with common local axial and angular cylindrical coordinates throughout the shape adaptation simulation. Because surface nodes were moved independently, additional smoothing methods were employed, based on SED gradient methods, 59 to reduce extreme differences in the local radial coordinates of neighboring nodes that may be calculated from Equation (5) at each shape adaptation iteration.…”

Section: Methodsmentioning

confidence: 99%

Strength adaptations of the tibia bone for prescribed sets of isometric forces and joint angles

Florio

2017

SIMULATION

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The isometric exercise induced tibial bone strength adaptations due to various prescribed net resultant forces generated by a leg arranged with specified hip, knee, and ankle joint angles were examined using a computationally based bone shape adaptation model. With the leg straight, or the knee flexed at 90°, and the hip either neutral or flexed by 45°, a force was repeatedly generated at the toe either anteriorly, posteriorly, superiorly, or inferiorly, in paired sequences of these directions, or in a clockwise pattern of all four directions. Model-predicted individual muscle forces, amounts of cortical bone surface accretion or resorption, and the resulting changes in bone stress distributions were compared. Similarities between adaptations to specific combinations of joint angles and net resultant force directions were found to follow similarities in the bone stress distributions rather than in muscle activity. The ratio of standard deviation to the surface-averaged measure of local stress was a good predictor of potential improvement in overall stress state uniformity. With flexed knee and neutral hip, greater adaptive improvements in tibial surface stress uniformity were found than with both joints flexed. Flexed configurations caused greater changes and overall strength improvements than exercises performed with a straight leg. Regions of local tibial cortical thickening were identified for specific joint angles and singleload resultant force directions. Sequential series of loads were also identified to enhance these effects and mitigate concurrent thinning in other regions. The presented information can aid in the design and analysis of targeted muscle and bone strengthening exercises.

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Section: Methodsmentioning

confidence: 99%

Strength adaptations of the tibia bone for prescribed sets of isometric forces and joint angles

Florio

2017

SIMULATION

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“…We analyze an energy-based p-adaptive algorithm, borrowing key ideas from [14,40] originally developed based on SED for problems in structural mechanics for problems in linear elasticity, exploring the extent they can be emulated in CEM to solve the time-domain Maxwell's equations. We further the analysis by showing that for the purpose of adaptivity indicators, EM energy in CEM does not assume the same role as strain energy in solid mechanics.…”

Section: The Practical Difficulty Of Incorporating a Fully Adaptive R...mentioning

confidence: 99%

“…The enhanced field Ψ * is suggested to be obtained from Ψ using simple averaging at nodes, or various projection methods. Gradient of SED is also used to compute a heuristic refinement criterion [14,40]. Luo et.…”

Section: Energy Driven Adaptivity 31 Role Of Strain Energy In Solid M...mentioning

confidence: 99%

Divergence Error Based p-adaptive Discontinuous Galerkin Solution of Time-domain Maxwell's Equations

Tiwari

Chatterjee

2022

PIER B

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A p-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the p-adaptive method. The nature of divergence error is explored, and that it is a direct consequence of the act of discretization is established. Its relation with relative truncation error is formed which enables the use of divergence error as an inexpensive proxy to truncation error. Divergence error is used as an indicator to dynamically identify and assign spatial operators of varying accuracy to substantial regions in the computational domain. This results in a reduced computational cost compared to a comparable discontinuous Galerkin time-domain solution using uniform degree piecewise polynomial bases throughout. Numerical results are presented to show performance of the proposed divergence error based p-adaptive solutions. It is shown that an accuracy similar to that of uniformly higher order solutions is obtained in terms of the scattering width, using fewer degrees of freedom.

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“…Mesh adjustment methods used in previous bone adaptation and structural shape optimization models usually involve remeshing and/or nodal smoothing . Because the developed routine is based on the changes in the positions of the surface nodes, it is desirable that the number of surface nodes remained constant in order to easily quantify the changes to the surface profile.…”

Section: Model Developmentmentioning

confidence: 99%

“…In this work, the weighting factor in the Laplacian smoothing of the outer surface nodes is selected through a previously developed method based on the gradients of the nodal strain energy densities . While the previously developed method adjusts the nodes in each of the three Cartesian coordinates, because the shape adaptation model in this work only alters the local radial coordinates of the surface nodes, the smoothing method is applied to the calculated change in radial position U k ( l ) in Equation rather than the nodal coordinates themselves X k ( l ) in Equation .…”

Section: Model Developmentmentioning

confidence: 99%

Development and implementation of a coupled computational muscle force optimization bone shape adaptation modeling method

Florio

2015

Numer Methods Biomed Eng

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Improved methods to analyze and compare the muscle-based influences that drive bone strength adaptation can aid in the understanding of the wide array of experimental observations about the effectiveness of various mechanical countermeasures to losses in bone strength that result from age, disuse, and reduced gravity environments. The coupling of gradient-based and gradientless numerical optimization routines with finite element methods in this work results in a modeling technique that determines the individual magnitudes of the muscle forces acting in a multisegment musculoskeletal system and predicts the improvement in the stress state uniformity and, therefore, strength, of a targeted bone through simulated local cortical material accretion and resorption. With a performance-based stopping criteria, no experimentally based or system-based parameters, and designed to include the direct and indirect effects of muscles attached to the targeted bone as well as to its neighbors, shape and strength alterations resulting from a wide range of boundary conditions can be consistently quantified. As demonstrated in a representative parametric study, the developed technique effectively provides a clearer foundation for the study of the relationships between muscle forces and the induced changes in bone strength. Its use can lead to the better control of such adaptive phenomena.

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r‐Adaptation algorithm guided by gradients of strain energy density

Cited by 5 publications

References 24 publications

Strength adaptations of the tibia bone for prescribed sets of isometric forces and joint angles

Strength adaptations of the tibia bone for prescribed sets of isometric forces and joint angles

Divergence Error Based p-adaptive Discontinuous Galerkin Solution of Time-domain Maxwell's Equations

Development and implementation of a coupled computational muscle force optimization bone shape adaptation modeling method

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