On the thermodynamic requirement of elastic stiffness anisotropy in isotropic materials

This paper deals with the design of an optimal cable-driven parallel robot (CDPR) for upper limb rehabilitation. The robot’s prescribed workspace is identified with the help of an occupational therapist based on three selected daily life activities, which are tracked using a Qualisys motion capture system. A preliminary architecture of the robot is proposed based on the analysis of the tracked trajectories of all the activities. A multi-objective optimization process using the genetic algorithm method is then performed, where the cable tensions and the robot size are selected as the objective functions to be minimized. The cables tensions are bounded between two limits, where the lower limit ensures a positive tension in the cables at all times and the upper limit represents the maximum torque of the motor. A sensitivity analysis is then performed using the Monte Carlo method to yield the optimal design selected out of the non-dominated solutions, forming the obtained Pareto front. The robot with the highest robustness toward the disturbances is identified, and its dexterity and elastic stiffness are calculated to investigate its performance.

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A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

Mathematics and Mechanics of Solids ◽

10.1177/10812865211001533 ◽

2021 ◽

pp. 108128652110015

Author(s):

YL Qu ◽

GY Zhang ◽

YM Fan ◽

F Jin

Keyword(s):

Classical Theory ◽

Couple Stress ◽

Couple Stress Theory ◽

Constitutive Relations ◽

Stress Theory ◽

Isotropic Materials ◽

Flexoelectric Effect ◽

Beam Bending ◽

Gradient Theories ◽

Anisotropic And Isotropic Materials

A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

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Finite element modeling of multiple density materials of bone specimens for biomechanical behavior evaluation

SN Applied Sciences ◽

10.1007/s42452-021-04760-9 ◽

2021 ◽

Vol 3 (9) ◽

Author(s):

Sebastián Irarrázaval ◽

Jorge Andrés Ramos-Grez ◽

Luis Ignacio Pérez ◽

Pablo Besa ◽

Angélica Ibáñez

Keyword(s):

Finite Elements ◽

Computational Models ◽

Reaction Force ◽

Elastic Stiffness ◽

Finite Elements Method ◽

Mechanical Resistance ◽

Assessment Procedure ◽

Axial Tomography ◽

Biomechanical Behavior ◽

Ct Data

AbstractThe finite elements method allied with the computerized axial tomography (CT) is a mathematical modeling technique that allows constructing computational models for bone specimens from CT data. The objective of this work was to compare the experimental biomechanical behavior by three-point bending tests of porcine femur specimens with different types of computational models generated through the finite elements’ method and a multiple density materials assignation scheme. Using five femur specimens, 25 scenarios were created with differing quantities of materials. This latter was applied to computational models and in bone specimens subjected to failure. Among the three main highlights found, first, the results evidenced high precision in predicting experimental reaction force versus displacement in the models with larger number of assigned materials, with maximal results being an R2 of 0.99 and a minimum root-mean-square error of 3.29%. Secondly, measured and computed elastic stiffness values follow same trend with regard to specimen mass, and the latter underestimates stiffness values a 6% in average. Third and final highlight, this model can precisely and non-invasively assess bone tissue mechanical resistance based on subject-specific CT data, particularly if specimen deformation values at fracture are considered as part of the assessment procedure.

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