scholarly journals Material Symmetries in Homogenized Hexagonal-Shaped Composites as Cosserat Continua

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 441 ◽  
Author(s):  
Nicholas Fantuzzi ◽  
Patrizia Trovalusci ◽  
Raimondo Luciano
Keyword(s):  
Degrees Of Freedom ◽  
Constitutive Law ◽  
Cosserat Theory ◽  
Rigid Particles ◽  
Hexagonal Shape ◽  
Elastic Interfaces ◽  
The Difference ◽  
Constitutive Parameters ◽  
Cosserat Continua ◽  
The Continuum

In this work, material symmetries in homogenized composites are analyzed. Composite materials are described as materials made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry described by a limited set of parameters. The purpose of this study is to analyze different geometrical configurations of the assemblies corresponding to various material symmetries such as orthotetragonal, auxetic and chiral. The problem is investigated through a homogenization technique which is able to carry out constitutive parameters using a principle of energetic equivalence. The constitutive law of the homogenized continuum has been derived within the framework of Cosserat elasticity, wherein the continuum has additional degrees of freedom with respect to classical elasticity. A panel composed of material with various symmetries, corresponding to some particular hexagonal geometries defined, is analyzed under the effect of localized loads. The results obtained show the difference of the micropolar response for the considered material symmetries, which depends on the non-symmetries of the strain and stress tensor as well as on the additional kinematical and work-conjugated statical descriptors. This work underlines the importance of resorting to the Cosserat theory when analyzing anisotropic materials.

scholarly journals New insights on homogenization for hexagonal-shaped composites as Cosserat continua

Meccanica ◽  
2021 ◽  
Author(s):  
Marco Colatosti ◽  
Nicholas Fantuzzi ◽  
Patrizia Trovalusci ◽  
Renato Masiani
Keyword(s):  
Continuum Theory ◽  
Representative Elementary Volume ◽  
Elementary Volume ◽  
Displacement Fields ◽  
Micropolar Continuum ◽  
Rigid Particles ◽  
Hexagonal Shape ◽  
Classical Models ◽  
Elastic Interfaces ◽  
Cosserat Continua

AbstractIn this work, particle composite materials with different kind of microstructures are analyzed. Such materials are described as made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry is described by a limited set of parameters. Three different textures are analyzed and static analyses are performed for a comparison among the solutions of discrete, micropolar (Cosserat) and classical models. In particular, the displacements of the discrete model are compared to the displacement fields of equivalent micropolar and classical continua realized through a homogenization technique, starting from the representative elementary volume detected with a numeric approach. The performed analyses show the effectiveness of adopting the micropolar continuum theory for describing such materials.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

Workspace, dexterity and dimensional optimization of microhexapod

2015 ◽  
Vol 35 (4) ◽  
pp. 341-347 ◽  
Author(s):  
E. Rouhani ◽  
M. J. Nategh
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Screw Theory ◽  
Design Parameters ◽  
Dimensional Synthesis ◽  
Content Type ◽  
Workspace Analysis ◽  
The Difference ◽  
Flexure Joints ◽  
6 Degrees Of Freedom

Purpose – The purpose of this paper is to study the workspace and dexterity of a microhexapod which is a 6-degrees of freedom (DOF) parallel compliant manipulator, and also to investigate its dimensional synthesis to maximize the workspace and the global dexterity index at the same time. Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Design/methodology/approach – Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Findings – It has been shown that the proposed procedure for the workspace calculation can considerably speed the required calculations. The optimization results show that a converged-diverged configuration of pods and an increase in the difference between the moving and the stationary platforms’ radii cause the global dexterity index to increase and the workspace to decrease. Originality/value – The proposed algorithm for the workspace analysis is very important, especially when it is an objective function of an optimization problem based on the search method. In addition, using screw theory can simply construct the homogeneous Jacobian matrix. The proposed methodology can be used for any other micromanipulator.

scholarly journals Design of a 2DoF Ankle Exoskeleton with a Polycentric Structure and a Bi-Directional Tendon-Driven Actuator Controlled Using a PID Neural Network

Actuators ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Taehoon Lee ◽  
Inwoo Kim ◽  
Yoon Su Baek
Keyword(s):  
Neural Network ◽  
Degrees Of Freedom ◽  
Plantar Flexion ◽  
Length Change ◽  
Talocrural Joint ◽  
Lower Limb Exoskeleton ◽  
Exoskeleton Robot ◽  
The Difference ◽  
Ankle Exoskeleton ◽  
The Stability

Lower limb exoskeleton robots help with walking movements through mechanical force, by identifying the wearer’s walking intention. When the exoskeleton robot is lightweight and comfortable to wear, the stability of walking increases, and energy can be used efficiently. However, because it is difficult to implement the complex anatomical movements of the human body, most are designed simply. Due to this, misalignment between the human and robot movement causes the wearer to feel uncomfortable, and the stability of walking is reduced. In this paper, we developed a two degrees of freedom (2DoF) ankle exoskeleton robot with a subtalar joint and a talocrural joint, applying a four-bar linkage to realize the anatomical movement of a simple 1DoF structure mainly used for ankles. However, bidirectional tendon-driven actuators (BTDAs) do not consider the difference in a length change of both cables due to dorsiflexion (DF) and plantar flexion (PF) during walking, causing misalignment. To solve this problem, a BTDA was developed by considering the length change of both cables. Cable-driven actuators and exoskeleton robot systems create uncertainty. Accordingly, adaptive control was performed with a proportional-integral-differential neural network (PIDNN) controller to minimize system uncertainty.

Maximum Total Point Motion of Five Points Versus All Points in Assessing Tibial Baseplate Stability

2021 ◽  
Author(s):  
Abigail Niesen ◽  
Anna L Garverick ◽  
Maury Hull
Keyword(s):  
Degrees Of Freedom ◽  
Stability Limit ◽  
3D Models ◽  
Six Degrees Of Freedom ◽  
Percent Error ◽  
Model Based ◽  
Point Motion ◽  
The Mean ◽  
The Difference ◽  
Total Point

Abstract Maximum total point motion (MTPM), the point on a baseplate that migrates the most, has been used to assess the risk of tibial baseplate loosening using radiostereometric analysis (RSA). Two methods for determining MTPM for model-based RSA are to use either 5 points distributed around the perimeter of the baseplate or to use all points on the 3D model. The objectives were to quantify the mean difference in MTPM using 5 points vs. all points, compute the percent error relative to the 6-month stability limit for groups of patients, and to determine the dependency of differences in MTPM on baseplate size and shape. A dataset of 10,000 migration values was generated using the mean and standard deviation of migration in six degrees of freedom at 6 months from an RSA study. The dataset was used to simulate migration of 3D models (two baseplate shapes and two baseplate sizes) and calculate the difference in MTPM using 5 virtual points vs. all points and the percent error (i.e. difference in MTPM/stability limit) relative to the 6-month stability limit. The difference in MTPM was about 0.02 mm, or 4% percent relative to the 6-month stability limit, which is not clinically important. Furthermore, results were not affected by baseplate shape or size. Researchers can decide whether to use 5 points or all points when computing MTPM for model-based RSA. The authors recommend using 5 points to maintain consistency with marker-based RSA.

Introducing a Projection-Based Method to Compare Three Approaches Computing the Accumulation of Geometric Variations

2018 ◽  
Author(s):  
Vincent Delos ◽  
Santiago Arroyave-Tobón ◽  
Denis Teissandier
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Geometric Constraints ◽  
Computational Time ◽  
Manufacturing Defects ◽  
Design Tolerance ◽  
Polyhedral Objects ◽  
The Difference ◽  
Bounded Sets ◽  
Accumulation Of Defects

In mechanical design, tolerance zones and contact gaps can be represented by sets of geometric constraints. For computing the accumulation of possible manufacturing defects, these sets have to be summed and/or intersected according to the assembly architecture. The advantage of this approach is its robustness for treating even over-constrained mechanisms i.e. mechanisms in which some degrees of freedom are suppressed in a redundant way. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In this work, we compare three methods for summing sets of constraints using polyhedral objects. The difference between them lie in the way the degrees of freedom (DOFs) (or invariance) of joints and features are treated. The first method proposes to virtually limit the DOFs of the toleranced features and joints to turn the polyhedra into polytopes and avoid manipulating unbounded objects. Even though this approach enables to sum, it also introduces bounding or cap facets which increase the complexity of the operand sets. This complexity increases after each operation until becoming far too significant. The second method aims to face this problem by cleaning, after each sum, the calculated polytope to keep under control the effects of the propagation of the DOFs. The third method is new and based on the identification of the sub-space in which the projection of the operands are bounded sets. Calculating the sum in this sub-space allows reducing significantly the operands complexity and consequently the computational time. After presenting the geometric properties on which the approaches rely, we demonstrate them on an industrial case. Then we compare the computation times and deduce the equality of the results of all the methods.

A Comprehensive Energy Formulation for General Nonlinear Material Continua

1997 ◽  
Vol 64 (2) ◽  
pp. 353-360 ◽  
Author(s):  
A. Carini ◽  
O. De Donato
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Small Strain ◽  
Constitutive Law ◽  
Nonlinear Material ◽  
Total Potential ◽  
Initial Boundary Value ◽  
Energy Formulation ◽  
The Continuum

By specialization to the continuum problem of a general formulation of the initial/boundary value problem for every nonpotential operator (Tonti, 1984) and by virtue of a suitable choice of the “integrating operator,” a comprehensive energy formulation is established. Referring to the small strain and displacement case in the presence of any inelastic generally nonlinear constitutive law, provided that it is differentiable, this formulation allows us to derive extensions of well-known principles of elasticity (Hu-Washizu, Hellinger-Reissner, total potential energy, and complementary energy). An illustrative example is given. Peculiar properties of the formulation are the energy characterization of the functional and the use of Green functions of the same problem in the elastic range for every inelastic, generally nonlinear material considered.

Insect Recognition Using Sparse Coding and Decision Fusion

2015 ◽  
pp. 124-145
Author(s):  
Hanqing Lu ◽  
Xinwen Hou ◽  
Cheng-Lin Liu ◽  
Xiaolin Chen
Keyword(s):  
Sparse Coding ◽  
Degrees Of Freedom ◽  
Decision Fusion ◽  
Classifier Fusion ◽  
Hard Problem ◽  
Classifier Selection ◽  
Image Patches ◽  
The Difference ◽  
Fusion Scheme ◽  
Heterogeneous Class

Insect recognition is a hard problem because the difference of appearance between insects is so small that only some entomologist experts can distinguish them. Besides that, insects are often composed of several parts (multiple views) which generate more degrees of freedom. This chapter proposes several discriminative coding approaches and one decision fusion scheme of heterogeneous class sets for insect recognition. The three discriminative coding methods use class specific concatenated vectors instead of traditional global coding vectors for insect image patches. The decision fusion scheme uses an allocation matrix for classifier selection and a weight matrix for classifier fusion, which is suitable for combining classifiers of heterogeneous class sets in multi-view insect image recognition. Experimental results on a Tephritidae dataset show that the three proposed discriminative coding methods perform well in insect recognition, and the proposed fusion scheme improves the recognition accuracy significantly.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

Sign in / Sign up

Export Citation Format

Share Document