In a Nutshell: Topological Interlocking and Geometric Stiffening as Complementary Strategies for Strong Plant Shells (Adv. Mater. 48/2020)

AbstractSince its introduction in 2001 [1], the concept of topological interlocking has advanced to reasonable maturity, and various research groups have now adopted it as a promising avenue for developing novel structures and materials with unusual mechanical properties. In this paper, we review the known geometries of building blocks and their arrangements that permit topological interlocking. Their properties relating to stiffness, fracture resistance and damping are discussed on the basis of experimental evidence and modeling results. An outlook to prospective engineering applications is also given.

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Short review on architectured materials with topological interlocking mechanisms

Material Design & Processing Communications ◽

10.1002/mdp2.31 ◽

2019 ◽

Vol 1 (1) ◽

pp. e31

Author(s):

Chao Gao ◽

Josef Kiendl

Keyword(s):

Short Review ◽

Architectured Materials ◽

Topological Interlocking

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Design and structural optimization of topological interlocking assemblies

ACM Transactions on Graphics ◽

10.1145/3355089.3356489 ◽

2019 ◽

Vol 38 (6) ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Ziqi Wang ◽

Peng Song ◽

Florin Isvoranu ◽

Mark Pauly

Keyword(s):

Structural Optimization ◽

Topological Interlocking

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CONSISTENT APPROXIMATION FOR THE STRAIN ENERGY OF A 3D ELASTIC BODY ADEQUATE FOR THE STRESS STIFFENING EFFECT

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455404001239 ◽

2004 ◽

Vol 04 (02) ◽

pp. 279-292 ◽

Cited By ~ 4

Author(s):

YU. VETYUKOV

Keyword(s):

Elastic Body ◽

Strain Energy ◽

Conventional Approach ◽

Deformation Model ◽

Geometrically Nonlinear ◽

Consistent Approximation ◽

New Strategy ◽

Geometric Stiffening ◽

Angular Velocities ◽

Stiffening Effect

Starting from the fully geometrically nonlinear deformation model of a 3D elastic body, a consistent approximation for the strain energy in the vicinity of a pre-deformed state is obtained. This allows for the stress (geometric) stiffening effect to be taken into account. Additional terms arise in the strain energy approximation in comparison to the conventional approach, in which stiffening is incorporated in the form of a so-called geometric stiffness matrix. Computational costs of the new model are of the same order as that of the conventional approach. When compared to the fully geometrically nonlinear theory, the numerical analysis shows the suggested model to describe the dynamics of an elastic rotating structure better than the conventional approach. A new strategy is suggested to treat the non-constant pre-deformation, which is important for the flexible multibody simulations when angular velocities and interaction forces vary in time.

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On Stability of a Nonlinear, Periodically Time Varying, Rotating Blade

Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B ◽

10.1115/detc2011-48574 ◽

2011 ◽

Author(s):

Fengxia Wang

Keyword(s):

Steady State ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Multiple Time ◽

Time Varying ◽

Rotating Blade ◽

Stability And Bifurcation ◽

Geometric Stiffening ◽

Rotational Motions ◽

The Stability

This paper discusses the stability of a periodically time-varying, spinning blade with cubic geometric nonlinearity. The modal reduction method is adopted to simplify the nonlinear partial differential equations to the ordinary differential equations, and the geometric stiffening is approximated by the axial inertia membrane force. The method of multiple time scale is employed to study the steady state motions, the corresponding stability and bifurcation for such a periodically time-varying rotating blade. The backbone curves for steady-state motions are achieved, and the parameter map for stability and bifurcation is developed. Illustration of the steady-state motions is presented for an understanding of rotational motions of the rotating blade.

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Topological Interlocking Materials

Architectured Materials in Nature and Engineering - Springer Series in Materials Science ◽

10.1007/978-3-030-11942-3_2 ◽

2019 ◽

pp. 23-49 ◽

Cited By ~ 3

Author(s):

A. V. Dyskin ◽

Yuri Estrin ◽

E. Pasternak

Keyword(s):

Topological Interlocking

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Study on the Stress-Stiffening Effect and Modal Synthesis Methods for the Dynamics of a Spatial Curved Beam

Journal of Applied Mechanics ◽

10.1115/1.4033515 ◽

2016 ◽

Vol 83 (8) ◽

Cited By ~ 3

Author(s):

Jianshu Zhang ◽

Xiaoting Rui ◽

Bo Li ◽

Gangli Chen

Keyword(s):

Small Deformation ◽

Dynamics Simulation ◽

Variation Principle ◽

Synthesis Methods ◽

Curved Beam ◽

The Finite Element Method ◽

High Rotational Speed ◽

Modal Synthesis ◽

Geometric Stiffening ◽

Stiffening Effect

In this paper, based on the nonlinear strain–deformation relationship, the dynamics equation of a spatial curved beam undergoing large displacement and small deformation is deduced using the finite-element method of floating frame of reference (FEMFFR) and Hamiltonian variation principle. The stress-stiffening effect, which is also called geometric stiffening effect, is accounted for in the dynamics equation, which makes it possible for the dynamics simulation of the spatial curved beam with high rotational speed. A numerical example is carried out by using the deduced dynamics equation to analyze the stress-stiffening effect of the curved beam and then verified by abaqus software. Then, the modal synthesis methods, which result in much fewer numbers of coordinates, are employed to improve the computational efficiency.

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Full Beam Formulation of a Rotating Beam-Mass System

Journal of Vibration and Acoustics ◽

10.1115/1.2930403 ◽

1994 ◽

Vol 116 (1) ◽

pp. 93-99 ◽

Cited By ~ 4

Author(s):

B. Fallahi ◽

S. H.-Y. Lai ◽

R. Gupta

Keyword(s):

Nonlinear Term ◽

Cross Coupling ◽

Automatic Generation ◽

Shape Functions ◽

Rotating Beam ◽

Mass System ◽

Computational Implementation ◽

Geometric Stiffening ◽

Rigid Body Motions ◽

Tip Mass

In this study a comprehensive approach for modeling flexibility for a beam with tip mass is presented. The method utilizes a Timoshenko beam with geometric stiffening. The element matrices are reported as the integral of the product of shape functions. This enhances their utility due to their generic form. They are utilized in a symbolic-based algorithm for the automatic generation of the element matrices. The time-dependent terms are factored after assembly for better computational implementation. The effect of speed and tip mass on cross coupling between the elastic and rigid body motions represented by Coriolis, normal and tangential accelerations is investigated. The nonlinear term (geometric stiffening) is modeled by introducing a tensor which plays the same role as element matrices for the linear terms. This led to formulation of the exact tangent matrix needed to solve the nonlinear differential equation.

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