The scaling of nonlinear structural dynamic systems

Davey, Keith; Atar, Muhammed; Sadeghi, Hamed; Darvizeh, Rooholamin

doi:10.1016/j.ijmecsci.2021.106631

Cited by 16 publications

(10 citation statements)

References 48 publications

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“…In this paper, the first-order finite similitude theory that its practicality was proven for different processes including impact mechanics, 21 fracture mechanics 22 and discrete vibrational systems 22–25 is used to find a solution for the open problem whether it is possible to mimic the physical behaviour of an impacted bi-material structure. By considering an impacted bi-material sandwich panel as the case study and conducting numerical experiments, the efficacy of the developed first-order scaling method, which for the first time enables us to simultaneously capture the scale effect of two different rate dependent materials, are examined.…”

Section: Introductionmentioning

confidence: 99%

“…21 The newly developed first-order finite similitude theory which provides us with more independent degrees of freedom and enables us to simultaneously fix two different parameters which they have same unit is the only available scaling method which can be employed to deal with the scale effect of rate dependent plastic behaviour represented by different parts of an impacted bi-material structure. 21 In this paper, the first-order finite similitude theory that its practicality was proven for different processes including impact mechanics, 21 fracture mechanics 22 and discrete vibrational systems [22][23][24][25] is used to find a solution for the open problem whether it is possible to mimic the physical behaviour of an impacted bimaterial structure. By considering an impacted bi-material sandwich panel as the case study and conducting numerical experiments, the efficacy of the developed first-order scaling method, which for the first time enables us to simultaneously capture the scale effect of two different rate dependent materials, are examined.…”

Section: Introductionmentioning

confidence: 99%

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Scaling of bi-material sandwich panels subjected to impact loadings

Al-Tamimi

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Scaling is a widely used concept in impact and explosion engineering which is mainly utilized to predict the response behaviour of large-scale mechanical structures by conducting experiments on scaled trial models. However, the practical application of currently available conventional scaling methodologies for impact and explosive processes are significantly restricted by their inability to properly capture the scale effects of strain rate and strain hardening. Also, they are suffering from an insufficient number of independent degrees of freedom. Furthermore, the zeroth-order finite similitude theory, which can annihilate the non-scalability of rate and hardening effects, doesn’t provide us with efficient scaling methods when the investigated structure is made out of different materials. More precisely, the zeroth-order finite similitude theory and the classical dimensional analysis, which are suffering from a limited number of independent degrees of freedom, cannot scale the elastic-plastic behaviour represented by different parts of a structure made out of different materials. In other words, classical scaling methodologies including dimensional analysis and even the zeroth-order finite similitude theory cannot fix two different features having the same unit using different degrees of freedom, which make them useless for structures made of more than one material such as bi-material sandwich panels. In the presented paper, a new scaling methodology is developed based on the recently proposed first-order finite similitude theory which for the first time enables us to capture the rate dependent plastic behaviour of an impacted structure made out of two different materials. A sandwich panel made of two different materials which is subjected to an impact loading is considered as the case study in order to investigate the efficiency of the proposed first-order based scaling technique. The numerical results are determined using Abaqus finite element software in which the Johnson-Cook constitutive equation is utilized to take into account the rate and hardening effects on the initial yield stress. The results reveal that the behaviour of impacted full-scale bi-material sandwich panels can be predicted with a high accuracy when the extra degree of freedom provided us with the first-order finite similitude (i.e. R1) is set to vary between −1 and 1 (i.e. [Formula: see text]). Furthermore, it is found that the pure mechanical and thermo-mechanical behaviour of the impacted core honeycomb are highly accurately predicted using scaled-down trial models which are made from dissimilar materials and designed based on the zeroth-order finite similitude theory.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scaling of bi-material sandwich panels subjected to impact loadings

Al-Tamimi

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…To overcome these deficiencies, the higher-order finite similitude theory is developed. [41][42][43][44][45][46][47][48][49][50][51][52] The higherorder theory, which on the contrary of the zeroth-order theory contains more than one scaled experiment, links the information of several scaled experiments at distinct scales to provide more independent degrees of freedom. The first-order finite similitude theory provides one more independent degree of freedom compared to conventional scaling methods and even the zeroth-order theory.…”

Section: Introductionmentioning

confidence: 99%

An experimental investigation into finite similitude for concrete structures

Momeni,

Alijani,

Rad

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Currently, available conventional scaling methodologies are suffering from many deficiencies, which the most important ones can be listed as: (i) the inability to systematically capture the different material properties of full- and small-scale models, (ii) the inability to simultaneously fix two parameters having the same unit, and (iii) a limited number of independent degrees of freedom. To overcome these issues, a new theory called finite similitude has recently been developed. This paper aims to employ the recently introduced finite similitude theory for the scaled analysis of concrete structures. By conducting static three-point bending test on concrete beams at distinct scales, it is revealed that the response behavior of the prototype can be predicted to a good accuracy using small-scale trial models. Scaled-down models are designed based on the zeroth-order finite similitude theory and made from same and different granulations than the prototype. Also, the developed zeroth-order based scaling methodology enables us to experiment scaled-down plaster-rock structures rather than concrete structures. It is found that small-scale plaster-rock models, which can be prepared in much less time and at a lower cost, predict both local and global response behavior of the full-scale concrete structure with a high accuracy. Moreover, using the first-order finite similitude theory to take into account the elastic behavior and considering the scaled-down plaster-rock models as the second trial models, predictions of small-scale concrete models from the local response behavior of the full-scale model are significantly enhanced.

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“…It is worth mentioning that it was employed to scale different problems including impact, 17,[41][42][43][44] biomechanics, 5,45 powder compaction, 46 and metal forming. 47 Also, the finite similitude theory was recently extended to contain more than one scaled model providing us with more degrees of freedom 48,49 and extended to enable us to anisotropically scale the geometry. 50 It was found that the scaling methods developed based on the finite similitude theory can deal with pure dimensional scaling and, also simultaneously, dimensional/material scaling.…”

Section: Introductionmentioning

confidence: 99%

A scaled framework for analysis of crack propagation in teeth using equivalent inorganic materials

Khoei

Darvizeh

Sadeghi

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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Experimental investigations of teeth are significantly impeded with the main impediments being small dimensions involved and ethical issues associated with in vivo testing. On the other hand, numerical simulations which can be used as an alternative method have their own inherent limitations which are being reliant on constitutive and boundary information, and also numerical predictions should be validated with experimental findings. Hence, it is necessarily required that experimental tests are conducted on equivalent models which should inevitably be made out of different materials. However, there is not any known method to predict the crack propagation and fracture behavior of structures using equivalent models made from different materials. The present paper aims to propose a scaling method based on the finite similitude theory which has recently been appeared in open literatures to investigate the crack propagation and fracture behavior of teeth in which different materials can even be used for scaled models. The effectiveness of the developed scaling method is examined using the Abaqus finite element software by employing the J-integral, cohesive zone model (CZM) and extended finite element method (XFEM). By conducting the compressive numerical experiments, it is revealed although the exact prediction of the behavior of a tooth using equivalent models made out of inorganic materials is impossible, it can be anticipated to a good accuracy. Also, the response characteristics of the tooth subjected to a cyclic loading which can be imposed during the act of chewing are anticipated to a good accuracy using the scaled up trial model made out of zirconia which demonstrates the high capability of the proposed method in practical applications.

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The scaling of nonlinear structural dynamic systems

Cited by 16 publications

References 48 publications

Scaling of bi-material sandwich panels subjected to impact loadings

Scaling of bi-material sandwich panels subjected to impact loadings

An experimental investigation into finite similitude for concrete structures

A scaled framework for analysis of crack propagation in teeth using equivalent inorganic materials

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