An energy-based approach for modelling the behaviour of packaging material during processing

2004 ◽  
Vol 218 (1) ◽  
pp. 105-118 ◽  
Author(s):  
B J Hicks ◽  
C Berry ◽  
G Mullineux ◽  
C J McPherson ◽  
A J Medl
Keyword(s):  
Theoretical Model ◽  
Minimum Energy ◽  
Packaging Material ◽  
Parametric Models ◽  
Machine Material ◽  
Software Model ◽  
Energy Principles ◽  
Improved Methods ◽  
Material Interaction ◽  
Modelling Approach

This paper deals with the investigation of improved methods for considering machine-material interaction during the design and production of packaging machinery. Minimum energy principles are used to create a theoretical model of the response of the packaging material during processing. The complex non-linear properties of the packaging material are encapsulated in parametric models generated through analysis of the physical measurement of the changing properties during processing. These two techniques are incorporated into a software model that represents the behaviour of a skillet during the erection process. This software model considers the material, the pack design and the machine system. The overall modelling approach is validated by comparison with a physical system, which shows a good correlation with the theoretical model.

scholarly journals Minimum energy bounds on longitudinal elastic constants of transversely isotropic unidirectional composites

2020 ◽  
Vol 476 (2239) ◽  
pp. 20190752
Author(s):  
Duc-Chinh pham
Keyword(s):  
Elastic Constants ◽  
Minimum Energy ◽  
Young Modulus ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Arithmetic Average ◽  
Energy Bounds ◽  
Cylindrical Phase ◽  
Elastic Composites ◽  
Energy Principles

We consider the n -component transversely isotropic unidirectional elastic composites, the longitudinal axis of which is parallel to those of the transversely isotropic components as well as the generators of the cylindrical phase boundaries between them. From the minimum energy and complementary energy principles, with appropriate constant strain and piece-wise constant stress trial fields, optimization and iteration techniques, a set of bounds for the macroscopic (effective) longitudinal elastic constants of the composites (including the simple lower arithmetic average estimate for longitudinal Young modulus E eff  ≥  E V ) are constructed. Numerical examples are provided to illustrate the obtained results.

scholarly journals Bounding of Flow and Transport Analysis in Heterogeneous Saturated Porous Media: A Minimum Energy Dissipation Principle for the Bounding and Scale-Up

Hydrology ◽  
2019 ◽  
Vol 6 (2) ◽  
pp. 33 ◽  
Author(s):  
Nelson ◽  
Williams
Keyword(s):  
Porous Media ◽  
Energy Dissipation ◽  
Heterogeneous System ◽  
Minimum Energy ◽  
Scale Up ◽  
Heterogeneous Porous Media ◽  
Porous Media Flow ◽  
Rotational Flow ◽  
Energy Principles

We apply minimum kinetic energy principles from classic mechanics to heterogeneous porous media flow equations to derive and evaluate rotational flow components to determine bounding homogenous representations. Kelvin characterized irrotational motions in terms of energy dissipation and showed that minimum dynamic energy dissipation occurs if the motion is irrotational; i.e., a homogeneous flow system. For porous media flow, reductions in rotational flow represent heterogeneity reductions. At the limit, a homogeneous system, flow is irrotational. Using these principles, we can find a homogenous system that bounds a more complex heterogeneous system. We present mathematics for using the minimum energy principle to describe flow in heterogeneous porous media along with reduced special cases with the necessary bounding and associated scale-up equations. The first, simple derivation involves no boundary differences and gives results based on direct Kelvin-type minimum energy principles. It provides bounding criteria, but yields only a single ultimate scale-up. We present an extended derivation that considers differing boundaries, which may occur between scale-up elements. This approach enables a piecewise less heterogeneous representation to bound the more heterogeneous system. It provides scale-up flexibility for individual model elements with differing sizes, and shapes and supports a more accurate representation of material properties. We include a case study to illustrate bounding with a single direct scale-up. The case study demonstrates rigorous bounding and provides insight on using bounding flow to help understand heterogeneous systems. This work provides a theoretical basis for developing bounding models of flow systems. This provides a means to justify bounding conditions and results.

Central burst defect analysis of the wire-drawing process using an accumulated damage parameter

2001 ◽  
Vol 215 (11) ◽  
pp. 1313-1319 ◽  
Author(s):  
P Phelan ◽  
J Brandon ◽  
M Hillery
Keyword(s):  
Theoretical Model ◽  
Wire Drawing ◽  
Damage Parameter ◽  
Theoretical Studies ◽  
Drawing Process ◽  
Defect Analysis ◽  
Material Instability ◽  
Accumulated Damage ◽  
Experimental And Theoretical Studies ◽  
Modelling Approach

The paper reviews the theoretical and empirical basis for predicting central burst defects in wire drawing under varying die semi-angle conditions. These are used to develop a numerical modelling approach, which results in an accumulated damage criterion to predict material instability. The predictions from the resulting theoretical model are consistent with previous experimental and theoretical studies in the literature.

scholarly journals Three-point correlation bounds on the effective bulk modulus of isotropic multicomponent materials

2012 ◽  
Vol 34 (2) ◽  
pp. 66-77
Author(s):  
Pham Duc Chinh ◽  
Vu Lam Dong
Keyword(s):  
Bulk Modulus ◽  
Minimum Energy ◽  
Previous Approach ◽  
Effective Bulk Modulus ◽  
Point Correlation ◽  
Energy Principles ◽  
Multicomponent Materials

Three-point correlation bounds based on minimum energy principles are constructed to give estimates on the effective elastic bulk modulus of disordered multi-component materials. The constructed trial fields are extensions of Hashin-Shtrikman polarization ones used in our previous approach and lead to tighter bounds. Some examples of applications are presented.

scholarly journals Numerical Modelling of the Mechanical Behaviour of Biaxial Weft-Knitted Fabrics on Different Length Scales

Materials ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 3693 ◽  
Author(s):  
Pham ◽  
Döbrich ◽  
Trümper ◽  
Gereke ◽  
Cherif
Keyword(s):  
Computational Cost ◽  
Parametric Models ◽  
Element Formulation ◽  
Knitted Fabrics ◽  
Macro Scale ◽  
Complex Shapes ◽  
Scale Modelling ◽  
Forming Characteristics ◽  
Meso Scale ◽  
Modelling Approach

Weft-knitted fabrics offer an excellent formability into complex shapes for composite application. In biaxial weft-knitted fabric, additional yarns are inserted in the warp (wale-wise) and weft (course-wise) directions as a reinforcement. Due to these straight yarns, the mechanical properties of such fabrics are better than those of unreinforced weft-knitted fabrics. The forming process of flat fabrics into 3D preforms is challenging and requires numerical simulation. In this paper, the mechanical behavior of biaxial weft-knitted fabrics is simulated by means of macro- and meso-scale finite element method (FEM) models. The macro-scale modelling approach is based on a shell element formulation and offers reasonable computational costs but has some limitations by the description of fabric mechanical characteristics and forming behavior. The meso-scale modelling approach based on beam elements can describe the fabric’s mechanical and forming characteristics better at a higher computational cost. The FEM models were validated by comparing the results of various simulations with the equivalent experiments. With the help of the parametric models, the forming of biaxial weft-knitted fabrics into complex shapes can be simulated. These models help to predict material and process parameters for optimized forming conditions without the necessity of costly experimental trials.

Bifurcation and Catastrophes in Metal-Cutting Processes

1998 ◽  
Vol 120 (4) ◽  
pp. 817-820 ◽  
Author(s):  
Hanmin Shi ◽  
Xibing Wang ◽  
Tao Lu
Keyword(s):  
Theoretical Model ◽  
Metal Cutting ◽  
Minimum Energy ◽  
Cutting Process ◽  
Cutting Processes

Based on a theoretical model and the Principle of Minimum Energy [1, 2, 3] the bifurcation and catastrophes in a non-free cutting process are theoretically predicted and experimentally verified. The phenomena lead to the complexity of a cutting process with very strong non-linearity and may be the source of the difficulties in its control.

scholarly journals The structure of the attitudes toward religion as measured by the Post-Critical Belief Scale: A structural modelling approach

2021 ◽  
Author(s):  
Piotr Szydłowski ◽  
Radosław Rogoza ◽  
Jan Cieciuch
Keyword(s):  
Structural Equation Modeling ◽  
Theoretical Model ◽  
Factor Structure ◽  
Structural Equation ◽  
Measurement Precision ◽  
Equation Modeling ◽  
Structural Modelling ◽  
Factor Solution ◽  
Belief Scale ◽  
Modelling Approach

AbstractThis paper investigates the structure of the Post-Critical Belief Scale (PCBS), which was designed by Hutsebaut (1996) to assess attitudes towards religion according to Wulff’s (1991) model. Existing results suggest ambiguous solutions, with two, three, or four factors, when only the four-factor solution is consistent with Wulff’s theoretical model. In the current study, we examined whether this hypothesized model indeed would be reflected in the data, when the more appropriate, newly-developed, Set-Exploratory Structural Equation modeling (Set-ESEM) is applied. The study was carried out on a sample of 952 participants. The results of the Set-ESEM modeling provided evidence for the good fit of the four-factor structure. Nevertheless, we also identified some shortcomings of the measure and identified items which may be removed in order to increase measurement precision.

Tunable Postbuckling Systems of Bi-Walled Nonuniform Beams

2020 ◽  
Author(s):  
Talal Salem ◽  
Pengcheng Jiao ◽  
Hamed Bolandi ◽  
Nizar Lajnef
Keyword(s):  
Theoretical Model ◽  
Minimum Energy ◽  
Axial Loading ◽  
Small Deformation ◽  
Structural Instability ◽  
Postbuckling Behavior ◽  
Response Curves ◽  
Total Potential ◽  
Proposed Model ◽  
Parametric Studies

Abstract Structural instability, in particular postbuckling resulted in predefined constraints, has been performing advantages in many applications given their promising mechanical characteristics. However, inadequate studies have been conducted to effectively control and tune the postbuckling behavior of bilaterally constrained nonuniform beams. This study develops postbuckling systems comprised of multiple nonuniform beams subjected to bilateral confinements. Theoretical model is developed using Euler-Bernoulli theory and small deformation assumptions to predict postbuckling response of the beam systems under quasi-static axial loading. To locate the minimum energy path of the deformed beam system, the minimization problem of total potential energies of the bi-walled beam systems is solved by Nelder-Mead algorithm. Snap-through transitions of buckled systems are shown by drops in the response curves. To validate the developed model with existing models in literature, the model was simplified to account for single uniform beam under displacement control. The proposed model is experimentally and numerically validated, and satisfactory agreements are obtained. Parametric studies are carried out to investigate the influence of varying the geometric parameters (i.e., length, thickness) of the nonuniform beams on the tunable systems. Using the presented theoretical model, the postbuckling events can be accurately controlled by the geometry properties of the nonuniform beams.

Linear correlates in the speech signal: Consequences of the specific use of an acoustic tube?

1998 ◽  
Vol 21 (2) ◽  
pp. 261-262 ◽  
Author(s):  
René Carré
Keyword(s):  
Theoretical Model ◽  
Speech Signal ◽  
Minimum Energy ◽  
Locus Equation ◽  
Model Based ◽  
Proposed Model

The debate on the origin of the locus equation is circular. In this commentary the locus equation is obtained by way of a theoretical model based on acoustics without recourse to articulatory knowledge or perceptual constraints. The proposed model is driven by criteria of minimum energy and maximum simplicity.

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