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Cannizzo A, Giordano S. Thermal effects on fracture and the brittle-to-ductile transition. Phys Rev E 2023; 107:035001. [PMID: 37073030 DOI: 10.1103/physreve.107.035001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
The fracture behavior of brittle and ductile materials can be strongly influenced by thermal fluctuations, especially in micro- and nanodevices as well as in rubberlike and biological materials. However, temperature effects, in particular on the brittle-to-ductile transition, still require a deeper theoretical investigation. As a step in this direction we propose a theory, based on equilibrium statistical mechanics, able to describe the temperature-dependent brittle fracture and brittle-to-ductile transition in prototypical discrete systems consisting in a lattice with breakable elements. Concerning the brittle behavior, we obtain closed form expressions for the temperature-dependent fracture stress and strain, representing a generalized Griffith criterion, ultimately describing the fracture as a genuine phase transition. With regard to the brittle-to-ductile transition, we obtain a complex critical scenario characterized by a threshold temperature between the two fracture regimes (brittle and ductile), an upper and a lower yield strength, and a critical temperature corresponding to the complete breakdown. To show the effectiveness of the proposed models in describing thermal fracture behaviors at small scales, we successfully compare our theoretical results with molecular dynamics simulations of Si and GaN nanowires.
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Affiliation(s)
- Andrea Cannizzo
- Univ. Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520, Institut d'Électronique de Microélectronique et de Nanotechnologie (IEMN), F-59000 Lille, France
- Politecnico di Bari, (DMMM) Dipartimento di Meccanica, Matematica e Management, Via Re David 200, I-70125 Bari, Italy
| | - Stefano Giordano
- Univ. Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, UMR 8520, Institut d'Électronique de Microélectronique et de Nanotechnologie (IEMN), F-59000 Lille, France
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2
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Ehret AE, Stracuzzi A. Variations on Ogden's model: close and distant relatives. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210322. [PMID: 36031841 PMCID: PMC9421379 DOI: 10.1098/rsta.2021.0322] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
The power law in terms of stretch, the truncated series representation and the Valanis-Landel hypothesis are distinguished features of Ogden's strain-energy density function. While they represent a set of special constitutive choices, they have also been shown recently to allow a particular molecular statistical interpretation of the model, where each of these ingredients can be associated with a step in the development of the strain-energy density of the polymer network from the statistical mechanics of long-chain molecules. The schematic of this perspective brings us into a position to vary these steps individually. By this means, Ogden's theory can be embedded in a certain family of models within the large class of isotropic hyperelastic materials, whose members can be identified as close and distant 'relatives'. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.
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Affiliation(s)
- A. E. Ehret
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092 Zürich, Switzerland
| | - A. Stracuzzi
- Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
- ETH Zurich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092 Zürich, Switzerland
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3
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Anssari-Benam A, Destrade M, Saccomandi G. Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models †. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210325. [PMID: 36031829 PMCID: PMC9421377 DOI: 10.1098/rsta.2021.0325] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
The Ogden model is often considered as a standard model in the literature for application to the deformation of brain tissue. Here, we show that, in some of those applications, the use of the Ogden model leads to the non-convexity of the strain-energy function and mis-prediction of the correct concavity of the experimental stress-stretch curves over a range of the deformation domain. By contrast, we propose a family of models which provides a favourable fit to the considered datasets while remaining free from the highlighted shortcomings of the Ogden model. While, as we discuss, those shortcomings might be due to the artefacts of the testing protocols, the proposed family of models proves impervious to such artefacts. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.
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Affiliation(s)
- Afshin Anssari-Benam
- Cardiovascular Engineering Research Lab (CERL), School of Mechanical and Design Engineering, University of Portsmouth, Anglesea Road, Portsmouth PO1 3DJ, UK
| | - Michel Destrade
- School of Mathematical and Statistical Sciences, NUI Galway, University Road, Galway, Ireland
- Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province and Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Giuseppe Saccomandi
- School of Mathematical and Statistical Sciences, NUI Galway, University Road, Galway, Ireland
- Dipartimento di Ingegneria, Università degli studi di Perugia, Via G. Duranti, Perugia 06125, Italy
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4
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Saccomandi G, Vergori L, Zanetti EM. Linear, weakly nonlinear and fully nonlinear models for soft tissues: which ones provide the most reliable estimations of the stiffness? PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210321. [PMID: 36031840 DOI: 10.1098/rsta.2021.0321] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Accepted: 04/06/2022] [Indexed: 06/15/2023]
Abstract
Benign and malignant lesions in tissues or organs can be detected by elastographic investigations in which pathological regions are spotted from local alterations of the stiffness. As is known, the shear modulus provides a measure of the stiffness of an elastic material. Based on the classical theory of linear elasticity, an elastogram yields estimations of the linear shear modulus from measurements of the speed of small-amplitude transverse waves propagating in the medium tested. In this paper, we show that the estimation of the shear modulus can be improved significantly by employing the fourth-order weakly nonlinear theory of elasticity (FOE), and indicate how the stiffness can be assessed more precisely with the use of FOE. We discuss also why FOE provides more reliable results than the fully nonlinear theory of elasticity. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.
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Affiliation(s)
- G Saccomandi
- Dipartimento di Ingegneria, Università degli Studi di Perugia,06125 Perugia, Italy
| | - L Vergori
- Dipartimento di Ingegneria, Università degli Studi di Perugia,06125 Perugia, Italy
| | - E M Zanetti
- Dipartimento di Ingegneria, Università degli Studi di Perugia,06125 Perugia, Italy
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5
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Modelling the rate-dependency of the mechanical behaviour of the aortic heart valve: An experimentally guided theoretical framework. J Mech Behav Biomed Mater 2022; 134:105341. [DOI: 10.1016/j.jmbbm.2022.105341] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 04/30/2022] [Accepted: 06/26/2022] [Indexed: 11/19/2022]
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6
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Hou J, Lu X, Zhang K, Jing Y, Zhang Z, You J, Li Q. Parameters Identification of Rubber-like Hyperelastic Material Based on General Regression Neural Network. MATERIALS 2022; 15:ma15113776. [PMID: 35683072 PMCID: PMC9181827 DOI: 10.3390/ma15113776] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 05/19/2022] [Accepted: 05/23/2022] [Indexed: 01/24/2023]
Abstract
In this study, we present a systematic scheme to identify the material parameters in constitutive model of hyperelastic materials such as rubber. This approach is proposed based on the combined use of general regression neural network, experimental data and finite element analysis. In detail, the finite element analysis is carried out to provide the learning samples of GRNN model, while the results observed from the uniaxial tensile test is set as the target value of GRNN model. A problem involving parameters identification of silicone rubber material is described for validation. The results show that the proposed GRNN-based approach has the characteristics of high universality and good precision, and can be extended to parameters identification of complex rubber-like hyperelastic material constitutive.
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Affiliation(s)
- Junling Hou
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China; (J.H.); (X.L.); (K.Z.); (Z.Z.)
- Research Institute of Xi’an Jiaotong University, Hangzhou 311215, China
- Xi’an Jiaotong University Suzhou Institute, Suzhou 215123, China
| | - Xuan Lu
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China; (J.H.); (X.L.); (K.Z.); (Z.Z.)
| | - Kaining Zhang
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China; (J.H.); (X.L.); (K.Z.); (Z.Z.)
| | - Yidong Jing
- Xi’an Modern Chemistry Research Institute, Xi’an 710065, China;
| | - Zhenjie Zhang
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China; (J.H.); (X.L.); (K.Z.); (Z.Z.)
| | - Junfeng You
- The 41st Institute of the Forth Academy of CASC, Xi’an 710025, China;
- Solid Rocket Motor National Key Laboratory of Combustion Flow and Thermo-Structure, Xi’an 710025, China
| | - Qun Li
- State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an 710049, China; (J.H.); (X.L.); (K.Z.); (Z.Z.)
- Correspondence:
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Anssari-Benam A, Horgan CO. New results in the theory of plane strain flexure of incompressible isotropic hyperelastic materials. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0773] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
New results on the classical problem of bending by end moments for incompressible isotropic hyperelastic materials within the framework of nonlinear elasticity are investigated and presented in this paper. The particular results of concern here include (i) the adaptation of Rivlin's standard analysis to the case where
one end
of the beam is
fixed
and the other end is subjected to a bending moment; and (ii) results on the finite bending of (infinitesimally)
thin
isotropic hyperelastic plates which are valid for
large deformations
, extending the classical results from the linear elasticity theory which are restricted to small deformations. An interesting feature observed in this context is that a flexed thin plate develops an oscillatory surface along the circular arc near the free end, due to local (small)
deviations
of the radius of curvature. A potential application to the bending of a biological soft tissue, namely the aortic valve leaflet, is briefly described by way of an example. Finally, some new results are obtained for finite bending of hyperelastic materials that exhibit limiting chain extensibility at the molecular level and involve constraints on the deformation. The amount of bending that such materials can sustain is limited by the constraint. On using a limiting chain extensibility model, closed-form solutions for the Cauchy stress components, the bending moment and the normal out-of-plane force required to sustain the bending deformation are derived.
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Affiliation(s)
- Afshin Anssari-Benam
- Cardiovascular Engineering Research Lab (CERL), School of Mechanical and Design Engineering, University of Portsmouth, Anglesea Road, Portsmouth PO1 3DJ, UK
| | - Cornelius O. Horgan
- School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22904, USA
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Snoeijer JH, Pandey A, Herrada MA, Eggers J. The relationship between viscoelasticity and elasticity. Proc Math Phys Eng Sci 2020; 476:20200419. [PMID: 33363441 PMCID: PMC7735292 DOI: 10.1098/rspa.2020.0419] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Accepted: 10/14/2020] [Indexed: 12/17/2022] Open
Abstract
Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ, over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.
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Affiliation(s)
- J H Snoeijer
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
| | - A Pandey
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
| | - M A Herrada
- Depto. de Mecánica de Fluidos e Ingeniería Aeroespacial, Universidad de Sevilla, 41092 Sevilla, Spain
| | - J Eggers
- School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK
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Destrade M, Murphy J, Saccomandi G. Rivlin's legacy in continuum mechanics and applied mathematics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2019; 377:20190090. [PMID: 30879418 PMCID: PMC6452037 DOI: 10.1098/rsta.2019.0090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Affiliation(s)
- Michel Destrade
- School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland
- e-mail:
| | - Jeremiah Murphy
- School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland
- Department of Engineering, Dublin City University, Dublin, Ireland
| | - Giuseppe Saccomandi
- School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland
- Dipartimento di Ingegneria, Università degli studi di Perugia, 06125 Perugia, Italy
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10
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Kmiecik B, Łabowska M, Detyna J. Determination of the difference between two complex polymer models simulating the behaviour of biological structures. Biocybern Biomed Eng 2019. [DOI: 10.1016/j.bbe.2019.04.001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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11
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Direct and inverse identification of constitutive parameters from the structure of soft tissues. Part 1: micro- and nanostructure of collagen fibers. Biomech Model Mechanobiol 2018; 17:1011-1036. [DOI: 10.1007/s10237-018-1009-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2017] [Accepted: 02/13/2018] [Indexed: 12/17/2022]
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12
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Orakdogen N, Boyacı T. Non-Gaussian elasticity and charge density-dependent swelling of strong polyelectrolyte poly(N-isopropylacrylamide-co-sodium acrylate) hydrogels. SOFT MATTER 2017; 13:9046-9059. [PMID: 29177310 DOI: 10.1039/c7sm01866e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The mechanical properties and charge density-dependent swelling of strong polyelectrolyte poly(N-isopropylacrylamide-co-sodium acrylate) P(NIPA-co-NaA) hydrogels prepared at a fixed total monomer concentration and crosslinker ratio, but at various charge densities, i.e. NaA content in the feed between 0 and 90 mol%, were investigated. The elasticity results were discussed to explain the relationship between the elastic free energy ΔGel and the swelling ratio α as well as to fit the existing theories to the swelling data. The implications of the obtained results for the deviation from the Gaussian chain statistics were considered. Given the swollen elastic modulus and the dependence of charge density on the equilibrium gel volume, it would seem that the latter factor is an important determinant of non-Gaussian elasticity of polyelectrolyte P(NIPA-co-NaA) hydrogels containing strongly dissociated groups. The dependence of the reduced modulus on the equilibrium gel volume was found to be Gr ≈ (Veq)-0.47 at low swelling degree and Gr ≈ (Veq)0.64 at high swelling degree and the deviation was interpreted as the non-Gaussian elasticity of equilibrium swollen P(NIPA-co-NaA) hydrogels. The detailed theoretical treatments of non-Gaussian elasticity of P(NIPA-co-NaA) hydrogels and, in particular, the influence of the charge density on the elasticity showed that the knowledge of several swollen state parameters and the effective charge density distribution of hydrogels were strongly required to explain the variation of the elastic properties depending on the ionic group content. Within this framework, the dominant mechanism responsible for the deviation from Gaussian elasticity and the finite chain extensibility of ionic P(NIPA-co-NaA) hydrogels was described and the results were used to explain the dependence of the elastic modulus on the equilibrium gel volume.
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Affiliation(s)
- Nermin Orakdogen
- Department of Chemistry, Soft Materials Research Laboratory, Istanbul Technical University, Istanbul, Maslak 34469, Turkey.
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Mihai LA, Goriely A. How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity. Proc Math Phys Eng Sci 2017; 473:20170607. [PMID: 29225507 PMCID: PMC5719638 DOI: 10.1098/rspa.2017.0607] [Citation(s) in RCA: 89] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Accepted: 11/03/2017] [Indexed: 01/22/2023] Open
Abstract
The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.
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Affiliation(s)
- L Angela Mihai
- School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK
| | - Alain Goriely
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK
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Computationally Informed Design of a Multi-Axial Actuated Microfluidic Chip Device. Sci Rep 2017; 7:5489. [PMID: 28710359 PMCID: PMC5511244 DOI: 10.1038/s41598-017-05237-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Accepted: 05/25/2017] [Indexed: 12/02/2022] Open
Abstract
This paper describes the computationally informed design and experimental validation of a microfluidic chip device with multi-axial stretching capabilities. The device, based on PDMS soft-lithography, consisted of a thin porous membrane, mounted between two fluidic compartments, and tensioned via a set of vacuum-driven actuators. A finite element analysis solver implementing a set of different nonlinear elastic and hyperelastic material models was used to drive the design and optimization of chip geometry and to investigate the resulting deformation patterns under multi-axial loading. Computational results were cross-validated by experimental testing of prototypal devices featuring the in silico optimized geometry. The proposed methodology represents a suite of computationally handy simulation tools that might find application in the design and in silico mechanical characterization of a wide range of stretchable microfluidic devices.
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Destrade M, Saccomandi G, Sgura I. Methodical fitting for mathematical models of rubber-like materials. Proc Math Phys Eng Sci 2017. [DOI: 10.1098/rspa.2016.0811] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
A great variety of models can describe the nonlinear response of rubber to uniaxial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three steps, which we delineate by relying on a simple formatting of the data, the so-called Mooney plot transform. First, the small-to-moderate regime, where the polymeric chains unfold easily and the Mooney plot is almost linear. Second, the strain-hardening regime, where blobs of bundled chains unfold to stiffen the response in correspondence to the ‘upturn’ of the Mooney plot. Third, the limiting-chain regime, with a sharp stiffening occurring as the chains extend towards their limit. We provide strain-energy functions with terms accounting for each stage that (i) give an accurate local and then global fitting of the data; (ii) are consistent with weak nonlinear elasticity theory and (iii) can be interpreted in the framework of statistical mechanics. We apply our method to Treloar's classical experimental data and also to some more recent data. Our method not only provides models that describe the experimental data with a very low quantitative relative error, but also shows that the theory of nonlinear elasticity is much more robust that seemed at first sight.
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Affiliation(s)
- Michel Destrade
- School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland
| | - Giuseppe Saccomandi
- School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland
- Dipartimento di Ingegneria, Università degli Studi di Perugia, Via G. Duranti, Perugia 06125, Italy
| | - Ivonne Sgura
- Dipartimento di Matematica e Fisica ‘E. De Giorgi’, Università del Salento, Via per Arnesano, 73100 Lecce, Italy
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16
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Mechanical characterization of biological tissues: Experimental methods based on mathematical modeling. Biomed Eng Lett 2016. [DOI: 10.1007/s13534-016-0222-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022] Open
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17
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Material parameters identification and experimental validation of damage models for rubberlike materials. Eur Polym J 2016. [DOI: 10.1016/j.eurpolymj.2016.03.036] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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