Multi-axial strain-stiffening elastic potentials with energy bounds: explicit approach based on uniaxial data

Yu, Lidan; Jin, Tianfu; Yin, Zheng‐Nan; Xiao, Heng

doi:10.1007/s10483-015-1955-9

Cited by 8 publications

(3 citation statements)

References 37 publications

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“…Accordingly, the latter three may be independently chosen in separately fitting test data for the three benchmark modes. Results have been presented by means of rational functions (Zhang et al, 2013(Zhang et al, , 2014, spline functions (Li et al, 2014), polynomial interpolating functions (Wang et al, 2014) and others (Jin et al, 2015;Yu et al, 2015;Xiao et al, 2017).…”

Section: Discussionmentioning

confidence: 99%

“…e.g. Xiao, 2012Xiao, , 2015Zhang et al, 2013Zhang et al, , 2014Li et al, 2014;Wang et al, 2014;Gu et al, 2015;Jin et al, 2015;Yu et al, 2015;Cao et al, 2016;Xiao et al, 2017;Ding et al, 2019). In this contribution, toward a further purpose of accurately and automatically matching test data, a new technique will be introduced to combine piecewise linear splines into a single smooth function.…”

Section: Introductionmentioning

confidence: 99%

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Parameter-free strain-energy function which automatically and accurately matches benchmark test data for soft elastic solids

Xiao

Yan

Zhan

et al. 2022

MMMS

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PurposeA new and explicit form of the elastic strain-energy function for modeling large strain elastic responses of soft solids is constructed based on Hencky's logarithmic strain tensor.Design/methodology/approachWell-designed invariants of the Hencky strain are introduced for characterizing deformation modes and, furthermore, a new interpolating technique is proposed for combining piecewise splines into a single smooth function.FindingsWith this new form and this new technique, objectives in three respects may be achieved for the first time.Originality/valueFirst, no adjustable parameters need to be treated. Second, large strain responses for three benchmark modes are derivable in a decoupled sense without involving strongly nonlinear coupling effects. Finally, large strain data may be automatically and accurately matched for three benchmark modes, including uniaxial, equi-biaxial and plane-strain extension. Numerical examples are presented and compared with usual approaches.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parameter-free strain-energy function which automatically and accurately matches benchmark test data for soft elastic solids

Xiao

Yan

Zhan

et al. 2022

MMMS

Self Cite

View full text Add to dashboard Cite

show abstract

“…With these new forms of elastic potentials, simulation results (Li et al , 2014; Wang et al , 2014; Zhang et al , 2013, 2014) are derived by means of interpolating procedures with polynomials, rational functions and spline functions, separately, and compared with classic data in Treloar (1975), Jones and Treloar (1975), etc. ; further results (Gu et al , 2015; Yuan et al , 2015; Jin et al , 2015; Yu et al , 2015a, b) are obtained based on Hermite interpolating procedures; and, most recently, results are extended to large strain responses up to breaking (Cao et al , 2016; Xiao et al , 2017).…”

Section: Introductionmentioning

confidence: 99%

A unified simulation for effects of gellan polymer concentrations on large strain elastic behaviors of gellan gels

Ding

Zhan

et al. 2019

MMMS

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Purpose A direct and unified approach is proposed toward simultaneously simulating large strain elastic behaviors of gellan gels with different gellan polymer concentrations. The purpose of this paper is to construct an elastic potential with certain parameters of direct physical meanings, based on well-designed invariants of Hencky’s logarithmic strain. Design/methodology/approach For each given value of the concentration, the values of the parameters incorporated may be determined in the sense of achieving accurate agreement with large strain uniaxial extension and compression data. By means of a new interpolating technique, each parameter as a function of the concentration is then obtained from a given set of parameter values for certain concentration values. Findings Then, the effects of gellan polymer concentrations on large strain elastic behaviors of gellan gels are studied in demonstrating how each parameter relies on the concentration. Plane-strain (simple shear) responses are also presented for gellan gels with different polymer concentrations. Originality/value A direct, unified approach was proposed toward achieving a simultaneous simulation of large elastic strain behaviors of gellan gels for different gellan polymer concentrations. Each parameter incorporated in the proposed elastic potential will be derived as a function of the polymer concentration in an explicit form, in the very sense of simultaneously simulating large strain data for different concentrations.

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Hencky Strain and Logarithmic Rate for Unified Approach to Constitutive Modeling of Continua

Wang

Zhan

et al. 2019

Advanced Structured Materials

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Multi-axial strain-stiffening elastic potentials with energy bounds: explicit approach based on uniaxial data

Cited by 8 publications

References 37 publications

Parameter-free strain-energy function which automatically and accurately matches benchmark test data for soft elastic solids

Parameter-free strain-energy function which automatically and accurately matches benchmark test data for soft elastic solids

A unified simulation for effects of gellan polymer concentrations on large strain elastic behaviors of gellan gels

Hencky Strain and Logarithmic Rate for Unified Approach to Constitutive Modeling of Continua

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