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

According to the well-known models for rubberlike elasticity with strain- stii~ening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi...

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Published inApplied mathematics and mechanics Vol. 36; no. 7; pp. 883 - 894
Main Authors Yu, Lidan, Jin, Tianfu, Yin, Zhengnan, Xiao, Heng
Format Journal Article
LanguageEnglish
Published Shanghai Shanghai University 01.07.2015
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, China
Subjects
Applications of Mathematics
Classical Mechanics
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
单轴
多轴向
应变硬化
弹性
测试数据
生长应力
硬化效应
能源
multi-axial potential
O34
O138
strain-stiffening effect
rubberlike elasticity
74B15
strain limit
energy bound
uniaxial data
O33
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Summary:According to the well-known models for rubberlike elasticity with strain- stii~ening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi-axial elastic potentials directly from the uniaxial potentials. Then, a new multi-axial potential is presented to characterize the strain-stiffening effect by prescribing suitable forms of uniaxia] potentials so that the strain energy is always bounded as the stress grows to infinity. Numerical examples show good agreement with a number of test data.
Bibliography:rubberlike elasticity, strain limit, strain-stiffening effect, energy bound,uniaxial data, multi-axial potential
31-1650/O1
According to the well-known models for rubberlike elasticity with strain- stii~ening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi-axial elastic potentials directly from the uniaxial potentials. Then, a new multi-axial potential is presented to characterize the strain-stiffening effect by prescribing suitable forms of uniaxia] potentials so that the strain energy is always bounded as the stress grows to infinity. Numerical examples show good agreement with a number of test data.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-015-1955-9