Time rates of generalized strain tensors Part II: Approximate basis-free formulas

Scheidler, Michael J.

doi:10.1016/0167-6636(91)90003-i

Cited by 9 publications

(5 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Kirchhoff stress τ is conjugate to the strain measure log V [112,113,214,215,134,179,208,257], where V = √ F F T is the left stretch tensor, i.e. τ, d dt log V = det V · σ, D is equal to the power per unit volume element in the reference configuration.…”

Section: Scope Of Investigationmentioning

confidence: 99%

The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity

Neff

Ghiba

Lankeit

2015

J Elast

126

View full text Add to dashboard Cite

We investigate a family of isotropic volumetric-isochoric decoupled strain energiesbased on the Hencky-logarithmic (true, natural) strain tensor log U , where µ > 0 is the infinitesimal shear modulus, κ = 2µ+3λ 3 > 0 is the infinitesimal bulk modulus with λ the first Lamé constant, k, k are dimensionless parameters, F = ∇ϕ is the gradient of deformation, U = √ F T F is the right stretch tensor and devn log U = log U − 1 n tr(log U ) • 1 1 is the deviatoric part of the strain tensor log U . For small elastic strains, W eH approximates the classical quadratic Hencky strain energywhich is not everywhere rank-one convex. In plane elastostatics, i.e. n = 2, we prove the everywhere rankone convexity of the proposed family W eH , for k ≥ 1 4 and k ≥ 1 8 . Moreover, we show that the corresponding Cauchy (true)-stress-true-strain relation is invertible for n = 2, 3 and we show the monotonicity of the Cauchy (true) stress tensor as a function of the true strain tensor in a domain of bounded distortions. We also prove that the rank-one convexity of the energies belonging to the family W eH is not preserved in dimension n = 3 and that the energiesare not rank-one convex.

show abstract

Section: Scope Of Investigationmentioning

confidence: 99%

The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity

Neff

Ghiba

Lankeit

2015

J Elast

126

View full text Add to dashboard Cite

show abstract

“…Therefore, the metric strain rates are much simpler to calculate than the rates of the stretch family (16) which remain complicate in spite of the many attempts to simplify them (Hill, 1978;Fitzgerald, 1980;Ball, 1984;Hoger and Carlson, 1984a,b;Carlson and Hoger, 1986;Guo, 1984;Curnier and Rakotomanana, 1991;Scheidler, 1991;Man and Guo, 1993;Xiao et al, 1998b;Guan-Suo et al, 1999;Rosati, 2000).…”

Section: Metric Strain Ratementioning

confidence: 96%

A family of metric strains and conjugate stresses, prolonging usual material laws from small to large transformations

Curnier

Zysset

2006

International Journal of Solids and Structures

View full text Add to dashboard Cite

A new family of simple generalized strains and conjugate stresses based on the material metric (right Cauchy-Green) tensor is proposed. It includes an interesting quasilinear pair. It is a close approximation of the Seth-Hill family, with the advantage of being easier to calculate. It extends the realm of application of the classical theories of linear elasticity and perfect plasticity from small to large transformations for isotropic and anisotropic materials without any modification.

show abstract

“…For a specific strain tensor e ( f ) , first e ( f ′ ) and the characteristic invariant a f 1 of e ( f ) should be determined by use of (114) and (24). Then the scalar invariant a, which is dependent on a f 1 , can be calculated appropriately.…”

Section: Basis-free Expression In the Case Of Double-coalescent Princmentioning

confidence: 99%

“…The corotational rates are those that can be defined in rotating frames specified by their own spin tensors. Gurtin and Spear [5], Dubey [1], Scheidler [23,24], and Xiao et al [29] have derived some expressions for the objective corotational rates of Eulerian kinematic tensors, specially the unified basis-free expression for an arbitrary objective corotational rate of the general Eulerian strain measures has been derived by Xiao et al [29].…”

mentioning

confidence: 99%

“…Hence, some authors have been attracted to derive expressions for them during the past decades. In the context of providing expressions for the material time derivative or material time rate of kinematic tensors, specially the material time rate of strain measures, the works of Hill [10,11], Gurtin and Spear [5], Guo [6], Guo and Dubey [7], Hoger and Carlson [13], Hoger [12], Mehrabadi and Nemat-Nasser [17], Guo et al [8], Scheidler [23,24], Wang and Duan [26], Man and Guo [16], Naghdabadi et al [19], Xiao [27,29] and Dui et al [2,3] can be mentioned.…”

mentioning

confidence: 99%

See 1 more Smart Citation

On The Objective Corotational Rates of Eulerian Strain Measures

Asghari

Naghdabadi

2008

J Elasticity

View full text Add to dashboard Cite

show abstract

Time rates of generalized strain tensors Part II: Approximate basis-free formulas

Cited by 9 publications

References 3 publications

The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity

The Exponentiated Hencky-Logarithmic Strain Energy. Part I: Constitutive Issues and Rank-One Convexity

A family of metric strains and conjugate stresses, prolonging usual material laws from small to large transformations

On The Objective Corotational Rates of Eulerian Strain Measures

Contact Info

Product

Resources

About