A note on the use of the additive decomposition of the strain tensor in finite deformation inelasticity

Eterovic, Adrian Luis; Bathe, Klaus‐Jürgen

doi:10.1016/0045-7825(91)90114-l

Cited by 13 publications

(8 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(9), which, with the above, yields (31) This expresses the objective rate of the left Cauchy-Green deformation tensor as a linear function of the rate of deformation tensor d, leading to the following hypoelastic form of the proposed model:…”

Section: Rate Form Hyperelasticitymentioning

confidence: 99%

“…As a result of unconditional integrability, the model returns a hyperelastic response which relates the Kirchhoff stress to the Hencky (logarithmic) strain in its integrated form. Based on experimental observations, [15] has been shown to be suitable for moderate elastic deformations of ductile metals [30][31][32]. General integrability conditions for hypoelasticity based on the logarithmic (D) rate with a stress dependent hypoelasticity tensor H(T) have been derived further by Xiao et al [26].…”

Section: Oxmentioning

confidence: 99%

“…[28][29][30][31][32][33][34][35][36] and references therein). In this approach, the stress is updated through a specified strain energy function on either the current or the original configuration while the fiow rule for the inelastic part of the deformation is specified in rate form on the original or on an intermediate configuration.…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part I: Rate-Form Hyperelasticity

Eshraghi

Papoulia

Jahed

2013

Journal of Applied Mechanics

View full text Add to dashboard Cite

An integrable Eulerian rate formulation of finite deformation elasticity is developed, which relates the Jaumann or other objective corotational rate of the Kirchhoff stress with material spin to the same rate of the left Cauchy-Green deformation measure through a deformation dependent constitutive tensor. The proposed constitutive relationship can be written in terms of the rate of deformation tensor in the form of a hypoelastic material model. Integrability conditions, under which the proposed formulation yields (a) a Cauchy elastic and (b) a Green elastic material model are derived for the isotropic case. These determine the deformation dependent instantaneous elasticity tensor of the material. In particular, when the Cauchy integrability criterion is applied to the stressstrain relationship of a hyperelastic material model, an Eulerian rate formulation of hyperelasticity is obtained. This formulation proves crucial for the Eulerian finite strain elastoplastic model developed in part II of this work. The proposed model is formulated and integrated in the fixed background and extends the notion of an integrable hypoelastic model to arbitrary corotational objective rates and coordinates. Integrability was previously shown for the grade-zero hypoelastic model with use of the logarithmic (D) rate, the spin of which is formulated in principal coordinates. Uniform deformation examples of rectilinear shear, closed path four-step loading, and cyclic elliptical loading are presented. Contrary to classical grade-zero hypoelasticity, no shear oscillation, elastic dissipation, or ratcheting under cyclic load is observed when the simple Zaremba-Jaumann rate of stress is employed.

show abstract

Section: Rate Form Hyperelasticitymentioning

confidence: 99%

Section: Oxmentioning

confidence: 99%

See 1 more Smart Citation

Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part I: Rate-Form Hyperelasticity

Eshraghi

Papoulia

Jahed

2013

Journal of Applied Mechanics

View full text Add to dashboard Cite

show abstract

“…In this framework, called hyperelastoplascity, the finite elastoplastic deformations are described by means of a multiplicative gradient decomposition ( [6][7][8][9][10]). In general, for elastoplastic materials under finite strains, the additive decomposition of the strain tensor, called Green-Naghdi decomposition [11], is not valid (see the work of [12] for further details). In this regime, the multiplicative decomposition, called Kröner-Lee decomposition [13,14], is more suitable and well-accepted.…”

Section: Introductionmentioning

confidence: 99%

Large deformation analysis of functionally graded elastoplastic materials via solid tetrahedral finite elements

Pascon¹,

Coda

2015

Computers & Structures

View full text Add to dashboard Cite

“…Following the method of the principal axes (see for example Reinhardt and Dubey [41], Hill [42], and Eterovic and Bathe [43]), the symmetric and skew-symmetric parts of the equation (22-1) give the following relations for the diagonalized plastic stretch tensor and its corresponding Lagrangian spin:…”

Section: -Proposed Constitutive Model Of Elastoplasticitymentioning

confidence: 99%

A Lagrangian model for hardening behaviour of materials at finite deformation based on the right plastic stretch tensor

Eshraghi

Jahed

Lambert

2010

Materials & Design (1980-2015)

View full text Add to dashboard Cite

A note on the use of the additive decomposition of the strain tensor in finite deformation inelasticity

Cited by 13 publications

References 2 publications

Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part I: Rate-Form Hyperelasticity

Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part I: Rate-Form Hyperelasticity

Large deformation analysis of functionally graded elastoplastic materials via solid tetrahedral finite elements

A Lagrangian model for hardening behaviour of materials at finite deformation based on the right plastic stretch tensor

Contact Info

Product

Resources

About