On the applicability and stress update formulations for corotational stress rate hypoelasticity constitutive models

Zhou, Xiangmin; Tamma, Kumar K.

doi:10.1016/s0168-874x(03)00059-3

Cited by 26 publications

(13 citation statements)

References 49 publications

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“…It is remarkable that all stress components, not only for the logarithmic rate, but also for the Cotter-Rivlin and Truesdell rates, return to the stress-free state at the end of cycle, while the behaviour of some stress components in these models are different. It is seen, that the components 33 for the Truesdell rate and 11 , 22 and 12 for the Cotter-Rivlin are zero, while these are noticeable for the logarithmic model. This result demonstrates again, that a non-integrable model may show no residual stress at the end of a closed deformation path.…”

Section: Example 3: Stress Response Of the Closed Deformation Pathmentioning

confidence: 89%

“…In these figures, stress components of 11 , 22 and 12 are expressed in normalized form ( /G, where G is the shear modulus). The analytical results are represented by the large symbols and the numerical results are shown by solid curves and small symbols.…”

Section: Example1: Simple Shear Deformationmentioning

confidence: 99%

“…4. For isothermal and isotropic processes, the Clausius-Duhem inequality based on the 2nd law of thermodynamics is satisfied [22].…”

Section: Introductionmentioning

confidence: 99%

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Finite element study of the energy dissipation and residual stresses in the closed elastic deformation path

Abbasi

Parsa

2006

Int. J. Numer. Meth. Engng

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SUMMARYIn this paper, energy dissipation and residual stress developments are numerically studied in threedimensional closed deformation paths. Different objective stress rates coded in a finite element program are compared.In order to update the stresses, implicit integration algorithm based on mid-point rule for corotational and non-corotational objective rates is used. Several corotational objective rates such as Jaumann, Green-Naghdi, Eulerian and Lagrangian triad-based rates and non-corotational rates such as Truesdell and Cotter-Rivlin rates are considered.It is shown in this work that in some cases also a non-integrable model may exhibit no dissipation energy at the end of a closed deformation path.This study underlines some results previously obtained by other researchers, i.e. among all considered stress rates the logarithmic rate manifests the best result in respect of elasticity requirements.

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Section: Example 3: Stress Response Of the Closed Deformation Pathmentioning

confidence: 89%

Section: Example1: Simple Shear Deformationmentioning

confidence: 99%

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Finite element study of the energy dissipation and residual stresses in the closed elastic deformation path

Abbasi

Parsa

2006

Int. J. Numer. Meth. Engng

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“…However, each of the corotational rates is proper for certain types of materials and one cannot pick them arbitrarily. Moreover, using the corotational rates result in some computational issues such as the Jaumann rate creates peculiar oscillations in shear stress response, and the Green-Naghdi and other rates have been reported to result in residual stress (Meyers et al, 2003;Zhou and Tamma, 2003). One way to handle this issue is hiring the stresses and strains that are defined in the natural state (material configuration), because such stress and strain fields are quantified in the same way by different observers.…”

Section: Large Deformation Generalizationmentioning

confidence: 99%

Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

Tehrani¹

2013

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Lightweight advanced materials are critical in the manufacturing of many Army vehicles. Recently, numerical tools have been utilized to customize experiments to achieve optimized behavior of micro/nano polymer composites (MNPCs). Most numerical studies are based on characterizing the MNPCs through simple microstructures, as circular particles or straight fibers embedded in a specific polymer matrix. Although these geometries are effective in virtually modeling some types of composite material behavior, they fail to address some critical key Names of Under Graduate students supportedPERCENT_SUPPORTED NAME FTE Equivalent:Total Number:The number of undergraduates funded by this agreement who graduated during this period with a degree in science, mathematics, engineering, or technology fields:The number of undergraduates funded by your agreement who graduated during this period and will continue to pursue a graduate or Ph.D. degree in science, mathematics, engineering, or technology fields:Number of graduating undergraduates who achieved a 3.5 GPA to 4.0 (4.0 max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education, Research and Engineering:The number of undergraduates funded by your agreement who graduated during this period and intend to work for the Department of DefenseThe number of undergraduates funded by your agreement who graduated during this period and will receive scholarships or fellowships for further studies in science, mathematics, engineering or technology fields: Student Metrics This section only applies to graduating undergraduates supported by this agreement in this reporting periodThe number of undergraduates funded by this agreement who graduated during this period: 0.00 ...... Names of Personnel receiving masters degrees Inventions (DD882) Scientific ProgressBecause the mechanical responses of polymers and many types of polymer composites are in the large deformation range, the Eulerian or Lagrangian concept is required for measuring the stress and strain. On the other hand, developing a large deformation based constitutive model requires a number of considerations, and should be performed from a thermodynamics point of view to study the motion of each component of the material. Even though such approach is precise and physically sound, it is limited to just one type of material. Furthermore, polymers show high dependency to the rate and time of the applied load; hence, employing viscoelastic, viscoplastic and viscodamage models is necessary. To address these issues, a consistent framework is developed to generalize elastic/viscoelastic and plastic/viscoplastic models from small strain to the large deformation range. The developed continuum based app...

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“…They proposed a modified Logarithmic rate (known as the Kinetic logarithmic rate) to correct this problem and showed the equivalence of multiplicative hyperelastic-plastic and additive hypoelastic-plastic material models. Further discussion on the Logarithmic rate is found from the works of Xiao et al (1998), Chen (2002), Xiao et al (2006), Zhou and Tamma (2003), Freed (2014), and Naumenko and Altenbach (2018).…”

Section: Objective Stress Ratementioning

confidence: 99%

Isogeometric shell analysis of incremental sheet forming

Hokkanen¹

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This thesis investigates the applicability and beneficiality of isogeometric analysis to the incremental sheet forming simulations. Incremental sheet forming (ISF) is a manufacturing process for sheet metals where the final shape is obtained incrementally using a blunt moving tool. ISF is a relatively slow process but does not need precise and expensive dies (which require a long lead time) in contrast to many other sheet forming processes. This makes it ideal for rapid prototyping, customized parts, and

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On the applicability and stress update formulations for corotational stress rate hypoelasticity constitutive models

Cited by 26 publications

References 49 publications

Finite element study of the energy dissipation and residual stresses in the closed elastic deformation path

Finite element study of the energy dissipation and residual stresses in the closed elastic deformation path

Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

Isogeometric shell analysis of incremental sheet forming

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