Finite Third-Order Gradient Elastoplasticity and Thermoplasticity

Reiher, Jörg Christian; Bertram, Albrecht

doi:10.1007/s10659-019-09736-w

Cited by 7 publications

(4 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some outlooks based on current research include, for example, 1. The higher order gradient elastoplasticity theory [32] and its numerical implementation.…”

Section: Discussionmentioning

confidence: 99%

A nonlocal operator method for finite deformation higher-order gradient elasticity

Ren

Zhuang

Nguyen-Thoi

et al. 2021

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the higher-order gradient solid along with boundary conditions of various orders are derived from a variational principle using integration by parts on the surface. The objectivity of the energy functional is achieved by carefully selecting the invariants under rigid-body transformation. The third-order gradient solid theory includes more than 10.000 material parameters. However, under certain simplifications, the material parameters can be greatly reduced; down to 3. With this simplified formulation, we develop a nonlocal operator method and apply it to several numerical examples. The numerical analysis shows that the high gradient solid theory exhibits a stiffer response compared to a 'conventional' hyperelastic solid. The numerical tests also demonstrate the capability of the nonlocal operator method in solving higher-order physical problems.

show abstract

“…Some outlooks based on current research include, for example, 1. The higher order gradient elastoplasticity theory [32] and its numerical implementation.…”

Section: Discussionmentioning

confidence: 99%

A nonlocal operator method for finite deformation higher-order gradient elasticity

Ren

Zhuang

Nguyen-Thoi

et al. 2021

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…We discuss materials with up to third gradients. Such materials have been studied, e.g., in [13][14][15].…”

Section: Boundary Conditions Derived From the Principle Of Virtual Powermentioning

confidence: 99%

Surface phenomena of gradient materials

Krawietz¹

2021

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

The behavior of third gradient materials is analyzed. They possess stress tensor fields of second, third and fourth order. Starting from the principle of virtual power, we derive the admissible boundary conditions. Those on free surfaces can only be obtained by the application of the divergence theorem of surfaces. On the other hand, such an application to fictitious internal cuts makes no sense although it is usually practiced. We prove that some of the boundary conditions on a free surface may be interpreted as the equilibrium conditions of a shell. So a crust shell exists on such a surface and a beam exists where patches of the surface meet. On the other hand, no such shells or beams can be found with fictitious surfaces in the interior of a continuum. Our finding does not depend on any specific constitutive assumption.

show abstract

“…In order to properly introduce the topic of the workshop to such a varied audience, the first day was devoted to three general introductory lectures. Albrecht Bertram, in his talk (''On the second and third order non-linear gradient theory''), has discussed the structure of second-and third-order nonlinear gradient theories in large deformation regimes [1][2][3][4][5]. In his contribution, fundamental issues arising during the generalization of classical theories of elasticity have been addressed.…”

Section: Topics Of the Workhop And Plenary Lecturesmentioning

confidence: 99%

Workshop on Encounter of the third kind on Generalized continua and microstructures in Arpino, 3–7 April 2018: A review of presentations and discussions

Laudato

Angelo

2019

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

The present article is a rational report of the workshop Encounter of the third kind on Generalized continua and microstructures (Arpino, 3–7 April 2018). The main goal of the workshop was to gather together experts in the framework of generalized continuum theories and microstructured materials to discuss and analyse the recent advancements in the field. The interested reader will find in this article a general discussion of the motivations and of the main topics discussed during the workshop as well as a detailed report of the talks and the relative bibliography. All the talks have been recorded and it is possible to watch them on the M&MOCS YouTube channel at https://www.youtube.com/playlist?list=PLWzlK5oO41smkt5HtiDQJV7nsbz5wnD01

show abstract

Finite Third-Order Gradient Elastoplasticity and Thermoplasticity

Cited by 7 publications

References 25 publications

A nonlocal operator method for finite deformation higher-order gradient elasticity

A nonlocal operator method for finite deformation higher-order gradient elasticity

Surface phenomena of gradient materials

Workshop on Encounter of the third kind on Generalized continua and microstructures in Arpino, 3–7 April 2018: A review of presentations and discussions

Contact Info

Product

Resources

About