A general and efficient multistart algorithm for the detection of loss of ellipticity in elastoplastic structures

Autor: Samuel Forest, Moubine Al Kotob, Matthieu Mazière, Tonya Rose, Christelle Combescure
Přispěvatelé: Centre des Matériaux (MAT), Centre National de la Recherche Scientifique (CNRS)-PSL Research University (PSL)-MINES ParisTech - École nationale supérieure des mines de Paris, Safran Tech, Laboratoire de Modélisation et Simulation Multi Echelle (MSME), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Paris-Est Marne-la-Vallée (UPEM), MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Modélisation et Simulation Multi-Echelle (MSME), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Mines Paris - PSL (École nationale supérieure des mines de Paris)
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Unit sphere
Imagination
Discretization
Computer science
media_common.quotation_subject
02 engineering and technology
[SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph]
Numerical method
[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]
01 natural sciences
Search engine
0203 mechanical engineering
[SPI.MECA.MEMA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph]
0101 mathematics
media_common
Numerical Analysis
Applied Mathematics
Numerical analysis
Elastoplasticity
General Engineering
Forming processes
Torsion (mechanics)
[SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]
Finite deformation
Finite element method
[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph]
010101 applied mathematics
020303 mechanical engineering & transports
Loss of ellipticty
Strain localization
Algorithm
Zdroj: International Journal for Numerical Methods in Engineering
International Journal for Numerical Methods in Engineering, Wiley, 2019, ⟨10.1002/nme.6247⟩
ISSN: 0029-5981
1097-0207
DOI: 10.1002/nme.6247⟩
Popis: International audience; The present paper proposes a new efficient and robust algorithm for evaluating the loss of ellipticity criterion. While commonly used in two-dimensional models for thin metal sheet forming processes, it is rarely evaluated in three-dimensional structures due to the computational cost. The proposed algorithm is based on a Newton-Raphson scheme and a multisampling optimization method based on a discretization method of the half unit sphere. First the new process is compared to the existing methods in the literature and then it is applied to a structural problem, namely tubes in torsion. The evolution of the loss of ellipticity in these structures is analyzed leading to conclusions about the failure of the structure. Meanwhile, the stability of the discretized problem is analyzed in order to better understand the loss of regularity of the finite element method problem. These results are then used to predict the failure of an experimentally tested torsion sample. K E Y W O R D S elastoplasticity, finite deformation, loss of ellipticty, numerical method, strain localization 1 INTRODUCTION Even though strain localization is one of the most critical phenomena leading to the failure of elasto-plastic structures, its emergence is still not fully understood. Indeed, the term "localization" itself is interpreted differently depending on the context. In a loose sense, localization means the development of high strains in a narrow region of the body, like in a shear band with through thickness necking in a thin plate in tension. A more precise definition is the emergence of strain rate discontinuities through surfaces usually associated with loss of ellipticity, and we use this latter definition in the present work. In some situations, both definitions may even coincide, for instance, a one-dimensional bar displaying a softening behavior experiences simultaneously necking and loss of ellipticity, 1,2 or in thin plates modeled under plane stress conditions. 3 However, these definitions do not coincide for three-dimensional (3D) models in general. When localization starts in complex structures and whether it leads to catastrophic failure is still an open problem in many situations , especially when certifying industrial components. The example of tubes loaded in torsion, 1 shows that even an apparently simple structure can lead to difficulties in defining localization and the localization's influence on the safety of the global structure. When dealing with localization, a first distinction needs to be made between types of loss of ellipticity. Strong ellipticity corresponds to definite positiveness of the eigenvalues of the symmetrized acoustic tensor whereas ellipticity refers to the absence of vanishing eigenvalue of the general acoustic tensor. 4,5 Int J Numer Methods Eng. 2019;1-25. wileyonlinelibrary.com/journal/nme
Databáze: OpenAIRE
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