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Evolution of Failure Mechanisms in Composite Shell Structures Using Different Models Read chapter Read first chapter

2018 | OriginalPaper | Chapter

A Micromorphic Damage-Plasticity Model to Counteract Mesh Dependence in Finite Element Simulations Involving Material Softening

Authors : Tim Brepols, Stephan Wulfinghoff, Stefanie Reese

Published in: Multiscale Modeling of Heterogeneous Structures

Publisher: Springer International Publishing

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Abstract

A gradient-extended damage-plasticity material model is presented which belongs to the class of micromophic media as proposed by Forest (J Eng Mech 135:117–131, 2009) [17]. A ‘two-surface’ formulation is utilized in which damage and plasticity are treated as independent but strongly coupled dissipative phenomena. To this end, separate yield and damage criteria as well as loading/unloading conditions are introduced. The model is thermodynamically consistent and accounts for both nonlinear kinematic and isotropic hardening as well as damage hardening. Various theoretical and numerical aspects of the formulation are discussed. Emphasis is also put on a procedure to enforce stress constraints at the local integration point level which provides, for instance, the basis for a straightforward integration of 3D gradient-extended material models into beam or shell elements or for their usage in 2D plane stress computations. A structural example problem illustrates the merits of the model and its ability to deliver mesh-independent results in coupled damage-plasticity finite element simulations.

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previous chapter Finite and Virtual Element Formulations for Large Strain Anisotropic Material with Inextensive Fibers
next chapter Modeling of Material Deformation Responses Using Gradient Elasticity Theory
Footnotes
1
\(\nabla ^{\text {s}}\left( \bullet \right) := \frac{1}{2} \left[ \left( \bullet \right) + \left( \bullet \right) ^{\text {T}} \right] \) denotes the symmetric part of a quantity \(\left( \bullet \right) \).
 
2
\(\left( \bullet \right) ^{\prime } := \left( \bullet \right) - \frac{1}{3}\,\text {trace}\left( \bullet \right) \,\mathbf {I}\) denotes the deviatoric part of a second-order tensor \(\left( \bullet \right) \).
 
3
In the following, if not explicitly denoted otherwise, any quantity is referred to time \(t_{n+1}=t_{n} + \varDelta t\).
 
4
The corresponding residuals in case of a purely elastoplastic step or elastic step with concurrently evolving damage are obtained by deleting either \(r_{3}\) or \(\mathbf {r}_{1}\) and \(r_{2}\) in (29), respectively.
 
5
Remember that, during the considered time interval, \(\varvec{\sigma }\) and D do additionally depend on the history variables at time \(t_{n}\) which are, however, constant within \([t_{n},\,t_{n+1}]\).
 
6
No extra symbols are introduced to avoid an excessive proliferation of notation. The change in meaning of the quantities is implicitly understood.
 
7
Quadrilateral elements are preferred in the meshing process, triangular ones are only used rarely as transitional elements.
 
8
The top and bottom values in the legends of the contour plots always indicate the corresponding minimum and maximum values attained in the computations.
 
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Metadata
Title
A Micromorphic Damage-Plasticity Model to Counteract Mesh Dependence in Finite Element Simulations Involving Material Softening
Authors
Tim Brepols
Stephan Wulfinghoff
Stefanie Reese
Copyright Year
2018
Book
Multiscale Modeling of Heterogeneous Structures

Print ISBN: 978-3-319-65462-1

Electronic ISBN: 978-3-319-65463-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-65463-8_12

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