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Lagrange and H(curl, B) based Finite Element formulations for the relaxed micromorphic model [article]

Jörg Schröder, Mohammad Sarhil, Lisa Scheunemann, Patrizio Neff
2021 arXiv   pre-print
These are a nodal standard formulation H^1( B) × H^1( B) and a nodal-edge formulation H^1( B) × H(curl, B), where the latter employs the Nédélec space.  ...  In this contribution, we present the significant aspects related to the relaxed micromorphic model realization with the finite element method.  ...  The authors gratefully acknowledge Jože Korelc for the development and ongoing support when using AceGen and AceFEM.  ... 
arXiv:2112.00382v1 fatcat:m7bx77zhnjgizjx63zlttw4xqu

A hybrid $$ H ^1\times H (\mathrm {curl})$$ finite element formulation for a relaxed micromorphic continuum model of antiplane shear

Adam Sky, Michael Neunteufel, Ingo Münch, Joachim Schöberl, Patrizio Neff
2021 Computational Mechanics  
This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations  ...  Our approach is to use base functions stemming from both Hilbert spaces $$ H ^1$$ H 1 and $$ H (\mathrm {curl})$$ H ( curl ) , demonstrating the central role of such combinations for this class of problems  ...  Funding Open Access funding enabled and organized by Projekt DEAL.  ... 
doi:10.1007/s00466-021-02002-8 fatcat:4q4klmnvw5flxcs3jje6edf73i

A hybrid H1xH(curl) finite element formulation for a relaxed micromorphic continuum model of antiplane shear [article]

Adam Sky, Michael Neunteufel, Ingo Münch, Joachim Schoeberl, Patrizio Neff
2021 arXiv   pre-print
This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations  ...  Our approach is to use base functions stemming from both Hilbert spaces H1 and H(curl), demonstrating the central role of such combinations for this class of problems.  ...  Neff acknowledges support in the framework of the DFG Priority Programme 2256 Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials Neff 902/10-1, No: 440935806.  ... 
arXiv:2009.13397v4 fatcat:wy3arq5nuvhl5bo42dvsh4zqum

Primal and mixed finite element formulations for the relaxed micromorphic model [article]

Adam Sky, Michael Neunteufel, Ingo Muench, Joachim Schöberl, Patrizio Neff
2022 arXiv   pre-print
Therefore, the natural spaces of the fields are [𝐻^1]^3 for the displacement and [𝐻(curl)]^3 for the microdistortion, leading to unusual finite element formulations.  ...  Further, we explore the numerical behaviour of the relaxed micromorphic model for both a primal and a mixed formulation.  ...  section existence and uniqueness of the weak formulation of the relaxed micromorphic continuum for both a primal and a mixed method is discussed.  ... 
arXiv:2202.08715v1 fatcat:6edx37xrsjb4lhoaaatfudicry

Identification of scale-independent material parameters in the relaxed micromorphic model through model-adapted first order homogenization [article]

Patrizio Neff , Angela Madeo Universität Siegen,
2019 arXiv   pre-print
We rigorously determine the scale-independent short range elastic parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure.  ...  We explain our idea of "maximal" stiffness of the unit-cell and use state of the art first order numerical homogenization methods to obtain the needed parameters for a given tetragonal unit-cell.  ...  The authors are also indebted to Lev Truskinovsky (ESPCI, Paris) for pertinent remarks which helped improve the paper.  ... 
arXiv:1909.13624v1 fatcat:tlkqsn26trboxnungzejmxxazu

A unifying perspective: the relaxed linear micromorphic continuum

Patrizio Neff, Ionel-Dumitrel Ghiba, Angela Madeo, Luca Placidi, Giuseppe Rosi
2013 Continuum Mechanics and Thermodynamics  
The new relaxed micromorphic model supports well-posedness results for the dynamic and static case.  ...  We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor.  ...  This can be done by introducing the so-called micro-structured or micromorphic continuum models, which are suitably formulated by means of a postulation process based on the principle of least action (  ... 
doi:10.1007/s00161-013-0322-9 fatcat:sk75tk6blzgg5m3dmt2asfplei

A variant of the linear isotropic indeterminate couple stress model with symmetric local force-stress, symmetric nonlocal force-stress, symmetric couple-stresses and complete traction boundary conditions [article]

Ionel-Dumitrel Ghiba and Patrizio Neff and Angela Madeo and Ingo Münch
2015 arXiv   pre-print
For this model we prove the existence of solutions for the equilibrium problem.  ...  Relations with other gradient elastic theories and the possibility to switch from a 4th order (gradient elastic) problem to a 2nd order micromorphic model are also discussed with a view of obtaining symmetric  ...  Acknowledgement We are grateful to Ali Reza Hadjesfandiari and Gary F. Dargush for sending us the paper [45] prior to publication. Discussions with X.L. Gao and S.  ... 
arXiv:1504.00868v1 fatcat:utspktbcqzf4zhgdhubbkmjhvi

D 2.3 Crystal plasticity

Vikram Phalke, Samuel Forest, Hyung-Jun Chang
2020 Zenodo  
The extension of classical continuum crystal plasticity to predict size effects called strain gradient crystal plasticity framework (reduced-order micromorphic and augmented Lagrangian SGP approach) is  ...  The objective of the present deliverable is to give an overview of the crystal plasticity framework and its industrial context.  ...  The strain gradient model based on the curl of the displacement gradient (curlH ∼ p ), which is a quantification of GNDs and subsequently takes account into the extra hardening due to strain gradients  ... 
doi:10.5281/zenodo.3884274 fatcat:vheqvltmdfbq5i5ca2u7r5dtqy

Continuum thermomechanics of nonlinear micromorphic, strain and stress gradient media

Samuel Forest
2020 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
It reconciles most existing frameworks and proposes some new extensions for micromorphic and strain gradient media.  ...  Finally, the stress gradient continuum theory emerges as a new research field for which an elastic-viscoplastic theory at finite deformations is provided for the first time.  ...  This model is also called relaxed micromorphic model in [54] .  ... 
doi:10.1098/rsta.2019.0169 pmid:32223410 fatcat:vowrn6jpkva5ng6vzsvsgkgitu

Crystal Plasticity with Micromorphic Regularization in Assessing Scale Dependent Deformation of Polycrystalline Doped Copper Alloys

Matti Lindroos, Tom Andersson, Jarkko Metsäjoki, Anssi Laukkanen
2021 Crystals  
The findings can be utilized to provide an improved basis for modeling the viscoplastic deformation behavior of the studied copper alloy and to assess the microstructural origins of any integrity concerns  ...  The reduced micromorphic crystal plasticity model, which is similar to strain gradient models, is used in this investigation. Firstly, the model's size dependent plasticity effects are evaluated.  ...  Acknowledgments: Samuel Forest from MINES ParisTech is acknowledged for discussions related to the modeling framework. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/cryst11080994 fatcat:xhh7dmbxkndo3n3nvnevp4rbfa

Dynamic problems for metamaterials: Review of existing models and ideas for further research

Dionisio Del Vescovo, Ivan Giorgio
2014 International Journal of Engineering Science  
The capability of continuum theories to describe the time evolution and the deformation of the micro-structure of complex mechanical systems was recognised in the very first formulations of continuum mechanics  ...  This paper is based on a really simple idea: construct a bridge between two different cultural environments which address the same relevant problems.  ...  The authors thank Francesco dell'Isola and Angelo Luongo for interesting discussions on the topics presented here, and Luca Placidi for his friendly criticism.  ... 
doi:10.1016/j.ijengsci.2014.02.022 fatcat:d2gdx5bnpfd6bltlmbq6kylrxm

Generalized Continuum Modelling of Crystal Plasticity [chapter]

Samuel Forest
2012 Generalized Continua and Dislocation Theory  
where the brackets denote ensemble averaging. The next correlation function then is :  ...  The constraint (208) can be strictly enforced if H χ is treated as a Lagrange multiplier in the variational formulation Tian-Hu (2004) .  ...  As expected, the finite element response is significantly harder for the smallest grain size.  ... 
doi:10.1007/978-3-7091-1222-9_3 fatcat:ldupgiicrffk7a25eqzdbj2k7m

Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture [article]

Jendrik Voss, Robert J. Martin, Oliver Sander, Siddhant Kumar, Dennis M. Kochmann, Patrizio Neff
2022 arXiv   pre-print
Here, we discuss a number of numerical approaches that can be used in the search for a counterexample to the quasiconvexity of a given function W.  ...  In a previous contribution, we have shown that quasiconvexity of this function would imply quasiconvexity for all rank-one convex isotropic planar energies W:GL^+(2)→ℝ with an additive volumetric-isochoric  ...  For this, we discretize the displacement field ϑ by Lagrange finite elements [16] . We use triangle grids and first-order finite elements only.  ... 
arXiv:2201.06392v1 fatcat:paubupulubgobeymzllqb5g27i

Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy [article]

Peter Lewintan and Stefan Müller and Patrizio Neff
2020 arXiv   pre-print
Let Ω⊂ℝ^3 be an open and bounded set with Lipschitz boundary and outward unit normal ν. For 11 if p = 3/2.  ...  Here, dev X := X -1/3tr(X) 1 denotes the deviatoric (trace-free) part of a 3 × 3 matrix X and the boundary condition is understood in a suitable weak sense.  ...  Acknowledgment The authors thank Ionel-Dumitrel Ghiba, University of Iasi, Romania, for helpful discussions. This work was initiated in the framework of the Priority Programme  ... 
arXiv:2011.10573v2 fatcat:aihvzf5nk5dznitghpj6c7w7wi

Continuum mechanics with torsion

Ilya Peshkov, Evgeniy Romenski, Michael Dumbser
2019 Continuum Mechanics and Thermodynamics  
in general and to studying and modeling turbulence in particular.  ...  Thus, in order to account for the rotational degrees of freedom of the irregular dynamics of small scale vortexes, we further generalize our unified first-order hyperbolic formulation of continuum fluid  ...  Acknowledgement The authors are thankful to A. Golovnev for the discussions of concepts of teleparallel gravity theories.  ... 
doi:10.1007/s00161-019-00770-6 fatcat:c6on5t5ysfcblhls3wmu5z6qka
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