Quasicontinuum Method Combined with Anisotropic Microplane Model

2017 ◽  
Vol 1144 ◽  
pp. 142-147 ◽  
Author(s):  
Karel Mikeš ◽  
Milan Jirásek
Keyword(s):  
Constitutive Relations ◽  
Material Model ◽  
Multiscale Simulation ◽  
Particle Systems ◽  
Particle Model ◽  
Material Microstructure ◽  
Microplane Model ◽  
Quasicontinuum Method ◽  
Elastic Links ◽  
Different Types

The quasicontinuum method (QC) is a multiscale simulation technique used in computational mechanics. The QC combines fast continuum and exact atomistic approaches. In the present work, the QC idea is applied to particle systems with elastic links representing the material microstructure. The material model based on the idea of microplanes is used to provide a continuous representation of microstructure. In the microplane model, the constitutive relations are defined on planes with various orientations and the macroscopic stress is obtained by integration over all possible directions of microplanes. But this approach do not work well in combination with the QC approach if the microplane orientations are assumed to be uniformly distributed. Therefore, an anisotropic version of the microplane model, which takes into account the specific directions of individual links, is proposed and implemented in finite element solver OOFEM. Accuracy and specific properties of QC-inspired approaches with different types of microplane models are evaluated by comparison with the fully resolved particle model.

Witnessing pairing correlations in identical-particle systems

2021 ◽  
Vol 21 (15&16) ◽  
pp. 1307-1319
Author(s):  
Cagan Aksak ◽  
Sadi Turgut
Keyword(s):  
Annihilation Operator ◽  
Identical Particle ◽  
Quantum Correlations ◽  
Particle Systems ◽  
Fermionic Systems ◽  
Different Types ◽  
Pairing Correlations

Quantum correlations and entanglement in identical-particle systems have been a puzzling question which has attracted vast interest and widely different approaches. Witness formalism developed first for entanglement measurement can be adopted to other kind of correlations. An approach is introduced by Kraus \emph{et al.}, [Phys. Rev. A \textbf{79}, 012306 (2009)] based on pairing correlations in fermionic systems and the use of witness formalism to detect pairing. In this contribution, a two-particle-annihilation operator is used for constructing a two-particle observable as a candidate witness for pairing correlations of both fermionic and bosonic systems. The corresponding separability bounds are also obtained. Two different types of separability definition are introduced for bosonic systems and the separability bounds associated with each type are discussed.

scholarly journals Identification of Fractional Damping Parameters in Structural Dynamics Using Polynomial Chaos Expansion

2021 ◽  
Vol 2 (4) ◽  
pp. 956-975
Author(s):  
Marcel S. Prem ◽  
Michael Klanner ◽  
Katrin Ellermann
Keyword(s):  
Polynomial Chaos ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Material Model ◽  
Polynomial Chaos Expansion ◽  
Computational Technique ◽  
Chaos Expansion ◽  
Material Damping ◽  
Fractional Damping ◽  
Assembly Technique

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.

Evolutive Laws and Constitutive Relations in Nonlocal Viscoplasticity

2012 ◽  
Vol 152-154 ◽  
pp. 990-996 ◽  
Author(s):  
Fabio de Angelis
Keyword(s):  
Constitutive Relations ◽  
Material Model ◽  
Standard Material ◽  
Viscoplastic Model ◽  
Proposed Model

In the present work the evolutive laws and the constitutive relations for a model of nonlocal viscoplasticity are analyzed. Nonlocal dissipative variables and suitable regularization operators are adopted. The proposed model is developed within the framework of the generalized standard material model. Suitable forms of the elastic and dissipative viscoplastic potentials are defined and the associated constitutive relations are specialized. The evolutive laws for the proposed nonlocal viscoplastic model are presented in a general form which can be suitably specialized in order to include different models of nonlocal viscoplasticity.

Microplane Model for Fracturing Damage of Triaxially Braided Fiber-Polymer Composites

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Ferhun C. Caner ◽  
Zdeněk P. Bažant ◽  
Christian G. Hoover ◽  
Anthony M. Waas ◽  
Khaled W. Shahwan
Keyword(s):  
Present Model ◽  
Material Model ◽  
Multiscale Model ◽  
Stress And Strain ◽  
Band Model ◽  
Braided Composites ◽  
Microplane Model ◽  
Explicit Finite Element ◽  
Crack Band ◽  
Strain Tensors

A material model for the fracturing behavior for braided composites is developed and implemented in a material subroutine for use in the commercial explicit finite element code ABAQUS. The subroutine is based on the microplane model in which the constitutive behavior is defined not in terms of stress and strain tensors and their invariants but in terms of stress and strain vectors in the material mesostructure called the “microplanes.” This is a semi-multiscale model, which captures the interactions between inelastic phenomena such as cracking, splitting, and frictional slipping occurring on planes of various orientations though not the interactions at a distance. To avoid spurious mesh sensitivity due to softening, the crack band model is adopted. Its band width, related to the material characteristic length, serves as the localization limiter. It is shown that the model can realistically predict the orthotropic elastic constants and the strength limits. More importantly, the present model can also fit the tests of size effect on the strength of notched specimens and the post-peak behavior, which have been conducted for this purpose. When used in the ABAQUS software, the model gives a realistic picture of the axial crushing of a braided tube by a divergent plug.

Effect of Critical Void Volume Fraction fF on Results of Ductile Fracture Simulation for S235JR Steel under Multi-Axial Stress States

2014 ◽  
Vol 598 ◽  
pp. 113-118 ◽  
Author(s):  
Paweł Grzegorz Kossakowski ◽  
Wiktor Wciślik
Keyword(s):  
Volume Fraction ◽  
Axial Stress ◽  
Material Model ◽  
Model Parameters ◽  
Material Microstructure ◽  
Fracture Simulation ◽  
Critical Volume Fraction ◽  
Stress States ◽  
The Impact ◽  
Critical Void

The article describes an example of the GTN material model parameters determination and application. The main objective of the study was to determine experimentally the value of the critical volume fraction of voids fFfor S235JR steel and to assess the impact of this parameter on the numerical force-elongation curve under the multi-axial stress state. Value of fFwas obtained by the quantitative analysis of the material microstructure at fracture surfaces. For a sake of comparison, two other values of fF, described in the literature, were also used in numerical simulations.

Plastic Response of Nested Systems under Static and Dynamic Loading Conditions Using FE and Experimental Techniques

2006 ◽  
Vol 3-4 ◽  
pp. 377-382
Author(s):  
Edmund Morris ◽  
Abdul Ghani Olabi ◽  
M.S.J. Hashmi
Keyword(s):  
Finite Element Method ◽  
Software Package ◽  
Material Model ◽  
Ring System ◽  
Plastic Response ◽  
Different Types ◽  
Out Of Plane ◽  
Dynamic Yield ◽  
Dynamic Loading Conditions ◽  
Static And Dynamic Loading

This paper presents the study of nested rings crushed laterally between rigid platens at 2 different velocities. In this investigation two different types of nested ring configurations are analysed: (A) In-Plane; where three rings of varying diameter are placed within each other and their axes are parallel. (B) Out of-Plane; where the rings have a 90 degree orientation. Material used was cold finished, drawn over mandrel (DIN 2393 ST 37-2) and is referred throughout the paper as mild steel. The Cowper-Symonds relation was used to predict the dynamic yield stress of the rings and this was included in the FE material model. The results obtained from experiments were compared to that of finite element method using the software package Ansys. Discussion is made on the post – collapse behaviour of these systems. It was found that the Out of-Plane ring system exhibited a more desirable force-deflection response due to its 90 degree orientation.

scholarly journals NUMERICAL MODELLING OF BIRD STRIKE ON A ROTATING ENGINE BLADES BASED ON VARIATIONS OF POROSITY DENSITY

2022 ◽  
Vol 23 (1) ◽  
pp. 412-423
Author(s):  
Sharis-Shazzali Shahimi ◽  
Nur Azam Abdullah ◽  
Ameen Topa ◽  
Meftah Hrairi ◽  
Ahmad Faris Ismail
Keyword(s):  
Numerical Modelling ◽  
Structural Integrity ◽  
Constitutive Relations ◽  
Material Model ◽  
Initial Stresses ◽  
Model Parameters ◽  
Bird Strike ◽  
Elastic Plastic ◽  
Engine Blade ◽  
The Impact

A numerical investigation is conducted on a rotating engine blade subjected to a bird strike impact. The bird strike is numerically modelled as a cylindrical gelatine with hemispherical ends to simulate impact on a rotating engine blade. Numerical modelling of a rotating engine blade has shown that bird strikes can severely damage an engine blade, especially as the engine blade rotates, as the rotation causes initial stresses on the root of the engine blade. This paper presents a numerical modelling of the engine blades subjected to bird strike with porosity implemented on the engine blades to investigate further damage assessment due to this porosity effect. As porosity influences the decibel levels on a propeller blade or engine blade, the damage due to bird strikes can investigate the compromise this effect has on the structural integrity of the engine blades. This paper utilizes a bird strike simulation through an LS-Dyna Pre-post software. The numerical constitutive relations are keyed into the keyword manager where the bird’s SPH density, a 10 ms simulation time, and bird velocity of 100 m/s are all set. The blade rotates counter-clockwise at 200 rad/s with a tetrahedron mesh. The porous regions or voids along the blade are featured as 5 mm diameter voids, each spaced 5 mm apart. The bird is modelled as an Elastic-Plastic-Hydrodynamic material model to analyze the bird’s fluid behavior through a polynomial equation of state. To simulate the fluid structure interaction, the blade is modelled with Johnson-Cook Material model parameters of aluminium where the damage of the impact can be observed. The observations presented are compared to previous study of a bird strike impact on non-porous engine blades. ABSTRAK: Penyelidikan berangka telah dijalankan ke atas bilah enjin berputar tertakluk kepada impak pelanggaran burung. Pelanggaran burung tersebut telah dimodelkan secara berangka sebagai silinder gelatin dengan hujungnya berbentuk hemisfera demi mensimulasikan impaknya ke atas bilah enjin yang berputar. Pemodelan berangka bilah-bilah enjin yang berputar tersebut menunjukkan bahawa pelanggaran burung mampu menyebabkan kerosakan teruk terhadap bilah enjin terutamanya apabila bilah enjin sedang berputar oleh sebab putaran menghasilkan tekanan asal di pangkal bilah enjin. Kajian ini mengetengahkan pemodelan berangka ke atas bilah-bilah enjin tertakluk kepada pelanggaran burung terhadap bilah-bilah enjin yg mempunyai keliangan demi menyelidik dan menilai kerosakan kesan daripada keliangan tersebut. Keliangan juga mempengaruhi tahap-tahap desibel ke atas bilah kipas ataupun bilah enjin, kerosakan hasil serangan burung boleh menterjemah tahap ketahanan struktur integriti bagi bilah-bilah enjin tersebut. Penyelidikan ini mengguna pakai perisian “LS-Dyna Pre-post” untuk simulasi pelanggaran burung. Hubungan konstitutif berangka telah dimasukkan sebagai kata kunci di mana ketumpatan SPH burung, masa simulasi 10ms, dan halaju burung ditetapkan kepada 100 m/s. Bilah tersebut berputar pada 200 rad/s arah lawan jam dengan jejaring tetrahedron. Kawasan berliang atau kosong di sepanjang bilah ditetapkan diameternya kepada 5 mm, dan dijarakkan 5 mm di antara satu sama lain. Burung pula dimodelkan sebagai material “Elastic-Plastic-Hydrodynamic” untuk mengkaji sifat bendalir burung melalui persamaan polinomial. Demi mensimulasi interaksi struktur bendalir, bilah tersebut dimodelkan sebagai parameter aluminium material “Johnson Cook” di mana kerosakan daripada impak tersebut dapat diteliti. Penelitian-penelitian tersebut dibandingkan dengan kajian terdahulu ke atas serangan burung terhadap bilah-bilah enjin tidak berliang.

Using Microplane Material Model for Concrete in Soft Missile Impact Analysis

2010 ◽  
Author(s):  
Jukka Ka¨hko¨nen ◽  
Pentti Varpasuo
Keyword(s):  
Numerical Integration ◽  
Impact Analysis ◽  
Constitutive Relations ◽  
Material Model ◽  
Medium Size ◽  
Test Case ◽  
Nonlinear Phenomena ◽  
Integration Formulas ◽  
The Impact ◽  
Concrete Model

The paper describes basis of a microplane concrete material model which was implemented in a commercial FE -code using user subroutine interface. The material model is called M4. The motivation for this implementation was a need for a concrete model which would perform well in a soft missile impact analysis. Numerical integration over the surface of a unit sphere is crucial to microplane material models. We tested our microplane implementation using several numerical integration formulas presented in literature. The two fairly simple test cases described in this paper revealed clearly the numerical anisotropy induced by the integration formulations. The impact problem was a medium size, medium velocity soft missile impact test case from an international research program. We compared our implementation of M4 model to a tensorial based damage plasticity concrete model and found out that the results were almost identical. However, the numerical results did not agree well with the measurements in this test case. We concluded this disagreement might be consequence of nonlinear phenomena beyond material constitutive relations.

Quasicontinuum Method Simulation of Nanometric Cutting of Single Crystal Copper

2009 ◽  
Vol 628-629 ◽  
pp. 381-386 ◽  
Author(s):  
Ying Chun Liang ◽  
Hong Min Pen ◽  
Qing Shun Bai
Keyword(s):  
Single Crystal ◽  
Strain Energy ◽  
Multiscale Model ◽  
Multiscale Simulation ◽  
Atomistic Simulations ◽  
Workpiece Material ◽  
Machined Surface ◽  
Quasicontinuum Method ◽  
Nanometric Cutting ◽  
Single Crystal Copper

A multiscale simulation model was built to study the nanometric cutting process of single crystal copper. This multiscale model distinctly reduces the degree of freedom of the whole system compared with full atomistic simulations. Through analyzing the fluctuations of tangential cutting force and strain energy with cutting distance, we confirm that the deformation mechanism of single crystal copper is plastic deformation caused by generation and evolution dislocation. The highest compressive stress locates in shear zone and highest tensile stress locates in the machined surface and subsurface. Simulation results show that there exists a high value of stress around dislocations, which reveals the local high value of stress is the main reason for the generation and evolution of dislocations in the workpiece material.

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