NDLI: A nonlinear visco-elastic constitutive model for large rotation finite element formulations

Content Provider	Springer Nature Link
Author	Mohamed, Abdel Nasser A. Shabana, Ahmed A.
Copyright Year	2011
Abstract	Although all known materials have internal damping that leads to energy dissipation, most existing large deformation visco-elastic finite element formulations are based on linear constitutive models or on nonlinear constitutive models that can be used in the framework of an incremental co-rotational finite element solution procedure. In this investigation, a new nonlinear objective visco-elastic constitutive model that can be implemented in non-incremental large rotation and large deformation finite element formulations is developed. This new model is based on developing a simple linear relationship between the damping forces and the rates of deformation vector gradients. The deformation vector gradients can be defined using the decomposition of the matrix of position vector gradients. In this paper, the decomposition associated with the use of the tangent frame that is equivalent to the QR decomposition is employed to define the matrix of deformation gradients that enter into the formulation of the viso-elastic constitutive model developed in this investigation. Using the relationship between the deformation gradients and the components of the Green–Lagrange strain tensor, it is shown that the damping forces depend nonlinearly on the strains and linearly on the classical strain rates. The relationship between the damping forces and strains and their rates is used to develop a new visco-elastic model that satisfies the objectivity requirements and leads to zero strain rates under an arbitrary rigid body displacement. The linear visco-elastic Kelvin–Voigt model frequently used in the literature can be obtained as a special case of the proposed nonlinear model when only two visco-elastic coefficients are used. As demonstrated in this paper, the use of two visco-elastic coefficients only leads to viscous coupling between the deformation gradients. The model developed in this investigation can be used in the framework of large deformation and large rotation non-incremental solution procedure without the need for using existing co-rotational finite element formulations. The finite element absolute nodal coordinate formulation (ANCF) that allows for straightforward implementation of general constitutive material models is used in the validation of the proposed visco-elastic model. A comparison with the linear visco-elastic model is also made in this study. The results obtained in this investigation show that there is a good agreement between the solutions obtained using the proposed nonlinear model and the linear model in the case of small deformations.
Starting Page	57
Ending Page	79
Page Count	23
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	26
Issue Number	1
e-ISSN	1573272X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-02-09
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear internal damping Visco-elastic constitutive equations Large rotation and large deformation problems Multibody system dynamics Absolute nodal coordinate formulation (ANCF) Vibration, Dynamical Systems, Control Optimization Electrical Engineering Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

A two-dimensional shear deformable ANCF consistent rotation-based formulation beam element

On the use of elastic middle surface approach in the large deformation analysis of moderately thick shell structures using absolute nodal coordinate formulation

A geometrically exact beam element based on the absolute nodal coordinate formulation

Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

Absolute nodal coordinate plane beam formulation for multibody systems dynamics

Absolute nodal coordinate formulation of large-deformation piezoelectric laminated plates

A nonlinear approach for modeling rail flexibility using the absolute nodal coordinate formulation

Three- and four-noded planar elements using absolute nodal coordinate formulation

Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates

A nonlinear visco-elastic constitutive model for large rotation finite element formulations

Similar Documents

A two-dimensional shear deformable ANCF consistent rotation-based formulation beam element

On the use of elastic middle surface approach in the large deformation analysis of moderately thick shell structures using absolute nodal coordinate formulation

A geometrically exact beam element based on the absolute nodal coordinate formulation

Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

Absolute nodal coordinate plane beam formulation for multibody systems dynamics

Absolute nodal coordinate formulation of large-deformation piezoelectric laminated plates

A nonlinear approach for modeling rail flexibility using the absolute nodal coordinate formulation

Three- and four-noded planar elements using absolute nodal coordinate formulation

Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates

A nonlinear visco-elastic constitutive model for large rotation finite element formulations