Comment on: “The finite element implementation of 3D fractional viscoelastic constitutive models” by Gioacchino Alotta, Olga Barrera, Alan Cocks, Mario Di Paola, Finite elements in analysis and design, 146 (2018) 28–41

2018 ◽  
Vol 152 ◽  
pp. 17
Author(s):  
Ergin Tönük
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Constitutive Models ◽  
Analysis And Design ◽  
Finite Element Implementation

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications

2011 ◽  
Vol 58 (3) ◽  
pp. 319-346 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Function Theory ◽  
Constitutive Models ◽  
Elasticity Tensor ◽  
Stored Energy ◽  
Energy Potential ◽  
Hyperelastic Materials ◽  
Finite Element Implementation ◽  
Living Tissues

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications This paper contains the full way of implementing a user-defined hyperelastic constitutive model into the finite element method (FEM) through defining an appropriate elasticity tensor. The Knowles stored-energy potential has been chosen to illustrate the implementation, as this particular potential function proved to be very effective in modeling nonlinear elasticity within moderate deformations. Thus, the Knowles stored-energy potential allows for appropriate modeling of thermoplastics, resins, polymeric composites and living tissues, such as bone for example. The decoupling of volumetric and isochoric behavior within a hyperelastic constitutive equation has been extensively discussed. An analytical elasticity tensor, corresponding to the Knowles stored-energy potential, has been derived. To the best of author's knowledge, this tensor has not been presented in the literature yet. The way of deriving analytical elasticity tensors for hyperelastic materials has been discussed in detail. The analytical elasticity tensor may be further used to develop visco-hyperelastic, nonlinear viscoelastic or viscoplastic constitutive models. A FORTRAN 77 code has been written in order to implement the Knowles hyperelastic model into a FEM system. The performance of the developed code is examined using an exemplary problem.

Comparison of Three-Dimensional Shape Memory Alloy Constitutive Models: Finite Element Analysis of Actuation and Superelastic Responses of a Shape Memory Alloy Tube

2013 ◽  
Author(s):  
Pingping Zhu ◽  
L. Catherine Brinson ◽  
Edwin Peraza-Hernandez ◽  
Darren Hartl ◽  
Aaron Stebner
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Benchmark Problems ◽  
Internal Variables ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Analysis And Design

Many three-dimensional constitutive models have been proposed to enhance the analysis and design of shape memory alloy (SMA) structural components. Phenomenological models are desirable for this purpose since they describe macroscopic responses using internal variables to govern the homogenized material response. Because they are computationally efficient on the scale of millimeters to meters, these models are often the only viable option when assessing the response of full-scale SMA components for engineering applications. Thus, many different 3D SMA constitutive models have been developed. However, for their intended user, the application engineer, a clear and straightforward methodology has not been established for selecting a model to use in a design process. A primary goal of the Consortium for the Advancement of Shape Memory Alloy Research and Technology (CASMART) modeling working group has been establishment of model selection methodology. One critical step in this process is the development of benchmark problems that clearly illustrate the capabilities and efficiencies of models. In this paper, we propose a set of benchmark problems centered on an SMA tube component. These problems have been selected to demonstrate both uniaxial and multiaxial, actuation and superelastic capabilities of 3D SMA models. We then use finite element simulations of these benchmark problems to compare and contrast both the material modeling and implementation of three unique SMA constitutive models.

scholarly journals The finite element implementation of 3D fractional viscoelastic constitutive models

2018 ◽  
Vol 146 ◽  
pp. 28-41 ◽  
Author(s):  
Gioacchino Alotta ◽  
Olga Barrera ◽  
Alan Cocks ◽  
Mario Di Paola
Keyword(s):  
Finite Element ◽  
Constitutive Models ◽  
Finite Element Implementation

Modelling Recrystallisation during Thermomechanical Processing Using CAFE

2004 ◽  
Vol 467-470 ◽  
pp. 623-628 ◽  
Author(s):  
S. Das ◽  
Eric J. Palmiere ◽  
I.C. Howard
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cellular Automata ◽  
Thermomechanical Processing ◽  
Constitutive Models ◽  
Computational Time ◽  
Physical Sciences ◽  
Element Mesh ◽  
Dislocation Densities ◽  
Macro Scale

A common feature that stimulates modelling efforts across the various physical sciences is that complex microscopic behaviour underlies apparently simple macroscopic effects. Mathematical formulations attempt to capture the initial and evolving microstructural entities either implicitly or explicitly and link their effects to measurable macroscopic variables such as load or stress by averaging out any microscopic fluctuations. The implicit formulations that ignore the inherent spatial heterogeneity in the deforming domain form the basis of constitutive models for input to finite element (FE) systems. On the other hand, explicit formulations to capture and link microstructural entities rely on narrowing down the size of each finite element, thereby increasing the number of finite elements in the deforming domain, an effect accompanied by a rapid growth in computational time. The model described here, Cellular Automata based Finite Elements (CAFE), utilises the Cellular Automata technique to represent initial and evolving microstructural features (e.g., dislocation densities, grain sizes, etc.) in C-Mn steels at an appropriate length scale by linking the macro-scale process variables obtained using an overlying finite element mesh. Differences will be illustrated between single and two-pass hot rolling experiments.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

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