A Method for the Validation of Predictive Computations Using a Stochastic Approach

2004 ◽  
Vol 126 (3) ◽  
pp. 227-234 ◽  
Author(s):  
Manuel Pellissetti ◽  
Roger Ghanem
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Material Properties ◽  
Stochastic Approach ◽  
Stochastic Property ◽  
Limited Data ◽  
Bernoulli Beam ◽  
Direct Differentiation Method ◽  
Stochastic Properties

Stochastic finite element methods provide predictions of the behavior of mechanical systems with randomly fluctuating material properties. Limited data is typically available for the characterization of these properties, introducing errors in their representation. In the present paper, the sensitivity of the response predictions with respect to the stochastic properties is analyzed, by means of the direct differentiation method (DDM). Explicit expressions for the dependence of certain statistics of the response on the statistics of the material property are obtained. The response sensitivities are then used to estimate the error in the response predictions, caused by the error in the representation of the stochastic property. Numerical results for a simple Bernoulli beam are presented.

Deep 3D Convolution Neural Network Methods for Brain White Matter Hybrid Computational Simulations

2020 ◽  
Author(s):  
Xuehai Wu ◽  
Assimina A. Pelegri
Keyword(s):  
Neural Network ◽  
Finite Element ◽  
White Matter ◽  
Finite Elements ◽  
Frequency Domain ◽  
Finite Element Methods ◽  
Material Properties ◽  
Output Data ◽  
Micro Scale ◽  
Brain White Matter

Abstract Material properties of brain white matter (BWM) show high anisotropy due to the complicated internal three-dimensional microstructure and variant interaction between heterogeneous brain-tissue (axon, myelin, and glia). From our previous study, finite element methods were used to merge micro-scale Representative Volume Elements (RVE) with orthotropic frequency domain viscoelasticity to an integral macro-scale BWM. Quantification of the micro-scale RVE with anisotropic frequency domain viscoelasticity is the core challenge in this study. The RVE behavior is expressed by a viscoelastic constitutive material model, in which the frequency-related viscoelastic properties are imparted as storage modulus and loss modulus for the composite comprised of axonal fibers and extracellular glia. Using finite elements to build RVEs with anisotropic frequency domain viscoelastic material properties is computationally very consuming and resource-draining. Additionally, it is very challenging to build every single RVE using finite elements since the architecture of each RVE is arbitrary in an infinite data set. The architecture information encoded in the voxelized location is employed as input data and is consequently incorporated into a deep 3D convolution neural network (CNN) model that cross-references the RVEs’ material properties (output data). The output data (RVEs’ material properties) is calculated in parallel using an in-house developed finite element method, which models RVE samples of axon-myelin-glia composites. This novel combination of the CNN-RVE method achieved a dramatic reduction in the computation time compared with directly using finite element methods currently present in the literature.

scholarly journals Stochastic inverse finite element modeling for characterization of heterogeneous material properties

2019 ◽  
Vol 6 (11) ◽  
pp. 115806
Author(s):  
Carlos Llopis-Albert ◽  
Francisco Rubio ◽  
Francisco Valero ◽  
Hunchang Liao ◽  
Shouzhen Zeng
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Material Properties ◽  
Heterogeneous Material ◽  
Element Modeling

Singular asymptotic expansion of the elastic solution along an edge around which material properties depend on the angular coordinate

2016 ◽  
Vol 22 (12) ◽  
pp. 2288-2308 ◽  
Author(s):  
Netta Omer ◽  
Zohar Yosibash
Keyword(s):  
Finite Element ◽  
Asymptotic Expansion ◽  
Stress Intensity ◽  
Asymptotic Solution ◽  
Finite Element Methods ◽  
Material Properties ◽  
Three Dimensional ◽  
Angular Coordinate ◽  
Angular Direction ◽  
Intensity Functions

The solution to the elasticity problem in three-dimensional polyhedral domains in the vicinity of an edge around which the material properties depend on the angular angle is addressed. This asymptotic solution involves a family of eigenpairs and their shadows which are being computed by means of p-finite element methods. In particular the examples we give explicitly provide the asymptotic solution for cracks and V-notch edges and explore the eigenvalues as a function of the change in material properties in the angular direction. We demonstrate that the singular exponents may change considerably by changing the material properties variation in the angular direction. These eigenpairs are necessary to allow the extraction of the edge stress intensity functions.

Characterization of Material Properties Using Strain Mapping and Reverse Engineering

2006 ◽  
Author(s):  
Lianshan Lin ◽  
Haiyan Li ◽  
Alex S. L. Fok
Keyword(s):  
Finite Element ◽  
Reverse Engineering ◽  
Material Properties ◽  
Good Accuracy ◽  
Strain Mapping ◽  
Linear Elastic ◽  
Highly Nonlinear ◽  
User Material Subroutine ◽  
Failure Predictions

For simplicity, the material properties used in engineering analysis are often assumed to be linear elastic, isotropic and homogeneous. These simplifications may lead to erroneous stress and failure predictions if the materials involved are highly nonlinear, anisotropic and inhomogeneous. Based on the techniques of strain mapping and reverse engineering, a simple finite-element-based method has been devised with the aim of characterizing the properties of such materials under load. The method has been implemented into the commercial finite element code ABAQUS, via its User Material Subroutine (UMAT), to allow material characterization to be performed easily. Verification of the method has been carried out using simulated examples and the results showed rapid convergence of the method with good accuracy. The method has also been applied successfully to actual mechanical testing of graphite.

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