scholarly journals Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Jaber Rezaei Mianroodi ◽  
Nima H. Siboni ◽  
Dierk Raabe
Keyword(s):  
Deep Neural Network ◽  
Solid Mechanics ◽  
Local Stress ◽  
Percentage Error ◽  
Elastic Media ◽  
Fast Solver ◽  
Plastic Materials ◽  
Local Stresses ◽  
Non Linear ◽  
Elastic Plastic Materials

AbstractWe propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The DNN model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical solvers.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

2021 ◽  
Vol 316 ◽  
pp. 936-941
Author(s):  
Natalya Ya. Golovina
Keyword(s):  
Mathematical Models ◽  
Strain Curve ◽  
Variational Model ◽  
Linear Deformation ◽  
Plastic Materials ◽  
Non Linear ◽  
Linear Sections ◽  
Elastic Plastic Materials ◽  
Deformation Section ◽  
St3sp Steel

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

scholarly journals A Hybrid Hidden Markov Model for Pipeline Leakage Detection

2021 ◽  
Vol 11 (7) ◽  
pp. 3138
Author(s):  
Mingchi Zhang ◽  
Xuemin Chen ◽  
Wei Li
Keyword(s):  
Neural Network ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Deep Neural Network ◽  
Hidden Markov ◽  
Gaussian Mixture ◽  
State Sequence ◽  
Non Linear

In this paper, a deep neural network hidden Markov model (DNN-HMM) is proposed to detect pipeline leakage location. A long pipeline is divided into several sections and the leakage occurs in different section that is defined as different state of hidden Markov model (HMM). The hybrid HMM, i.e., DNN-HMM, consists of a deep neural network (DNN) with multiple layers to exploit the non-linear data. The DNN is initialized by using a deep belief network (DBN). The DBN is a pre-trained model built by stacking top-down restricted Boltzmann machines (RBM) that compute the emission probabilities for the HMM instead of Gaussian mixture model (GMM). Two comparative studies based on different numbers of states using Gaussian mixture model-hidden Markov model (GMM-HMM) and DNN-HMM are performed. The accuracy of the testing performance between detected state sequence and actual state sequence is measured by micro F1 score. The micro F1 score approaches 0.94 for GMM-HMM method and it is close to 0.95 for DNN-HMM method when the pipeline is divided into three sections. In the experiment that divides the pipeline as five sections, the micro F1 score for GMM-HMM is 0.69, while it approaches 0.96 with DNN-HMM method. The results demonstrate that the DNN-HMM can learn a better model of non-linear data and achieve better performance compared to GMM-HMM method.

On Determining Elastic Modulus from Instrumented Indentation

2013 ◽  
Vol 668 ◽  
pp. 616-620
Author(s):  
Shuai Huang ◽  
Huang Yuan
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Plastic Material ◽  
Instrumented Indentation ◽  
Computational Simulations ◽  
Elastic Plastic ◽  
Modified Method ◽  
Plastic Materials ◽  
Elastic Plastic Material ◽  
Elastic Plastic Materials

Computational simulations of indentations in elastic-plastic materials showed overestimate in determining elastic modulus using the Oliver & Pharr’s method. Deviations significantly increase with decreasing material hardening. Based on extensive finite element computations the correlation between elastic-plastic material property and indentation has been carried out. A modified method was introduced for estimating elastic modulus from dimensional analysis associated with indentation data. Experimental verifications confirm that the new method produces more accurate prediction of elastic modulus than the Oliver & Pharr’s method.

The Propagation of Plasticity in Uniaxial Compression

1948 ◽  
Vol 15 (3) ◽  
pp. 256-260 ◽  
Author(s):  
M. P. White ◽  
LeVan Griffis
Keyword(s):  
Uniaxial Compression ◽  
Thin Sheet ◽  
High Stress ◽  
Stress And Strain ◽  
Velocity Range ◽  
Plastic Materials ◽  
The Face ◽  
Elastic Plastic Materials ◽  
The Impact ◽  
Type Of Behavior

Abstract A theoretical investigation of the mechanism of uniaxial compression impact on elastic-plastic materials is described in this paper. The method of analysis is similar in some respects to that previously given for tension impact on such materials. It is concluded that four different kinds of behavior can occur, depending upon the impact velocity. In the lowest velocity range the behavior in compression is similar to that found in tension. In this case stress and strain are propagated from the point of impact as a zone or wave front of ever-increasing length. This type of behavior ends at a velocity corresponding to the “critical” velocity found in tension impact. Within the next higher velocity range, stress and strain are propagated as a shock-type wave, or wave of very small length in which the transition from low to high stress and strain is very abrupt. At still higher impact velocities, there occurs “flowing deformation” in which the material is too weak to maintain coherency. Here there is a steady flow of the material toward and against the hammer, after which it flows in a thin sheet radially outward over the face of the hammer. The final possible state occurs at impact velocities greater than the speed of an elastic wave, so that no disturbance can escape from the hammer into the medium. Here the behavior is essentially that of a fluid, impact force being independent of strength of material.

scholarly journals Advances in the DEM and Coupled DEM and FEM Techniques in Non Linear Solid Mechanics

2017 ◽  
pp. 309-335 ◽  
Author(s):  
Eugenio Oñate ◽  
Francisco Zárate ◽  
Miguel A. Celigueta ◽  
José M. González ◽  
Juan Miquel ◽  
...  
Keyword(s):  
Solid Mechanics ◽  
Non Linear

scholarly journals A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics

2018 ◽  
Vol 63 (6) ◽  
pp. 1243-1260 ◽  
Author(s):  
I. Iaconeta ◽  
A. Larese ◽  
R. Rossi ◽  
E. Oñate
Keyword(s):  
Solid Mechanics ◽  
Material Point Method ◽  
Material Point ◽  
Point Method ◽  
Non Linear
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