Critical Plane Analysis of Rubber

2020 ◽  
Author(s):  
W. V. Mars
Keyword(s):  
Critical Plane ◽  
Plane Analysis

Computing Tire Component Durability via Critical Plane Analysis

2019 ◽  
Vol 47 (1) ◽  
pp. 31-54 ◽  
Author(s):  
William V. Mars ◽  
Yintao Wei ◽  
Wang Hao ◽  
Mark A. Bauman
Keyword(s):  
Strain Energy ◽  
Fatigue Behavior ◽  
Stress Singularity ◽  
Crack Development ◽  
Fatigue Threshold ◽  
Critical Plane ◽  
Plane Analysis ◽  
Scalar Invariant ◽  
Edge Separation ◽  
Design Guidance

ABSTRACT Tire developers are responsible for designing against the possibility of crack development in each of the various components of a tire. The task requires knowledge of the fatigue behavior of each compound in the tire, as well as adequate accounting for the multiaxial stresses carried by tire materials. The analysis is illustrated here using the Endurica CL fatigue solver for the case of a 1200R20 TBR tire operating at 837 kPa under loads ranging from 66 to 170% of rated load. The fatigue behavior of the tire's materials is described from a fracture mechanical viewpoint, with care taken to specify each of the several phenomena (crack growth rate, crack precursor size, strain crystallization, fatigue threshold) that govern. The analysis of crack development is made by considering how many cycles are required to grow cracks of various potential orientations at each element of the model. The most critical plane is then identified as the plane with the shortest fatigue life. We consider each component of the tire and show that where cracks develop from precursors intrinsic to the rubber compound (sidewall, tread grooves, innerliner) the critical plane analysis provides a comprehensive view of the failure mechanics. For cases where a crack develops near a stress singularity (i.e., belt-edge separation), the critical plane analysis remains advantageous for design guidance, particularly relative to analysis approaches based upon scalar invariant theories (i.e., strain energy density) that neglect to account for crack closure effects.

Finite Element Modeling and Critical Plane Analysis of a Cut-and-Chip Experiment for Rubber

2020 ◽  
Author(s):  
Christopher G. Robertson ◽  
Jesse D. Suter ◽  
Mark A. Bauman ◽  
Radek Stoček ◽  
William V. Mars
Keyword(s):  
Finite Element ◽  
Impact Force ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Critical Plane ◽  
Element Analysis ◽  
Rate Laws ◽  
Plane Analysis ◽  
Chip Experiment ◽  
The Impact

ABSTRACT Rubber surfaces exposed to concentrated, sliding impacts carry large normal and shearing stresses that can cause damage and the eventual removal of material from the surface. Understanding this cut-and-chip (CC) effect in rubber is key to developing improved tread compounds for tires used in off-road or poor road conditions. To better understand the mechanics involved in the CC process, an analysis was performed of an experiment conducted on a recently introduced device, the Coesfeld Instrumented Chip and Cut Analyser (ICCA), which repetitively impacts a rigid indenter against a rotating solid rubber wheel. The impact process is carefully controlled and measured on this lab instrument, so that the contact time, normal force, and shear force are all known. The numerical evaluation includes Abaqus finite element analysis (FEA) to determine the stress and strain fields during impact. The FEA results are combined with rubber fracture mechanics characteristics of the material as inputs to the Endurica CL elastomer fatigue solver, which employs critical plane analysis to determine the fatigue response of the specimen surface. The modeling inputs are experimentally determined hyperelastic stress-strain parameters, crack growth rate laws, and crack precursor sizes for carbon black–filled compounds wherein the type of elastomer is varied in order to compare natural rubber (NR), butadiene rubber (BR), and styrene-butadiene rubber (SBR). At the lower impact force, the simulation results were consistent with the relative CC resistances of NR, BR, and SBR measured using the ICCA, which followed the order BR > NR > SBR. Impact-induced temperature increases need to be considered in the fatigue analysis of the higher impact force to provide lifetime predictions that match the experimental CC resistance ranking of NR > SBR > BR.

Critical plane analysis for interpreting experimental results on anisotropic rocks

2018 ◽  
Vol 14 (4) ◽  
pp. 1215-1225
Author(s):  
Mehdi Pouragha ◽  
Richard Wan ◽  
Mahdad Eghbalian
Keyword(s):  
Experimental Results ◽  
Critical Plane ◽  
Plane Analysis ◽  
Anisotropic Rocks

scholarly journals A Geometric Perspective on Information Plane Analysis

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 711
Author(s):  
Mina Basirat ◽  
Bernhard C. Geiger ◽  
Peter M. Roth
Keyword(s):  
Neural Network ◽  
Mutual Information ◽  
Geometric Interpretation ◽  
Neural Network Training ◽  
Neural Network Learning ◽  
Network Learning ◽  
Plane Analysis ◽  
Network Training ◽  
Hidden Layer ◽  
The Impact

Information plane analysis, describing the mutual information between the input and a hidden layer and between a hidden layer and the target over time, has recently been proposed to analyze the training of neural networks. Since the activations of a hidden layer are typically continuous-valued, this mutual information cannot be computed analytically and must thus be estimated, resulting in apparently inconsistent or even contradicting results in the literature. The goal of this paper is to demonstrate how information plane analysis can still be a valuable tool for analyzing neural network training. To this end, we complement the prevailing binning estimator for mutual information with a geometric interpretation. With this geometric interpretation in mind, we evaluate the impact of regularization and interpret phenomena such as underfitting and overfitting. In addition, we investigate neural network learning in the presence of noisy data and noisy labels.

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