Application of Fractal Image Analysis by Scale-Space Filtering in Experimental Mechanics

Bauer, Anna; Volk, Wolfram; Hartmann, Christoph

doi:10.3390/jimaging8090230

Cited by 3 publications

(3 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The aim of this work is to investigate the energy-based variational model in the context of in situ measured displacement field data, which are readily available for a wide range of experiments and processes [ 28 , 29 ]. This becomes even more important with the increasing accuracy and precision of full-field optical measurement techniques [ 30 , 31 , 32 , 33 ]. The first goal of this work was to adapt the energy-based variational model to the special case of given displacement fields.…”

Section: Objectivementioning

confidence: 99%

“…The parameters A, B, C, n, and q are material constants; ε0 is a reference strain rate; T m is the melting temperature; and T r is the reference temperature (which is usually room temperature). The term in the first set of parentheses in Equation (33) gives a stress as a function of strain, where B is the strain hardening coefficient and n is the strain hardening exponent. The terms in the second and third sets of parentheses represent the effects of strain rate and temperature, respectively [48].…”

Section: Adjustment To the Johnson-cook Plasticity Modelmentioning

confidence: 99%

“…Combining the two equations gives β σ εp = Y εp . Rearranging and using Equations ( 13) and (33) in the form Y = ∂ψ * ∂ εp finally yields…”

Section: Calculation Of the Taylor-quinney Coefficientmentioning

confidence: 99%

See 2 more Smart Citations

Plasticity-Induced Heating: Revisiting the Energy-Based Variational Model

Hartmann,

Obermeyer

2024

Materials

Self Cite

View full text Add to dashboard Cite

Temperature evolution during plastic deformation is of great importance for the design of manufacturing processes, as well as for the analysis and prediction of tool wear. However, the results from experimental- and numerical-type research are still often contradictory. In this paper, we analyze methods for estimating plasticity-induced heating directly from displacement fields that can be recorded during experiments or extracted from simulation results. In terms of computational methodology, the thermodynamically motivated energy-based variational formulation of the coupled thermo-mechanical boundary-value problem is adapted to the problem at hand. Since an analysis of this variational formulation exhibits challenges and distinct inconsistencies with respect to the problem at hand, an alternative approach is proposed. This alternative approach is essentially a purely thermal finite element simulation, and it is conducted using a heat source term that is empirically based on the fraction of irreversible deformation work converted to heat. Our approach estimates plasticity-induced heating based on the strain and strain rate data derived from displacement fields. We therefore incorporate thermo-visco-plastic constitutive behavior (Johnson–Cook) with a thermodynamically motivated model that specifies the fraction of plastic work converted to heat (the Taylor–Quinney coefficient).

show abstract

Section: Objectivementioning

confidence: 99%

Section: Adjustment To the Johnson-cook Plasticity Modelmentioning

confidence: 99%

See 1 more Smart Citation

Plasticity-Induced Heating: Revisiting the Energy-Based Variational Model

Hartmann,

Obermeyer

2024

Materials

Self Cite

View full text Add to dashboard Cite

show abstract

Non-invasive Point-of-care System for Disease Detection through Fingernail

Ingole,

Khandelwal

2024

2024 IEEE 9th International Conference for Convergence in Technology (I2CT)

View full text Add to dashboard Cite

Numerical integration of bivariate fractal interpolation functions on rectangular domains

Aparna

Paramanathan

2023

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

This paper primarily focuses on the derivation of fractal numerical integration for the data sets corresponding to two variable signals defined over a rectangular region. Evaluating numerical integration results through the fractal method helps achieve accurate results with minimum computation effort. The formulation of the fractal numerical integration is achieved by considering the recursive relation satisfied by the bivariate fractal interpolation functions for the given data set. The points in the data set have been used to evaluate the coefficients of the iterated function systems. The derivation of these coefficients considering the index of the subrectangles, and the integration formula has been proposed using these coefficients. The bivariate fractal interpolation functions constructed using these coefficients are then correlated with the bilinear interpolation functions. Also, this paper derives a formula for the freely chosen vertical scaling factor that has been used in reducing the approximation error. The obtained formula of the vertical scaling factor is then used in establishing the convergence of the proposed method of integration to the traditional double integration technique through a collection of lemmas and theorems. Finally, the paper concludes with an illustration of the proposed method of integration and the analysis of the numerical integral results obtained for the data sets corresponding to four benchmark functions.

show abstract

Application of Fractal Image Analysis by Scale-Space Filtering in Experimental Mechanics

Cited by 3 publications

References 37 publications

Plasticity-Induced Heating: Revisiting the Energy-Based Variational Model

Plasticity-Induced Heating: Revisiting the Energy-Based Variational Model

Non-invasive Point-of-care System for Disease Detection through Fingernail

Numerical integration of bivariate fractal interpolation functions on rectangular domains

Contact Info

Product

Resources

About