Verification tests in solid mechanics

Kamojjala, Krishna; Brannon, Rebecca M.; Sadeghirad, Alireza; Guilkey, James

doi:10.1007/s00366-013-0342-x

Cited by 40 publications

(40 citation statements)

References 21 publications

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“…and the convected particle domain interpolation scheme of Sadeghirad et al . (for some more insights on available interpolations see ). In this paper, the GIMP version of the material point method has been adopted, primarily because of the quality and robustness of its implementation in the open source Uintah software (available from Utah University).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of material point method for use in geotechnics

Sołowski

Sloan

2014

Num Anal Meth Geomechanics

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SUMMARYThe first part of the paper presents a material point method solution for the bearing capacity of a deep foundation in purely cohesive soil, which is a widely known engineering problem. The results computed with the generalised interpolation material point method are compared to the results obtained previously with an advanced limit analysis code. The second part of the paper shows material point method simulations of collapsing piles of granular material and compares the results with experimental observations from the literature. The problems considered are problematic to solve using the displacement finite element method as they generally include very large deformations.

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Section: Introductionmentioning

confidence: 99%

Evaluation of material point method for use in geotechnics

Sołowski

Sloan

2014

Num Anal Meth Geomechanics

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“…For our baseline simulations, we use initially cuboidal particle domains to discretize the geometry. This leads to a poor representation of the curved cylindrical and spherical surfaces as discussed in [23]. Figure 1 shows a comparison between the default cuboidal particle geometry (figure 1a) and the same geometry discretized using particle domains that more closely conform to the boundaries of the geometry (figure 1b).…”

Section: Simulation Approach and Setupmentioning

confidence: 97%

A Quantitative Approach to Comparing High Velocity Impact Experiments and Simulations Using XCT Data

Tonge

Leavy

LaSalvia

et al. 2015

Procedia Engineering

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While computational models of impact events have the potential to accelerate the design cycle, one's confidence in a material model should be related to the extent of validation work that has been performed for that model. Quantities of interest used for validation are often either scalar volume-averaged quantities (such as the average density, or the force applied to a boundary) or field quantities (such as the strain field obtained from digital image correlation, or density maps computed from X-ray computed tomography (XCT)). Volume averaged quantities are easy to compare quantitatively since they are either a single value or a simple time series. However, these averaged quantities do not capture differences in the failure process within a material and can be blunt instruments for validation efforts. Field quantities provide spatial information, but are difficult to reduce to a scalar that quantifies the goodness of a particular model with respect to another model. This work describes an approach to using XCT data to quantify how well a particular simulation agrees with simulation data while accounting for the statistical nature of failure in brittle materials.

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“…Steffen et al applied MMS for a 2D axis‐aligned vibration problem; Wallstedt and Guilkey adopted MMS to study the convergence rate of GIMP by simulating a large deformation radial expansion of a ring. Later, Kamojjala et al presented a serial of verification tests for solid mechanics including a MMS generalized vortex problem. In this paper, the axis‐aligned vibration, the radial expansion of a ring and the MMS generalized vortex of a ring were used to study the convergence rate of the CPDI and the CPLS, presenting in Section 4.2, 0 and 4.4, respectively.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Later, Kamojjala et al presented a serial of verification tests for solid mechanics including a MMS generalized vortex problem. In this paper, the axis‐aligned vibration, the radial expansion of a ring and the MMS generalized vortex of a ring were used to study the convergence rate of the CPDI and the CPLS, presenting in Section 4.2, 0 and 4.4, respectively. This section summarizes the general derivation of the method of manufacture solution for hyper‐elastic materials.…”

Section: Numerical Examplesmentioning

confidence: 99%

A convected particle least square interpolation material point method

Tran

Sołowski

Berzins

et al. 2019

Numerical Meth Engineering

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Summary Applying the convected particle domain interpolation (CPDI) to the material point method has many advantages over the original material point method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The convected particle least square interpolation (CPLS) material point method assumes the velocity field inside the material point domain as nonconstant. This velocity field in the material point domain is mapped to the background grid nodes with a moving least squares reconstruction. In this paper, we apply the improved moving least squares method to avoid the instability of the conventional moving least squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the method of manufactured solutions.

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Verification tests in solid mechanics

Cited by 40 publications

References 21 publications

Evaluation of material point method for use in geotechnics

Evaluation of material point method for use in geotechnics

A Quantitative Approach to Comparing High Velocity Impact Experiments and Simulations Using XCT Data

A convected particle least square interpolation material point method

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