Internal State Variable Theory

McDowell, D. L.

doi:10.1007/978-1-4020-3286-8_58

Cited by 38 publications

(15 citation statements)

References 22 publications

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“…where G i and K i are the shear and bulk elastic moduli of material filling the element i, the mean stress r i mean is calculated using (3) and (15).…”

Section: Elastic-plastic Modelmentioning

confidence: 99%

“…Today, there are different practical implementations of the discussed methodology. The most rigorous and advanced implementations take into account the kinetics of deformation, including relaxation, processes on lower scales through the introduction of additional input parameters (internal variables) governed by special evolution equations [13,15].…”

Section: Introductionmentioning

confidence: 99%

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Overcoming the limitations of distinct element method for multiscale modeling of materials with multimodal internal structure

Shilko

Psakhie

Schmauder

et al. 2015

Computational Materials Science

108

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“…where G i and K i are the shear and bulk elastic moduli of material filling the element i, the mean stress r i mean is calculated using (3) and (15).…”

Section: Elastic-plastic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Overcoming the limitations of distinct element method for multiscale modeling of materials with multimodal internal structure

Shilko

Psakhie

Schmauder

et al. 2015

Computational Materials Science

108

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“…Alternatively, one can consider a statistical volume element (rSVE) and construct an ensemble average for the concerned behavior by repeatedly collecting observations (from simulation or experiment) over some number of realizations. McDowell (1997McDowell ( , 2005 has considered various cases involving evolution of microstructure and their implications for the size of the rRVE for each considered response function, clearly distinguishing the rRVE size between stationary (e.g., elastic stiffness of microstructure ensemble) and evolving cases (plastic deformation and damage).…”

Section: Discussion Of Internal State Variable Theorymentioning

confidence: 99%

A hierarchical framework for the multiscale modeling of microstructure evolution in heterogeneous materials.

Luscher¹

2010

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ACKNOWLEDGEMENTSAs far as I am concerned, there is no better way to celebrate a success than to share the credit with those that have contributed to the effort. Here I share credit with those people that have had tremendous impact to the successful completion of requirements for my PhD degree at Georgia Tech, including this dissertation.Of primary importance in this acknowledgement is to convey how substantial I consider my wife's sacrifices over the last five years. With the sole exception of unmarried PhD candidates, Ido not imagine that there exists a PhD thesis whose acknowledgement section does not make reference to the author's spouse. So I strive to make this acknowledgement of my wife's contributions to my success so compelling and unique that it escapes the status of 'formality'. To attempt this, I will provide a single anecdote selected from five years of worthy material.Stephanie Luscher endured months alone keeping our house in Los Alamos while I was in Atlanta attending classes and fulfilling residency requirements. During that time, she continued working as an engineering design review coordinator at Los Alamos National Lab. While in Oregon to visit family during the winter of 2004-5, a water pipe inside our Los Alamos house froze and burst. Over the next week, 90,000 gallons of water flowed throughout our house ruining just about everything. We returned home and opened soggy Christmas presents from the relative comfort of our car parked in the driveway while contemplating our next course of action.Our house required extensive repairs including a new heating system, kitchen cabinets, flooring, and complete refinishing of the interior walls. We lived in a motor home, a rented house, and a hotel over the course of six months of these repairs. Within two weeks of this happening, I was back in Atlanta and Stephanie was left to manage the reconstruction effort by herself. Of course, this is a single example of how Stephanie has sacrificed, and tended to the many details of life, in order to allow me to focus attention on the work presented within this thesis. Stephanie, I thank iv you for the support and sacrifice you have made to help me accomplish this goal. I'm glad you embraced "my goal" as "our goal."Well in advance of thoughts regarding graduate school, my parents instilled a few helpful traits in me. As a young boy, during hot summers spent roofing with my Dad, Mark Luscher, I learned to work hard and to play hard. My Dad taught me that sometimes "getting the job done" is not elegant; it simply requires you to roll up your sleeves and get to work. As a complement to this, my Mom taught me the importance of precision and attention to detail. Together, my parents have taught me the importance of family, which supersedes all else. Engineering division leader (W-DO), gave me opportunities to excel within the weapons program. Ryan Maupin, group leader for Advanced Engineering Analysis (W-13) has enthusiastically supported and trusted me, both as my manager and friend, to pursue a course of research th...

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“…To end this section we should note that other constructive reviews dealing with internal variables of state (but essentially in deformable solids) have been given by Horstemeyer andBamman (2010), andMcDowell (2005).…”

Section: ( )mentioning

confidence: 99%

The saga of internal variables of state in continuum thermo-mechanics (1893–2013)

Maugin

2015

Mechanics Research Communications

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Internal State Variable Theory

Cited by 38 publications

References 22 publications

Overcoming the limitations of distinct element method for multiscale modeling of materials with multimodal internal structure

Overcoming the limitations of distinct element method for multiscale modeling of materials with multimodal internal structure

A hierarchical framework for the multiscale modeling of microstructure evolution in heterogeneous materials.

The saga of internal variables of state in continuum thermo-mechanics (1893–2013)

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