Question: What type of studyn does Morton Gurtin and Archive for Rational Mechanics and Analysis have in common?

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Indiana University Mathematics Journal: The Indiana University Mathematics Journal (ISSN 0022-2518  ) is a journal of mathematics published by Indiana University.  Its first volume was published in 1952, under the name Journal of Rational Mechanics and Analysis and edited by Václav Hlavatý and Clifford Truesdell.  In 1957, Eberhard Hopf became editor, the journal name changed to the Journal of Mathematics and Mechanics, and Truesdell founded a separate successor journal, the "Archive for Rational Mechanics and Analysis", now published by Springer-Verlag.  The "Journal of Mathematics and Mechanics" later changed its name again to the present name.  s of 2013 , the managing editor is Chris Judge.

Alexandru Froda: Alexandru Froda (July 16, 1894, Bucharest, Romania – October 7, 1973, Bucharest, Romania) was a well-known Romanian mathematician with important contributions in the field of mathematical analysis, algebra, number theory and rational mechanics.  In his 1929 thesis he proved what is now known as Froda's theorem.

Rational data type: Some programming languages provide a built-in (primitive) rational data type to represent rational numbers like 1/3 and -11/17 without rounding, and to do arithmetic on them.  Examples are the codice_1 type of Common Lisp, and analogous types provided by most languages for algebraic computation, such as Mathematica and Maple.  Many languages that do not have a built-in rational type still provide it as a library-defined type.

Group of rational points on the unit circle: In mathematics, the rational points on the unit circle are those points ("x", "y") such that both "x" and "y" are rational numbers ("fractions") and satisfy "x" + "y" = 1.  The set of such points turns out to be closely related to primitive Pythagorean triples. Consider a primitive right triangle, that is, with integral side lengths "a", "b", "c", with "c" the hypotenuse, such that the sides have no common factor larger than 1.  Then on the unit circle there exists the rational point ("a"/"c", "b"/"c"), which, in the complex plane, is just "a"/"c" + "ib"/"c", where "i" is the imaginary unit.  Conversely, if ("x", "y") is a rational point on the unit circle in the 1st quadrant of the coordinate system (i.e. "x" > 0, "y" > 0), then there exists a primitive right triangle with sides "xc", "yc", "c", with "c" being the least common multiple of "x" and "y" denominators.  There is a correspondence between points ("x","y") in the "x"-"y" plane and points "x" + "iy" in the complex plane which will be used below, with ("a", "b") taken as equal to "a" + "ib".

LBR (file format): The . LBR file format was an archive file format used on CP/M and DOS operating systems during the early 1980s.  . LBR files were created by the LU program; later programs like NULU arrived for . LBR creation, and many tools such as LT and QL were capable of extracting from . LBR archives.  . LBR is an abbreviation of "Library", and, resembling the . tar file format, member files were only stored in the . LBR file, not compressed.  As transfer of LBR files by modem was common, it was typical practice for archiving a collection of files to compress them using the SQ or CRUNCH programs then store them in an . LBR archive, or else (more rarely) store the files in the LBR archive, then use SQ or CRUNCH to compress the archive.  A compressed LBR archive file was given the extension ". LQR" (if squeezed) or ". LZR" (if crunched); however, it was more common to compress the members of the archive than to compress the archive as a whole.

Damage mechanics: Damage mechanics is concerned with the representation, or modeling, of damage of materials that is suitable for making engineering predictions about the initiation, propagation, and fracture of materials without resorting to a microscopic description that would be too complex for practical engineering analysis.  Damage mechanics illustrates the typical engineering approach to model complex phenomena.  To quote Dusan Krajcinovic, "It is often argued that the ultimate task of engineering research is to provide not so much a better insight into the examined phenomenon but to supply a rational predictive tool applicable in design".  Damage mechanics is a topic of applied mechanics that relies heavily on continuum mechanics.  Most of the work on damage mechanics uses state variables to represent the "effects" of damage on the stiffness and remaining life of the material that is damaging as a result of thermomechanical load and ageing.  The state variables may be measurable, e.g., crack density, or inferred from the "effect" they have on some macroscopic property, such as stiffness, coefficient of thermal expansion, remaining life, etc.  The state variables have conjugate thermodynamic forces that motivate further damage.  Initially the material is pristine, or "intact".  A damage activation criterion is needed to predict damage initiation.  Damage evolution does not progresses spontaneously after initiation, thus requiring a damage evolution model.  In plasticity like formulations, the damage evolution is controlled by a hardening function but this requires additional phenomenological parameters that must be found through experimentation, which is expensive, time consuming, and virtually no one does.  On the other hand, micromechanics of damage formulations are able to predict both damage initiation and evolution without additional material properties.

Integer triangle: An integer triangle or integral triangle is a triangle all of whose sides have lengths that are integers.  A rational triangle can be defined as one having all sides with rational length; any such rational triangle can be integrally rescaled (can have all sides multiplied by the same integer, namely a common multiple of their denominators) to obtain an integer triangle, so there is no substantive difference between integer triangles and rational triangles in this sense.  Note however, that other definitions of the term "rational triangle" also exist: In 1914 Carmichael used the term in the sense that we today use the term Heronian triangle; Somos uses it to refer to triangles whose ratios of sides are rational; Conway and Guy define a rational triangle as one with rational sides and rational angles measured in degrees—in which case the only rational triangle is the rational-sided equilateral triangle.

Morton Gurtin: Morton E. Gurtin is a mechanical engineer who became a mathematician and "de facto" mathematical physicist.  He is an emeritus professor of mathematical sciences at Carnegie-Mellon University, where for many years he held an endowed chair as the Alumni Professor of Mathematical Science.  His main work is in materials science, in the form of the mathematical, rational mechanics of non-linear continuum mechanics and thermodynamics, in the style of Clifford Truesdell and Walter Noll, a field also known under the combined name of "continuum thermomechanics".  He has published over 250 papers, many among them in Archive for Rational Mechanics and Analysis, as well as a number of books.

Archive for Rational Mechanics and Analysis: The Archive for Rational Mechanics and Analysis is a scientific journal that is devoted to research in mechanics as a deductive, mathematical science.  The current editors in chief of the journal are John M. Ball and Richard D. James.  It was founded in 1956 by Clifford Truesdell when he moved from Indiana University to Johns Hopkins and lost control of a similar journal he had founded a few years previously, the "Journal of Rational Mechanics and Analysis" (now the "Indiana University Mathematics Journal").

Lumped damage mechanics: Lumped damage mechanics or LDM is a branch of structural mechanics that is concerned with the analysis of frame structures.  It is based on continuum damage mechanics and fracture mechanics.  It combines the ideas of these theories with the concept of plastic hinge LDM can be defined as the fracture mechanics of complex structural systems.  In the models of LDM, cracking or local buckling as well as plasticity are lumped at the inelastic hinges.  As in continuum damage mechanics, LDM uses state variables to represent the effects of damage on the remaining stiffness and strength of the frame structure.  In reinforced concrete structures, the damage state variable quantifies the crack density in the plastic hinge zone; in unreinforced concrete components and steel beams, it is a dimensionless measure of the crack surface; in tubular steel elements, the damage variable measures the degree of local buckling The LDM evolution laws can be derived from continuum damage mechanics or fracture mechanics.  In the latter case, concepts such as the energy release rate or the stress intensity factor of a plastic hinge are introduced.  LDM allows for the numerical simulation of the collapse of complex structures with a fraction of the computational cost and human effort of its continuum mechanics counterparts.  LDM is also a regularization procedure that eliminates the mesh-dependence phenomenon that is observed in structural analysis with local damage models

Supporting paragraphs: Morton Gurtin Archive for Rational Mechanics and Analysis
Answer: mathematical science