001463412 000__ 04839cam\a2200613\i\4500 001463412 001__ 1463412 001463412 003__ OCoLC 001463412 005__ 20230601003319.0 001463412 006__ m\\\\\o\\d\\\\\\\\ 001463412 007__ cr\cn\nnnunnun 001463412 008__ 230425s2023\\\\sz\a\\\\ob\\\\001\0\eng\d 001463412 019__ $$a1376922728$$a1379548681 001463412 020__ $$a9783031296321$$qelectronic book 001463412 020__ $$a303129632X$$qelectronic book 001463412 020__ $$z9783031296314 001463412 020__ $$z3031296311 001463412 0247_ $$a10.1007/978-3-031-29632-1$$2doi 001463412 035__ $$aSP(OCoLC)1377284858 001463412 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDX 001463412 049__ $$aISEA 001463412 050_4 $$aQA808.2$$b.K67 2023 001463412 08204 $$a531/.7$$223/eng/20230425 001463412 1001_ $$aKorobeynikov, Sergey,$$eauthor. 001463412 24510 $$aObjective algorithms for integrating hypoelastic constitutive relations based on corotational stress rates /$$cSergey Korobeynikov, Alexey Larichkin. 001463412 264_1 $$aCham, Switzerland :$$bSpringer,$$c[2023] 001463412 300__ $$a1 online resource (xiii, 107 pages) :$$billustrations (some color). 001463412 336__ $$atext$$btxt$$2rdacontent 001463412 337__ $$acomputer$$bc$$2rdamedia 001463412 338__ $$aonline resource$$bcr$$2rdacarrier 001463412 4900_ $$aSpringerBriefs in applied sciences and technology, Continuum mechanics 001463412 504__ $$aIncludes bibliographical references and index. 001463412 5050_ $$a1. Introduction -- 2. Preliminaries -- 3. Incremental tensors and the incremental objectivity of tensors -- 4. Incrementally objective algorithms for integrating CRs for Hooke-like hypoelastic models in the Eulerian form -- 5. Absolutely objective algorithms for integrating CRs for Hooke-like hypoelastic models -- 6. Comparative analysis and veriļ¬cation of objective algorithms -- 7. Concluding remarks. A. Flowcharts of objective algorithms for integrating hypoelastic constitutive relations -- B. Algorithms for determining the polar decomposition -- C. The Rodrigues formula for determining an incremental rotation tensor. 001463412 506__ $$aAccess limited to authorized users. 001463412 520__ $$aThis book provides readers with a deep understanding of the use of objective algorithms for integration of constitutive relations (CRs) for Hooke-like hypoelasticity based on the use of corotational stress rates. The purpose of objective algorithms is to perform the step-by-step integration of CRs using fairly large time steps that provide high accuracy of this integration in combination with the exact reproduction of superimposed rigid body motions. Since Hooke-like hypoelasticity is included as a component in CRs for elastic-inelastic materials (e.g., in CRs for elastic-plastic materials), the scope of these algorithms is not limited to hypoelastic materials, but extends to many other materials subjected to large deformations. The authors performed a comparative analysis of the performance of most currently available objective algorithms, provided some recommendations for improving the existing formulations of these algorithms, and presented new formulations of the so-called absolutely objective algorithms. The proposed book will be useful for beginner researchers in the development of economical methods for integrating elastic-inelastic CRs, as well as for experienced researchers, by providing a compact overview of existing objective algorithms and new formulations of these algorithms. The book will also be useful for developers of computer codes for implementing objective algorithms in FE systems. In addition, this book will also be useful for users of commercial FE codes, since often these codes are so-called black boxes and this book shows how to test accuracy of the algorithms of these codes for integrating elastic-inelastic CRs in modeling large rotations superimposed on the uniform deformation of any sample. 001463412 588__ $$aDescription based on online resource; title from digital title page (viewed on May 25, 2023). 001463412 650_0 $$aContinuum mechanics$$xMathematics. 001463412 650_0 $$aCalculus of tensors. 001463412 655_0 $$aElectronic books. 001463412 7001_ $$aLarichkin, Alexey,$$eauthor. 001463412 77608 $$iPrint version: $$z3031296311$$z9783031296314$$w(OCoLC)1371585155 001463412 852__ $$bebk 001463412 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-29632-1$$zOnline Access$$91397441.1 001463412 909CO $$ooai:library.usi.edu:1463412$$pGLOBAL_SET 001463412 980__ $$aBIB 001463412 980__ $$aEBOOK 001463412 982__ $$aEbook 001463412 983__ $$aOnline 001463412 994__ $$a92$$bISE