On path-independent integrals within the linear theory of elasticity
Source abstract
Abstract
Conservation laws and associated path-independent integrals play a dominant role in field theories ranging from theoretical physics to applied engineering. Especially, material conservation laws are widely used to assess structural components with flaws like defects or cracks. Within the linear theory of elasticity, a complete set of conservation laws are derived by employing the so-called Neutral-Action method. An illustrative application is discussed.
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Research context
OpenAlex topics: Numerical methods in engineering · Elasticity and Material Modeling · Fatigue and fracture mechanics
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References (11)
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1. Bessel-Hagen E (1921) Über die erhaltungssätze der elektrodynamik. Math Ann 84: 256–27610.1007/BF01459410 ↗
2. Budiansky B, Rice JR (1973) Conservation laws and energy-release rates. J Appl Mech 40: 201–20310.1115/1.3422926 ↗
3. Honein T, Chien N, Herrmann G (1991) On conservation laws for dissipative systems. Phys lett A 155: 223–22410.1016/0375-9601(91)90472-K ↗
4. Kienzler R (1993) Konzepte der bruchmechanik. Vieweg, Braunschweig
5. Kienzler R, Herrmann G (2000) Mechanics in material space. Springer, Berlin10.1007/978-3-642-57010-0 ↗
6. Murakami Y (1987) Stress intensity factors handbook. Pergamon, Oxford
7. Noether E (1918) Invariante variationsprobleme. Nachrichten der königlichen gesellschaft der wissenschaften. Göttingen 2: 235–257
8. Olver PJ (1984) Conservation laws in elasticity. II. Linear homogeneous isotropic elasticity. Arch Ration Mech Anal 85: 131–16010.1007/BF00281448 ↗
9. Olver PJ (1998) Applications of lie groups to differential equations, 2nd edn. Springer, New York
10. Rice JR (1968) A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J Appl Mech 35: 379–38610.1115/1.3601206 ↗
11. Tada H, Paris PC, Irwin GR (1973) The stress analysis of cracks handbook. Hellertown, Pennsylvania