Theory of residual stresses with application to an arterial geometry

• Autorzy: Klarbring A. , Olsson T. , Stalhand J.
• Konferencja: Solid Mechanics Conference (35 ; 04-08.09.2006 ; Cracow, Poland)
• Języki publikacji: EN

Abstrakty

EN

This paper presents a theory of residual stresses, with applications to biomechanics, especially to arteries. For a hyperelastic material, we use an initial local deformation tensor K as a descriptor of residual strain. This tensor, in general, is not the gradient of a global deformation, and a stress-free reference configuration, denoted ..., therefore, becomes incompatible. Any compatible reference configuration ... will, in general, be residually stressed. However, when a certain curvature tensor vanishes, there actually exists a compatible and stress-free configuration, and we show that the traditional treatment of residual stresses in arteries, using the opening-angle method, relates to such a situation. Boundary value problems of nonlinear elasticity are preferably formulated on a fixed integration domain. For residually stressed bodies, three such formulations naturally appear: (i) a formulation relating to ... with a non-Euclidean metric structure; (ii) a formulation relating to ... with a Euclidean metric structure; and (iii) a formulation relating to the incompatible configuration ... . We state these formulations, show that (i) and (ii) coincide in the incompressible case, and that an extra term appears in a formulation on ... , due to the incompatibility.

Słowa kluczowe

EN

residual stresses; biomechanics; balance and constitutive laws; arterial geometry; Riemannian manifold; boundary value; Piola identity

PL

naprężenia własne; biomechanika; równania konstytutywne; geometria tętnic; rozmaitość Riemanna; wartość brzegowa; tożsamość Piola

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2007
• Tom: Vol. 59, nr 4-5
• Strony: 341--364
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Klarbring A.

autor

Olsson T.

autor

Stalhand J.

• Division of Mechanics Institute of Technology, Linkoping University SE 581 83 Linkoping, Sweden

Bibliografia

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