Summary
A finite element investigation of the problem of large strains, formulated in terms of true stress and logarithmic strain, is presented. Large displacements as well as material nonlinearity are incorporated in the formulation. The concept of true stress and logarithmic strain, originally defined for a uniaxial state of stress, is applied to the formulation of the problem. Tetrahedra with linear variations of displacements are employed as finite elements. Two incremental solution procedures — the initial load approach and the tangential stiffness approach — are discussed. The proposed concept is applied to the elastoplastic problem of the uniaxial stretching and shortening of a rectangular plate under the plane state of stress.
Zusammenfassung
In diesem Aufsatz wird das Problem großer Verzerrungen, formuliert mittels wahrer Spannungen und logarithmischer Verzerrungen, mit Hilfe der Methode der Finiten Elemente untersucht. In der Formulierung werden sowohl große Verschiebungen als auch physikalische Nichtlinearität berücksichtigt. Das Konzept der wahren Spannungen und logarithmischen Verzerrungen, das ursprünglich für den eindimensionalen Spannungszustand entwickelt worden ist, wird auf die Formulierung der Probleme angewendet. Als Finite Elemente gelangen Tetraeder zum Einsatz. Lineare Verschiebungsansätze werden gewählt. Zwei verschiedene inkrementelle Lösungsverfahren — die Methode der Anfangslasten sowie das Tangentensteifigkeitsverfahren — werden diskutiert. Das vorgeschlagene Konzept wird auf das elastoplastische Problem der eindimensionalen Ausdehnung und Verkürzung von einer rechteckigen Platte im ebenen Spannungszustand angewendet.
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Dedicated to Professor John H. Argyris in honour of his 65th birthday.
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Tanaka, M. Finite element investigation of the problem of large strains, formulated in terms of true stress and logarithmic strain. Acta Mechanica 34, 129–141 (1979). https://doi.org/10.1007/BF01176262
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DOI: https://doi.org/10.1007/BF01176262