Applications of tensor functions to the formulation of yield criteria for anisotropic materials |
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| Institution: | 1. Pontifical Catholic University of Rio de Janeiro, PUC-Rio, Rua Marquês de São Vicente 225, Rio de Janeiro 22451-900, Brazil;2. Federal University of South and Southeast of Pará, UNIFESSPA, Avenida dos Ipês s/n, Marabá 68500-000, Brazil;1. Structure Institute, National University of Tucumán, Av. Independencia 1800, San Miguel de Tucumán CP 4000, Argentina;2. GIDMA, Department of Civil Engineering, Regional Faculty of Córdoba, National Technological University, Maestro M. López esq. Cruz Roja, Córdoba X5016ZAA, Argentina;3. CONICET, Av. Rivadavia 1917, Buenos Aires, Argentina;1. Fields, Gravity & Strings, CTPU, Institute for Basic Science, Daejeon 34126, Republic of Korea;2. Department of Physics & Astronomy, University of Lethbridge, Alberta, T1K 3M4, Canada;3. School of Physics & Astronomy, Seoul National University, Seoul 08826, Republic of Korea |
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| Abstract: | Yielding of anisotropic materials can be characterized by yield criteria which are scalar-valued functions of the stress tensor and of material tensors, for instance, of rank two or four, characterizing the anisotropic properties of the material. Because of the requirement of invariance, a yield criterion can be expressed as a single-valued function of the integrity basis. In finding an integrity basis involving the stress tensor and material tensors, the constitutive equations are first formulated based on the tensor function theory. Since the plastic work characterizes the yield process, we read from this scalar expression the essential invariants to formulate a yield criterion. Some examples for practical use are discussed in detail. |
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