Some Indentities for the Gradient of the Principal Invariants, Traces and Determinants via Grassmann Calculus |
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Authors: | Antônio Francisco Neto |
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Institution: | 1. Departamento de Engenharia de Produ??o, Administra??o e Economia, Escola de Minas, UFOP, Campus Morro do Cruzeiro, 35400-000, Ouro Preto, MG, Brazil
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Abstract: | Let A be a second order tensor in a finite dimensional space. In this work we determine the gradient of the principal invariants of A and obtain some trace and determinant identities using only some standard rigorous statements concerning Grassmann calculus. We recover some of the results of Dui et al. (J. Elast. 75:193–196, 2004) and of Truesdell and Noll (The Non-linear Field Theories of Mechanics, Springer, Berlin, 2002) and solve an old problem proposed in SIAM Review concerning a determinant identity from a new perspective in a concise and simple manner. |
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