Finite element stress formulation for dynamic elastic-plastic analysis |
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Authors: | Johnny H Biffle Eric B Becker |
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Affiliation: | Applied Mechanics Division I, Sandia Laboratories, Albuquerque, New Mexico 87115, USA;Aerospace Engineering and Engineering Mechanics Department University of Texas at Austin, Austin, Texas 78712, USA |
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Abstract: | The solution to wave propagation problems in solids with elastic-plastic material properties is obtained by using the finite element method directly in terms of the stresses. A variational principle due to Gurtin is modified by including a plastic strain tensor in the constitutive relationship. The resulting finite element equations, which represent the strain-displacement equations written in terms of the stresses, are simultaneous integral equations in time. With a transformation of variables, a set of simultaneous differential equations is obtained of the form, where is a symmetric positive-semidefinite matrix, and is a symmetric positive-definite matrix. The stresses and the plastic strains are represented by and , respectively.Finite element equations are developed for an axisymmetric ring element with an arbitrary quadrilateral cross section in which the stresses and the plastic strains vary linearly along the sides of the elements. The equations are numerically integrated with respect to time by Newmark's generalized acceleration method.An iterative procedure is presented, which uses the finite element strain-displacement equations and the plasticity relationships, to determine the state of stress at the end of the time step. Several examples are used to demonstrate the solution technique for elastic and elastic-plastic problems. |
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