Stress resultant constitutive laws for plates and shells of plastic materials and its applications to sheet metal forming.

A stress resultant theory is developed to efficiently model the nonlinear material behavior of plates and shells. This theory is expected to save computer time and memory compared to the three-dimensional theory, which is based on stresses. The theory includes a stress resultant constitutive law for deformation plasticity power-law materials, and a yield function, a flow rule, and a hardening rule in the stress resultant space for elastic-plastic power-law materials. First, a stress resultant constitutive law is developed for power-law hardening materials. With the Kirchhoff assumption and the J$\sb2$ deformation plasticity theory, the constitutive law is derived under proportional straining conditions for thin plates. In analogy to the work of Storen and Rice, a flow rule is proposed to define plastic flow rates. A yield function, defined as the equivalent stress resultant, is approximated in a quadratic form of stress resultant invariants with two parameters. These parameters are determined from complementary potential surfaces, which are constructed using the stress resultant constitutive law. With normality of plastic flow, this yield function leads to an equivalent work-conjugate increment of plastic generalized strains. A hardening rule, which describes the relation between the equivalent stress resultant and the equivalent plastic generalized strain, is derived using the stress resultant constitutive law. This stress resultant theory is then examined in proportional loading, pre-loading, and unloading cases. Next, a stress resultant theory is developed for elastic-plastic materials. Under the assumption that the generalized strain rate can be additively decomposed into elastic and plastic parts, the incremental form of the constitutive law is derived with the normality, the yield function, and the hardening rule. Based on this stress resultant theory, its finite element formulation is constructed and a finite element program is developed to simulate a hemispherical punch stretching operation. The results of the simulation are quite acceptable from engineering viewpoints.PhDApplied MechanicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105672/1/9208516.pdfDescription of 9208516.pdf : Restricted to UM users only