Non-uniform Hardening Constitutive Model for Compressible Orthotropic Materials with Application to Sandwich Plate Cores

A constitutive model for the elastic-plastic behavior of plastically compressible orthotropic materi- als is proposed based on an ellipsoidalyield surface with evolving ellipticity to accommodate non-uniform hard- ening or softening associated with stressing in different directions. Themodel incorporatesrate-dependencearis- ing from material rate-dependence and micro-inertial ef- fects. The basic inputs are the stress-strain responses under the six fundamental stress histories in the or- thotropicaxes. Special limitsofthemodel includeclassi- cal isotropichardening theory, the Hill model for incom- pressible orthotropic solids, and the Deshpande-Fleck model for highly porous isotropic foam metals. A pri- mary motivation is application to metal core structure in sandwich plates wherein the core is modeled by a con- tinuumconstitutivemodel. The constitutivemodel is im- plemented withinafinite element framework to represent the behavior of square honeycomb metal cores of sand- wich plates subject to quasi-static and dynamic loads. Input identification is illustrated for numerical formula- tionsthatemployoneelement throughthecorethickness. Representationsof the core with oneelement through the thickness are shown to be able to capture most of the im- portant influences of nonlinear core behavior on overall response of sandwich plates under both quasi-static and dynamic loadings. a general class of plastically compressible, orthotropic solids based on an ellipsoidal yield surface which incor- porates non-uniform hardening. The constitutive model has considerable flexibility. Limits of the model include many of the important phenomenologicalconstitutivere- lations for elastic-plastic solids: classical isotropic plas- ticity, Hill's theory for incompressible orthotropic plas- ticity, and the Deshpande-Fleck theory for highly com- pressible isotropic metal foams. A salient feature of the formulation is its ability to model distinct hardening or softening behaviors under different stressing conditions, with applicationto both plasticallyincompressiblesolids and highly compressible materials. For application to metal sandwich cores, the approach requires inputsspecifyingthe stress-strainbehaviorchar- acterizing single component stressing in orthotropicaxes for each of the six components of stress. These basic inputs can be obtained from theoretical models, exper- imental data or numerical simulations, or combinations of all three. Once the inputs are characterized, the con- stitutive model can be used to represent the core in con- nection with standard finite element codes. In this paper, the commercial code ABAQUS Explicithas been used in connection with a user-supplied subroutinethat has been constructed based on the constitutive model. The pa- per illustrates the process of identifying the input stress- strain data for square honeycomb cores. It also demon- strates that representing the core by elements extending all the way through the core can be accurate and highly efficient in the analysis of sandwich plates deformed un- der quasi-static and dynamic loads to large deflections. Simulations based on full three-dimensional meshing of the core demonstrate the validity of the approach. The present paper continues the effort underway for sev- eral years by a number of groups to develop contin- uum constitutiverelations to characterize a range of core structures and to validate them for structural applica- tions (Deshpande, Fleck and Ashby (2001); Hanssen, Langseth and Hopperstad (2002); Mohr and Doyoyo