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A system of partial differential equations (PDEs) is derived to compute thefull-field stress from an observed kinematic field when the flow rule governingthe plastic deformation is unknown. These equations generalize previouslyproposed equations that assume pure plastic behavior without elasticity. Amethod to numerically solve these equations is also presented. In addition toforce balance, the equations are derived from the elastic-plastic decompositionof the deformation gradient, the assumption of isotropy, and the assumptionthat the function mapping the elastic strain to stress is known. The system ofequations can be directly applied to complex geometries, finite deformation,non-linear elasticity and plasticity, compressible materials, rate dependentmaterials, and a variety of hardening laws. This system of PDEs is non-linearand time dependent. Furthermore, it overcomes an important prior limitation: itcan be directly applied to cases where some regions of a body are elasticallydeforming while others are elasto-plastically deforming. A two-dimensional casestudy of necking in a uniaxial tensile specimen is investigated to illustrateand validate the method. The governing equations are numerically solved usingstrain fields output from a finite element simulation and validated againstthis same simulation showing accurate results.

Partial differential equations to determine elasto-plastic stress-strain behavior from measured kinematic fields