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Recently, a widely applicable system of hyperbolic partial differentialequations has been derived that enables the deterministic computation of a fullheterogeneous stress field from a measured deformation field, for example, froma strain field obtained via digital image correlation. This information enablesthe determination of material properties, making this approach an alternativeto finite element model updating or the virtual fields method. This articlefocuses on developing a finite volume discretization of this system ofequations to address instabilities that arise from violations of theCourant-Friedrichs-Lewy condition. The developed discretization enables thesystem of equations to be applied to irregular geometries and finitedeformation. We determine how, in general, one may translate knowledge of thetraction at the boundary into boundary conditions, so that the numerical methodcan be applied to a variety of loading conditions. We analyse the solutionstructure in the case of deformation discontinuities, and the results areapplied to account for discontinuities at the interfaces between finite volumes(this has relevance to other applications such as composite materials).Interestingly, the discontinuities cause reflection and transmission of theprincipal stresses.  The finite volume discretization is validated using data output fromcommercial finite element software. Furthermore, the discretization is appliedto an experimental uniaxial tension test with plastic deformation and necking.The strain field is obtained using digital image correlation, and the stressfield is computed using the developed finite volume discretization. Together,these give the stress-strain behavior for each material element.

On discontinuities when computing the stress-field from the strain: a finite volume discretization