Explicit analysis technique for nonlinear inverse mechanics problems

Abstract

Nonlinear material models are conventionally used in forward analysis to predict the global mechanical response of boundary value problems. Such models are not expected to exactly reproduce global experimental response in all cases. Accordingly, the measured global response at specific domain or surface points can guide an inverse nonlinear structural analysis to successively recover a representative material model. By assuming an initial set of stress-strain data points, the load-displacement response at the control points is computed in a forward incremental analysis without iterations. This analysis retains the stresses at the integration points. The corresponding strains are not expected to be accurate since the computed displacements are not anticipated to match the measured displacements at the control points. Therefore, a conjugate incremental displacement analysis is performed at the same load steps to correct for displacements and strains everywhere by matching the measured displacements at the control points. It is found that the predicted stress-strain data set at the most highly stressed integration point provides the most accurate representation of an improved material model. This data set is used in the next two-phase incremental analysis pass as the material model. The process is repeated until the forward analysis phase reproduces the measured displacements at the control points requiring no corrections. Accordingly, the selection of a single stress-strain data set yields an explicit recovery of the nonlinear elasticity material model without any interpolation or averaging schemes, which significantly reduces data storage and computational effort. The applicability of the present explicit approach is demonstrated on simple mechanical models, a skeletal structural system and a 2D finite element mesh.