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A reverse updated Lagrangian finite element formulation for determining material properties from measured force and displacement data. (English) Zbl 1309.74072

Summary: The mechanical response of solids exhibiting complex material behavior has traditionally been determined by fitting constitutive models of specified functional form to experimentally derived force-displacement (stress-strain) data. However, characterizing the nonlinear mechanical behavior of complex materials requires a method of quantifying material behavior that is not restricted by a specific constitutive relation. To this end, a new method, termed the reverse updated Lagrangian finite element method (RULFEM), which is based on the three-dimensional displacement field of the deformed solid and the finite element method, is developed for incrementally linear materials. Using the RULEFM, the body is discretized by finite elements and its material properties are determined element-wise, i.e., the properties are assumed to be uniform at the element level and may vary from one element to another. The validity of RULFEM is demonstrated by three noise-free numerical examples and three numerical examples with various input noise levels. Two methods to assess the global and local errors of the results due to error in the measured input data (noisy data) are also discussed.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74G75 Inverse problems in equilibrium solid mechanics
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