Devising smart finite elements for adaptive analysis of inverse structural problems

Inverse problems have recently attracted a lot of attention. Many challenges in the present engineering practice necessitate dealing with problems that fall under this category. Identification of material properties and models is one of the recent examples of inverse problems. Material models are the key ingredients to accurately capture the global mechanical response of structural systems. Conventional material modeling uses mathematical formulas to describe material behavior. These functions are not expected to exactly reproduce global experimental response. Furthermore, the increase in the material complexity results in an increase in the number of model parameters to be identified, which in turn limits the practicality of implementation of such models. Alternatively, the measured global response at specific domain or surface points can be used to guide the nonlinear structural analysis in the lack of a reliable material model. By imposing the measured displacement at the monitoring points on to the solution that uses an approximate material model, a set of modified stress-strain data points are generated throughout the domain. The stress-strain data point at the highly stressed integration point is then selected to develop an adaptively improved material model. The partially improved material model is then used within a multi-pass incremental non-linear finite element analysis in order to recover the actual material response. Plasticity formulation is used to build the nonlinear material matrices. As a result, the discrepancy between the measured and the predicted structural response at the monitoring points is gradually minimized leading to suitably predicted material models. The applicability of the proposed approach is first demonstrated by solving inverse problems of simple mechanical models and structural systems. Then, the proposed method is extended to a 2D finite element procedure to study its applicability in predicting the constitutive behavior of continuum 2D problems with coupled stresses and strains. Another inverse formulation for predicting the nonlinear material response of fiber reinforced polymer composites from angle-ply laminates response is presented. The data from uniaxial 0° degree coupons, (+/-theta 1°)n and (+/-theta2°) n angle-ply specimens is utilized to determine material response. Excellent results are obtained showing great potential of the present approach in health monitoring and nondestructive testing applications.