Modern day imaging techniques and algorithms enable measurement of strain fields with high spatial and temporal resolution. Since the material response is determined by the deformation and stress field, we want to calculate the stress field based on the obtained deformation field. This in known as the inverse problem. The existing approaches to solving the inverse problem are generally overdetermined and require the use of statistical methods. The solution is performed by minimizing the cost function, which includes the differences between the measured and calculated values. Such a solution is difficult from the point of view of implementation, accuracy and computational time, and it is also necessary to assume a constitutive model. This thesis presents a deterministic formulation of the inverse problem, which is based on a single assumption – the codirectionality assumption. The advantage of such an approach is that we arrive at a system of equations that can be solved exactly without an assumed constitutive model for a wide range of materials. We developed a finite element equasion for solving the inverse problem and confirmed the performance of the method with a numerical experiment. We found that the inverse problem can be solved in this way with comparable accuracy and significantly faster than with existing approaches.
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