Final answer:
The components of the Green-Lagrange strain tensor are computed using the formula Eij = (1/2)(Uij + Uji + UkjUki), where Uij are the components of the deformation gradient tensor and the sum is taken over repeated indices.
Step-by-step explanation:
The Green-Lagrange strain tensor is a measure of finite strains at a point in a deformed material body. It computes the strains taking into account the undeformed and deformed configurations, which makes it especially useful for large deformations. The tensor is a second-order tensor and its components can be derived as follows:
Eij = (1/2)(Uij + Uji + UkjUki)
where Eij represent the components of the Green-Lagrange strain tensor, Uij are the components of the deformation gradient tensor, and UkjUki indicate the product of deformation gradient tensor components implying a sum over repeated indices k. The deformation gradient tensor itself is defined based on the displacement of particles from their initial positions, and the overall strain tensor accounts for both the diagonal (stretching or compression) and off-diagonal (shearing) components of the strain.