Almansi's theorem, also known as the Almansi strain tensor, is a fundamental concept in the field of elasticity. It describes the relationship between the strain tensor and the displacement field in a deformable body. According to Almansi's theorem, the strain tensor can be expressed as the difference between the symmetric part of the displacement gradient tensor and half of its skew-symmetric part. Mathematically, it can be written as: ε = 1/2 (grad(u) + grad(u)^T) - 1/2 (grad(u) - grad(u)^T) where ε represents the strain tensor and grad(u) is the displacement gradient tensor. This theorem provides a useful way to decompose the strain tensor into its symmetric and skew-symmetric components, allowing for easier analysis of elastic deformations in solids. It is widely used in elasticity literature to understand and predict material behavior under different loading conditions. # Who proved Almansi theorem The Almansi theorem is named after the Italian mathematician Angelo Almansi. He is credited with proving the theorem in the late 19th century. [[Gautam Dasgupta]] proved the [Almansi theorem](app://obsidian.md/Almansi%20theorem) in anisotropic elasticity and developed the finite element modeling of infinite domains.