Eigenstrain

Eigenstrain is a concept used in mechanics and materials science to describe the inelastic deformation of a material that occurs independent of external stress. It represents a self-equilibrated strain within a body. This means that if the body were isolated, the eigenstrain would exist without any applied forces or tractions on its boundaries. The term "eigen" originates from the German word for "own" or "characteristic," highlighting that this strain is an intrinsic property or characteristic of the material or its internal state.

Eigenstrain can arise from various sources, including phase transformations, plastic deformation, thermal expansion, swelling due to moisture absorption, or the presence of inclusions. For instance, if a material undergoes a phase change that involves a volume expansion, this expansion would manifest as an eigenstrain. Similarly, plastic deformation, where the material permanently deforms beyond its elastic limit, introduces an eigenstrain.

The significance of eigenstrain lies in its ability to induce internal stresses even in the absence of external loads. When an eigenstrain is present within a body, it attempts to deform the material. However, because the eigenstrain is self-equilibrated, it cannot cause overall rigid body motion. Instead, it generates internal stress fields that resist this deformation, leading to a state of stress within the material. This internal stress can then interact with externally applied stresses, influencing the material's overall mechanical response. Understanding and quantifying eigenstrain is crucial for analyzing the behavior of materials under various conditions, particularly in situations involving complex material microstructures or internal transformations.