Final answer:
The right Cauchy-Green deformation tensor is a mathematical concept used to describe the deformation of materials in three-dimensional space when they are subjected to forces.
Step-by-step explanation:
The right Cauchy-Green deformation tensor is a tensor that describes the deformation of a material in three-dimensional space. This tensor is important in the context of continuum mechanics and material science, as it helps to quantify the deformation of a body when subjected to forces. Deformation in materials involves concepts such as strain, stress, and the elastic free energy, which are all interconnected. Strain refers to the changes in the shape or size of an object due to applied forces, which is resisted by the material's internal forces, resulting in stress. The stress tensor, together with the material's elastic properties like the elastic moduli, can describe the elastic behavior of different materials under various forms of stress, such as tension, compression, and shear.