  This paper proposes a modeling structure for the relativistic constitutive
equations of inelastic deformation in materials moving at high speeds. While
the theory of relativity has successfully approximated material motion in
space-time, most existing models only consider elastic behavior, neglecting
inelastic deformation. A comprehensive relativistic inelasticity model is
necessary to objectively measure inelastic deformation for observers with
varying velocities, including those near the speed of light. The proposed model
expands classical deformation tensors to four-dimensional tensors in
space-time, referred to as relativistic Cauchy-Green deformation tensors. By
introducing constitutive equations based on these tensors, objective
measurements of inelastic deformation are achieved while satisfying the second
law of thermodynamics. An illustrative example demonstrates the application of
this theory and explains the physical interpretations of the model. Moreover,
it is shown that the proposed relativistic inelasticity model converges to a
classical inelasticity model under slower motion compared to the speed of
light.
