indicialresponse

Indicial response is the time-dependent response of a physical system to a sudden, localized excitation, typically analyzed in a semi-infinite or otherwise simplified domain. It is used to characterize how a material or field variable responds to a unit step input applied at a boundary or point, before the full geometrical constraints influence the field. The concept appears in areas such as diffusion, heat conduction, and viscoelasticity, where linear systems allow the response to be summarized by a single function that can be used to construct responses to arbitrary inputs through convolution.

In linear, time-invariant problems, the indicial response function i(t) describes the output produced by a unit step input. The actual response to any input can then be obtained by convolving the input with i(t). The derivative of the indicial response corresponds to the impulse response in many formulations. Thus, the indicial function provides a compact way to capture the time-dependent behavior of the system’s boundary-to-field transfer characteristics.

Applications include the creep and relaxation analysis of viscoelastic materials, transient heat or mass diffusion from a boundary, and related problems in geophysics and contact mechanics. It is particularly useful when the geometry can be approximated as semi-infinite and the material behaves linearly, enabling the construction of solutions for complex loading histories via superposition.

Limitations include nonlinearity, finite or complex geometries, and boundary conditions that deviate from the assumed setup. In such cases, the indicial response may depend on position or orientation, and numerical methods or more detailed models are required.