A Coupled 1D–3D Finite Element Framework for Calibrating Nonlocal-in-Time Hereditary Damping in GFRP Frame Structures Under Seismic Excitation

Abstract

Classical local damping models, viscous (Rayleigh) or hysteretic assume that the instantaneous dissipative force at a point depends only on the current velocity, an assumption increasingly at odds with the internal-friction behavior of fiber-reinforced polymer composites, whose energy dissipation is governed by the entire deformation history rather than its present state. This paper develops and cross-validates a finite element framework for nonlocal-in-time (hereditary) damping in which the damping force is expressed as a convolution of the velocity history with a Gaussian memory kernel governed by a single relaxation (“nonlocality”) parameter, . A planar Euler–Bernoulli finite element model of a glass-fibre-reinforced-plastic (GFRP) portal frame is assembled and the resulting hereditary equation of motion is integrated using an implicit Newmark scheme extended with a discretized convolution sum. Because  cannot be measured directly, we propose a dual-fidelity calibration strategy that matches the transient nodal response of the reduced-order one-dimensional (1D) model against a full three-dimensional (3D), modal-superposition finite element model of the same frame. The procedure yields a calibrated value  for the GFRP material considered here, and this single value is subsequently shown to reproduce the reference 3D response without re-calibration for a second frame of different span and column height. The calibrated model is then used to compute the seismic response of the GFRP frame to the recorded ground-acceleration history of the 28 March 2025, $M_w$7.9 Myanmar earthquake, and the result is contrasted with the response obtained from unscaled, effectively local, damping parameters. The comparison illustrates that neglecting hereditary (memory) effects can materially misrepresent the seismic displacement and velocity demand on composite frame structures. The proposed 1D–3D calibration strategy offers a computationally efficient route to introducing physically grounded hereditary damping into frame-type composite structures without requiring detailed three-dimensional time-history analysis at every design iteration.