A memory-saving algorithm with variable increment size for fractional viscoelastic models of asphalt concrete in finite element analysis

Abstract

Finite element analysis of the fractional viscoelastic model of asphalt concrete (AC) is typically performed on small specimens, with algorithms that suffer from high memory consumption and low computational efficiency, limiting their application to large-scale structures. This paper proposes a memory-saving algorithm with variable increment size for fractional viscoelastic models of AC in finite element analysis. First, the parameters of the modified fractional Zener model (MFZM) of AC were identified from the experiments. Subsequently, based on the differential formula of MFZM, the incremental iteration method, and the non-classical method, a memory-saving algorithm with variable increment size for MFZM was proposed, followed by the complied user material subroutine. The efficiency and accuracy of the proposed algorithm were verified by the Euler algorithm and the Grünwald-Letnikov (GL) method. Finally, a mechanical analysis of asphalt pavement using MFZM was conducted. The results show that the proposed algorithm does not require time domain relaxation or creep expressions, only needs to store the current mechanical responses, and supports variable increment size, thus making it superior to the existing method. The influence of the MFZM parameter on the mechanical response of pavement structures is related to the structure type and mechanical indexes.