Domain heterogeneities in geomaterial modeling: Integrating multi-scale FEMxDEM and second-gradient approaches

¹ Faculty of Building and Industrial Construction, Hanoi University of Civil Engineering, Hanoi, Vietnam
² School of Transportation Engineering, Danang Architecture University, Da Nang city, Vietnam
³ Office of Research Administration, Danang Architecture University, Da Nang city, Vietnam
⁴ Univ Grenoble Alpes, CNRS, Grenoble INP - UGA, 3SR, F-38000 Grenoble, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 1 December 2025

Abstract

In the context of finite element modelling, the boundary value problem is often considered to be initially homogeneous. However, such assumption contradicts the observation of real geo-engineering problems and may affect the behaviour of geo-structure. It is thus necessary to consider a heterogeneous domain with a certain degree of variability. In this paper, we tackle this question by using a multi-scale FEM×DEM model with a second gradient enhancement. Pressuremeters are modelled in which, at the macro-scale, FEM model with a second gradient enhancement is used, while at micro-scale, an assembly of grains (called VE – volume elements) is used to numerically derive the constitutive response of geomaterials. Several VEs are simultaneously employed in a single finite element mesh in order to describe the heterogeneity of real engineering issues. The results suggest that when a certain heterogeneity is introduced, the set of possible numerical solutions seems more restrained even though the uniqueness of the solution is not guaranteed.