Lattice modelling of quasi-brittle materials such as concrete is a discrete, mesoscale, description of the material in which constitutive relations are prescribed at a lower scale compared to the scale at which continuum-based constitutive relations are written usually. The meso-structure of the material is represented explicitly. Complex nonlinear responses at the macroscale are obtained, while keeping the constitutive model at the mesoscale simple and less phenomenological compared to macroscale ones. Prediction capabilities and accuracy of the description of the mechanical response at the global level are, in many cases, better than those obtained with continuum-based models.

The superior capability of lattice approaches has a price: extensive computational cost in structural analyses. In this lecture, we implement a coarse graining approach based on averaging the equations of conservation to obtain coarse-grained, continuum-based, stress versus strain responses from the Lattice Discrete Particle Model (LDPM). Because stresses and strains are coarse-grained independently, their relationship yields a database of macroscopic continuum responses that can be compared to some existing constitutive models. This database is used to reconstruct an equivalent isotropic scalar nonlocal damage model. We obtain from the analysis a set of data points that represent the relationship between the variable that is assumed to control damage (strain-based quantity) and the damage variable itself (degradation of stiffness). Calculations show that the best set is obtained for an internal length that is about three times the maximum aggregate size, and that the internal length is independent from the coarse graining length.

Still, the resulting isotropic damage model is an approximation as the coarse-grained mechanical response is much more complex. Simulations of structural size effect provide estimates of such an approximation, along with maps of differences between the stress and strain distribution nearby the crack.

Most of the physical phenomena in engineering problems occur under non-isothermal conditions. Moreover, even if the physical system is initially in a state of thermodynamic equilibrium, the physical phenomena or chemical reactions that occur may lead to local temperature changes and consequently to heat transfer. Therefore, understanding heat transfer in particulate systems is of great importance to many engineering applications such as environmental science, chemical and food processing, powder metallurgy, energy management, geomechanics and geological engineering. The need to consider the effect of heat transfer becomes critical in analyses of many multi-field problems in porous and fractured materials.

A novel DEM-based pore-scale 3D thermo-hydro-mechanical model of two-phase fluid flow and heat transfer in fluid and solids is based on a direct numerical simulation approach. The model's original concept is based on the notion that in a physical system, two domains coexist: the 3D discrete (solid) domain and the 3D continuous (fluid) domain. Both domains are discretized into a coarse mesh of tetrahedra.

The coupled thermal-hydraulic-mechanical (THM) model was validated by comparing the numerical results with the analytical solution of the classic 1D heat transfer problem. Numerical calculations were carried out for bonded granular specimens with a 3D DEM fully coupled with 3D CFD (based on a fluid flow network) and 3D heat transfer that linked discrete mechanics with fluid mechanics and heat transfer at the meso-scale. The heat transfer was related to both the fluid (diffusion and advection) and bonded particles (conduction). Bonded particle assemblies with two different grain distributions were considered. Perfect accordance was obtained between numerical and analytical outcomes. In addition, the effects of advection on the cooling of a bonded particle assembly were numerically shown (Figure 1). Finally, the authors' previously developed DEM-based 2D THM model was compared with a novel 3D pore-scale THM model.

The impact of free water on the static and dynamic compressive and tensile characteristics of concrete in two-dimensional (2D) mesoscale conditions was examined. An improved pore-scale hydro-mechanical model based on a fully coupled DEM/CFD approach was used to simulate the behavior of totally and partially fluid-saturated concrete. The idea behind the approach was a network of channels in a continuous area between discrete elements to create a fluid movement. A two-phase laminar fluid flow (water and air) was proposed in wet concrete that had a low porosity of 5%. Geometry and volumes of pores/cracks were considered to correctly track the liquid/gas content. A series of static and dynamic numerical simulations were run on bonded granular specimens of a simplified spherical mesostructure mimicking concrete in both dry and wet conditions. It was discovered that the saturation level had a major impact on how concrete behaved mechanically. As fluid saturation rose, so did the dynamic compressive and tensile strength. However, the static compressive and tensile strength diminished. In the dynamic range, the concrete mesostructure prevented fluid migration as a result of the rapid loading brought on by the high strain rate, and there were relatively few changes in pore fluid pressures and velocities. As a result, the pore fluid pressures slowed the rate of fracture, which led to increased strength. In the static range, the concrete mesostructure allowed for fluid migration as a result of the slow deformation, and there were changes in pore fluid pressures and velocities. As a result, the pore fluid pressures accelerated the rate of fracture, which led to declined strength. The numerical DEM-CFD results were in agreement with the corresponding laboratory test outcomes from the literature.

Cement and concrete, acknowledged as the most globally utilized materials, possess mechanical characteristics intricately linked to their long-term durability. Despite centuries of use, a complete understanding of these materials remains elusive. Calcium silicate hydrate (C-S-H), a fundamental component of cement, serves as the primary binding agent, crucial in determining concrete strength. The hierarchical structure of C-S-H encompasses various strength-related attributes across multiple levels. Numerous studies extensively delve into the molecular-scale mechanical properties, yielding significant insights. Additionally, comprehending the material's microscale mechanical properties is essential for its engineering functionality. At the microscale, it can be envisioned as a granular substance with a cohesive-frictional solid phase, reminiscent of porous media.

Significant time-dependent phenomena including creep and stress relaxation, occur in concrete subjected to constant loading, particularly within C-S-H in cement paste, and play a crucial role in the long-term volume change of the material. Despite decades of research, accurately simulating such a complex phenomenon at the microscale remains challenging. For instance, molecular dynamics simulations typically deal with relatively small systems due to computational limitations. C-S-H exhibits complex nanostructures, requiring a larger scale to fully capture its mechanical behaviour. This complexity poses challenges in accurately representing its microstructure in finite element simulations.

In this study, a novel discrete element method based on solid mechanics was employed to model creep and stress relaxation in C-S-H and explore microstructure development during these processes. Our simulations exhibit good agreement with nanoindentation creep tests, with detailed analysis conducted on the influencing factors affecting bulk mechanical responses. It was discovered that deviatoric stress, friction coefficient, and adhesion between surfaces significantly influence particle sliding, partially determining creep behaviours. These findings offer valuable insights into understanding the mechanism of creep in terms of microstructure change and can aid in nanoengineering C-S-H gels to minimize creep for enhancing concrete properties.

The Lattice Discrete Particle Model (LDPM) is a discrete mesoscale model of concrete that can accurately describe the macroscopic behavior of concrete during elastic, fracturing, softening, and hardening regimes. LDPM has been calibrated and validated extensively through the analysis of a large variety of experimental tests. LDPM can reproduce with great accuracy the response of concrete under uniaxial and multiaxial stress states in both compression and tension and under both quasi-static and dynamic loading conditions.

The LDPM formulation is obtained by modeling the interaction among coarse meso-scale aggregate pieces as the interaction among polyhedral cells (each containing one aggregate particle) whose external surfaces are defined by sets of triangular facets. At each facet strain and stress vectors are used to formulate the constitutive law describing physical mechanisms such as tensile fracture, cohesion, friction, etc.

The presentation will give an overview of recent implementations of LDPM in various computational platforms. LDPM was implemented in the following software packages: Abaqus/Explicit via user subroutine; Project Chrono, a physics-based modeling and simulation infrastructure based on a platform-independent open-source design; Cast3m a multi-physics software developed by CEA; Open Academic Solver, an open-source software developed at Brno University; JAX-LDPM, an open-source GPU-based software in active development by researchers from the Hong Kong University of Science and Technology; and FE-MultiPhys, developed at Virginia Tech. The different implementations will be compared by simulating typical failure tests for concrete, including, but not limited to, unconfined compression test, three-point bending test, and splitting tensile strength test.

Finally the presentation will provide a vision for future LDPM developments that will likely be implemented in these software packages.