Even with the computational power currently available, the adoption of nano/micro/meso-scale (discrete) approaches become computationally intractable in the case of fine grained materials, such as nano-composites, ceramics, rocks, metallic powders, etc., or in the case of large structures, such as tall buildings, dams, bridges, etc. For this reason there is clearly a need for effective multiscale techniques suitable for upscaling discrete systems. Our research group is currently exploring, evaluating the effectiveness, and further extending a variety of multiscale techniques recently developed to bridge atomistic and continuum scales.
Lattice Discrete Particle Model Formulation
Our group primarily utilizes the Lattice Discrete Particle Model (LDPM), which is suitable for the simulation of the failure behavior of concrete. LDPM simulates concrete at the meso-scale considered to be the length scale of coarse aggregate pieces. LDPM is formulated in the framework of discrete models for which the unknown displacement field is not continuous but only defined at a finite number of points representing the center of aggregate particles. Size and distribution of the particles are obtained according to the actual aggregate size distribution of concrete. Discrete compatibility and equilibrium equations are used to formulate the governing equations of the LDPM computational framework. Particle contact behavior represents the mechanical interaction among adjacent aggregate particles through the embedding mortar. Such interaction is governed by meso-scale constitutive equations simulating meso-scale tensile fracturing with strain-softening, cohesive and frictional shearing, and nonlinear compressive behavior with strain-hardening.
LDPM can simulate tensile fracturing as demonstrated by the successful simulation of three-point bending tests on notched
specimens. It is able to reproduce pre-peak nonlinearity as well as softening post-peak behavior. It reproduces realistically the
development of a crack pattern due to tensile stresses. It predicts correctly size effect on specimen load carrying capacity.
Discrete Modeling of Mesoscale Poromechanics
This project formulated a three-dimensional multiphysics lattice discrete particle model (M-LDPM) to investigate the fracture permeability behavior of shale. The framework features a dual lattice system mimicking the mesostructure of the material and simulates coupled mechanical and flow behavior. The mechanical lattice model simulates the granular internal structure of shale, and describes heterogeneous deformation by means of discrete compatibility and equilibrium equations. The network of flow lattice elements constitutes a dual graph of the mechanical lattice system. A discrete formulation of mass balance for the flow elements is presented to model fluid flow along cracks and intact materials. The overall computational framework is implemented with a mixed explicit–implicit integration scheme and a staggered coupling method that makes use of the dual lattice topology enabling the seamless two-way coupling of the mechanical and flow behaviors.
Computational multimodel framework for coupled hygro-thermo-mechanical analyses of lattice systems
The mechanical behaviors of porous materials, particularly their susceptibility to cracking, can be influenced by various chemical and physical phenomena. Changes in environmental conditions can have opposing effects on different materials: for example, rise in temperature makes porous materials either stronger and more brittle (e.g., early-age concrete) or weaker and more ductile (e.g., wood and composites) within a typical application temperature range. Likewise, variations in moisture content or temperature can cause volumetric changes that, when restrained, lead to the development of stress within the material. In addition to mechanical loading, hygral or thermal effects may also contribute to crack initiation and propagation. Consequently, the durability of materials is often affected by a combination of mechanical, hygral, and/or thermal processes, which typically commence at production stages and evolve over the life cycle of the material. Therefore, for many applications, fracture analysis should be modeled under a multiphysics context. This research proposes a newly developed computational pipeline for coupled multiphysics and fracture analyses of topologically dual lattice systems for porous materials, through the Inter-Process Communication (IPC) between mechanical and flow/transport solvers, with a particular emphasis on the mesoscale hygro-thermo-mechanical modeling of wood and concrete.