A simple method to simulate shrinkage-induced cracking in cement-based composites by lattice-type modeling

Abstract

A new numerical procedure is proposed to investigate cracking behaviors induced by mismatch between the matrix phase and aggregates due to matrix shrinkage in cement-based composites. This kind of failure processes is simplified in this investigation as a purely spontaneous mechanical problem, therefore, one main difficulty during simulating the phenomenon lies that no explicit external load serves as the drive to propel development of this physical process. As a result, it is different from classical mechanical problems and seems hard to be solved by using directly the classical finite element method (FEM), a typical kind of "load → medium → response" procedures. As a solution, the actual mismatch deformation field is decomposed into two virtual fields, both of which can be obtained by the classical FEM. Then the actual response is obtained by adding together the two virtual displacement fields based on the principle of superposition. Then, critical elements are detected successively by the event-by-event technique. The micro-structure of composites is implemented by employing the generalized beam (GB) lattice model. Numerical examples are given to show the effectiveness of the method, and detailed discussions are conducted on influences of material properties.

On the Load–Unload (L–U) and Force–Release (F–R) Algorithms for Simulating Brittle Fracture Processes via Lattice Models

“…This method is developed by tracing the release process of internal forces of ruptured elements under the quasi-static assumption O(T loading ) ) O(T elem ) ) O(T lattice ) (Li et al, 2002;Liu, 2007;Liu et al, 2009b). Honestly, the concept of force-releasing operation has a long history, nevertheless a detailed multi-stage release version is developed firstly by Liu (2007).…”

“…Liu et al extended the lattice elements, i.e. beams and springs into a more general entity with the capability of including materials' heterogeneities in every single element (Liu et al, 2008a(Liu et al, , 2010aLiu and Liang, 2009;Liu et al, 2009aLiu et al, ,2009bLiu et al, , 2010b. More recently, lattice methods have been adopted as a quantitative approach to study the material properties and typical damage modes of polycrystalline microstructures such as ceramics in the smalldeformation regime (Rinaldi et al, 2008;Rinaldi, 2009).…”

“…Since the lattice-type model seems promising for studying significant mechanical problems, it is worthy to explore its numerical implementation so that we may formulate more robust algorithms to make the model more accurate and reasonable. For this purpose, our attention is focused on analyzing and comparing the loadunload (L-U) (Bolander and Saito, 1998;Karihaloo et al, 2003;Ostoja-Starzewski, 2002;Rots et al, 2008) and forcerelease (F-R) method (Elias et al, 2010;Li et al, 2002;Liu, 2007;Liu et al, 2009b).…”

“…When it comes to the FR method (Elias et al, 2010;Li et al, 2002;Liu, 2007;Liu et al, 2009b), a trial displacement field is constructed to be compatible with the controlled-displacements all over the failure process including non-equilibrium processes between successive equilibrium states. The elemental internal forces to be released are regarded as static actions, which are supposed to release from the initial value to zero.…”

Influences of Domain Symmetry on Supersonic Combustion Modeling

“…Case 2 is the same as Case 1 except that the viscous effect is excluded. Namely, it is simulated by the previous quasistatic lattice model [13,37,39] . Now we have v • t v 1 → 0 .…”