Abstract
The subject of this paper is to present the application of MultiGrid (MG) methods in 3D composite material simulations through the solution of the elastic equations. An efficient MG solver is further developed for modeling composite structures with strong discontinuities. Different types of boundary conditions are imposed in the solver. The model is validated by comparing the MG numerical results with the theoretical results existing in the literature and Finite Element (FE) results and a good agreement is found. The potential of MG methods with respect to the homogenization process is illustrated. Then an ideal laminated structure is analyzed and a real topology is simulated for the first time by a MG model. The effect of fiber orientation, interface layer thickness, fiber layer thickness and the ratio of material properties on the surface displacement are investigated. MG results show the detailed local behavior and provide new insights into possible initiation of delamination.
Highlights
Composite materials have been widely used in many industrial fields in past decades due to their excellent mechanical properties as well as the adaptation under specific loading conditions
For the homogenization process in a composite material, there are two interesting boundary conditions extended from the above boundary conditions: one called Homogeneous Strain Boundary Condition (HSBC) and another called Periodic Boundary Condition (PBC)
HSBC [15] is suitable for the case where the representative volume element (RVE) of the composite structure is not periodic
Summary
Composite materials have been widely used in many industrial fields in past decades due to their excellent mechanical properties as well as the adaptation under specific loading conditions. One of the currently used methods is to consider the heterogeneous material as a ‘‘homogeneous” layer and obtain the averaged material properties of each component This kind of approximation is commonly referred to as the homogenization process [1], which takes the microscopic structure into account and is capable to predict the macroscopic mechanical behavior of a composite. Despite the globally correct predictions, the homogenization results lose the microscopic details related to the local physical mechanisms These mechanisms may induce premature material failure, such as cracks. The advantage is that the cost of MG methods depends linearly on the number of unknowns, which provides a unique potential for solving large scale problems They were first introduced in the early 1960s, it was not until the mid-seventies that Brandt [2,3] enriched the related theories and made them efficient in various scientific and engineering fields. The possible factors which may effect the delamination process are investigated as well
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