Macroscopic Modeling Lecture 2 L2. 2 Analysis posite Materials with Abaqus Overview ? Introduction ? Some Notes on Anisotropic Elasticity ? Thermal Expansion ? Material Orientation ? Almost pressible Behavior Introduction L2. 4 Analysis posite Materials with Abaqus Introduction ? In this technique posite is modeled as a single orthotropic material or a single fully anisotropic material. ? posite is usually considered elastic. ? In addition, Hill ’ s anisotropic plasticity model is sometimes used to model inelastic deformation. ? The reinforcements and elements do not need to be aligned. ? The deformation field is homogeneous. L2. 5 Analysis posite Materials with Abaqus Introduction ? Macroscopic analysis is used to model the overall behavior of structural components built out posites. ? Nonlinear material behavior and local failure often are not considered because of plex nature of modeling these effects ? Note: Abaqus does have progressive damage and delamination/decohesion modeling capabilities, if these effects are important. ? Structural failure (buckling and collapse) monly studied without taking into account material failure such as delamination. ? Post-analysis checks are used to establish whether this approach is acceptable. Some Notes on Anisotropic Elasticity L2. 7 Analysis posite Materials with Abaqus Some Notes on Anisotropic Elasticity ? For the macroscopic modeling of posites, it is essential to define anisotropic elasticity coefficients accurately. ? Improper specification leads to incorrect results or can even lead to loss of material stability. ? In Abaqus several types of anisotropic elastic behavior are available. ? All anisotropic models have the general form where D = D (?, f i ) is a symmetric matrix with a maximum dimension of 6 ?6 , ? = temperature, f i = predefined field variables, and ? th = ? th(?) is the strain due to thermal expansion. ????: th th ij ijkl kl kl D ? ??? ? ?