Cohesive Micromechanics: A New Approach for Progressive Damage Modeling in Laminated Composites

Abstract

A new cohesive micromechanical modeling framework is presented for the progressive damage analysis of laminated composite materials and structures. The cohesive micromechanics (CM) modeling approach is based on simplified 3D unit cell with incremental and damage formulations. The unidirectional CM model formulated in this paper is implemented in a local—global nonlinear damage modeling framework that recognizes the fiber and matrix constituents along with the cohesive interface/interphase subcells at the lower level. The cohesive elements are embedded between the fiber—fiber, fiber—matrix, and matrix—matrix subcells. Separate tension and compression traction-separation constitutive relations are used for the cohesive subcells in order to degrade the traction and internal resisting force across the plane between the two adjacent constituents. As a result, progressive damage modeling in the structural level can be achieved at the micromechanical level while maintaining the full advantage of using concurrent nonlinear micromechanical modeling prior and during damage progression spanning the entire structure. The proposed CM damage framework allows nonlinear anisotropic response, including strain softening, and damaged elastic loading/unloading behavior. Robust and efficient numerical stress correction algorithms have been also developed in order to satisfy the local traction continuity and strain compatibility of the micromechanical model. The effectiveness of the proposed modeling approach is demonstrated by predicting the response of composite plates with an open hole under tension and compression loading using available test results from the literature.

Micromechanical finite element predictions of a reduced coefficient of thermal expansion for 3D periodic architectured interpenetrating phase composites

“…Moreover, the highest compressive stress localization takes place in the matrix of the gyroid-TPMS. Generally, debonding affects the effective properties of composites [67][68][69][70][71]. The constituents in IPCs are three-dimensionally continuous; consequently, the possibility of debonding is reduced [34].…”

Nucleation of cracks in an isotropic medium with periodic system of rigid inclusions under transverse shear

“…Substituting to the left side of boundary condition (14) instead of 3 (τ ), 3 (τ ), 3 (τ ) and 3 (τ ) their expansion in Laurent series in the vicinity of z = 0, and to the right side of (14) the Fourier series (16) and comparing the coefficients at the same degrees of e iθ we get two infinite systems of algebraic equations with respect to the coefficients α 2k and β 2k ,…”

“…Here, the size of the pre-fracture zone is unknown in advance and has to be determined when solving the problem. Investigations [16,[18][19][20][21] of the occurrence of domains with disrupted structure of the material show that during the initial stage the pre-fracture zones have the form of a narrow elongated layer, and then, when the load is increased, a secondary system of zones suddenly appears, and these zones contain the material with partially ruptured bonds.…”

“…As these zones (interlayers in the material) are small, as compared with the remaining part of the elastic medium with a periodic system of circular holes, they may be mentally removed and replaced by cuts whose surfaces interact with each other according to a certain law corresponding to the action of the removed material [12][13][14]. We use a model of pre-fracture zone with bonds between faces that provides experimental verification [15][16][17][18] for composite material. Allowance for these effects in problems of fracture mechanics is an important but also a difficult problem.…”

Nonlinear micromechanical formulation of the high fidelity generalized method of cells

“…Great care was given to the numerical formulation using consistent plasticity tangent operators and integration scheme suitable for cyclic loading and finite increments. Haj-Ali et al (2001), Haj-Ali andKilic (2003), Haj-Ali and Muliana (2004), Haj-Ali (2005, 2008) and Haj-Ali (2008, 2009 developed different numerical formulations for fiber reinforced plastic (FRP) class of composites applied for the GMC and other nonlinear micromechanical models including timedependent, nonlinear and damage effects.…”