Nested nonlinear micromechanical and structural models for the analysis of thick-section composite materials and structures

Rami Haj-Ali*, Hakan Kilic, Anastasia Muliana

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An effective integration of a three-dimensional (3D) micromechanical and finite element (FE) modeling framework is proposed for the analysis of thick-section fiber reinforced plastic (FRP) composite materials and structures. The proposed modeling framework is applied to a pultruded composite system. It consists of two alternating layers with unidirectional fiber (roving) and continuous filaments mat (CFM) reinforcements. Nonlinear 3D micromechanical models representing the different composite layers are used to generate through-thickness composite's effective responses. Approximate traction continuity and strain compatibility relations in the micromechanical models are expressed in terms of the average stresses and strains of the sub-cells that recognize the fiber and matrix responses. The nonlinear elastic behavior is attributed only to the matrix sub-cells. The nested nonlinear micromechanical models are implemented at each integration (Gaussian) point in the FE structural analyses. A linearized structural response will produce a trial strain increment for each Gaussian integration point and an iterative solution is performed until a structural-level convergence criterion is met. At every iteration, the micromechanical models are called to provide effective material responses. An efficient numerical implementation of the micromodels is required in order to achieve accurate solutions and accelerate the structural-level convergence. Thus, stress correction algorithm is performed in each level of the nested micromodels. Axial tension and compression tests on off-axis E-glass/vinylester coupons and notched specimens are used to calibrate the in situ material properties of the fiber and matrix and verify the prediction ability of the nested micromodels. The nonlinear calibration of the matrix is done by using the overall axial shear stress-strain response generated from Iosipescu (V-notched) specimens. Good agreement is shown for all off-axis angles when comparing the experimental stress-strain curves with those predicted by the analyses with the proposed micromodels.

Original languageEnglish
Pages (from-to)1993-2004
Number of pages12
JournalComposites Science and Technology
Issue number10
StatePublished - Aug 2007
Externally publishedYes


  • A. Polymer-matrix composites (PMCs)
  • B. Mechanical properties
  • B. Non-linear behaviour
  • B. Stress/strain curves
  • C. Finite element analysis (FEA)


Dive into the research topics of 'Nested nonlinear micromechanical and structural models for the analysis of thick-section composite materials and structures'. Together they form a unique fingerprint.

Cite this