Micromechanical Analyses of Strain Gradient Plasticity in Fibre-Reinforced Polymers

  • Carvalho Alves, Ana Francisca (INEGI)
  • Rodrigues Lopes, Igor André (INEGI)
  • Klavzer, Nathan (INEGI)
  • Pardoen, Thomas (iMMC, UCLouvain)
  • Camanho, Pedro (DEMEC, FEUP)

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The accurate representation of the constitutive behaviour of epoxy resins is essential for the micromechanical simulations of fibre-reinforced polymers (FRPs). Conventional plasticity models often exhibit excessive strain localisation when applied to confined matrix regions, leading to inaccurate predictions of crack initiation and composite strength. Previous works have highlighted the need to account for strain gradients or interphases to capture these effects more realistically [1]. Strain gradient plasticity has been successfully used in metals to describe size-dependent strengthening mechanisms, but its application to polymers remains limited. Within this context, the present contribution proposes a pressure-dependent implicit strain-gradient plasticity model for epoxy resins, extending the constitutive framework of Melro et al. [2]. The model captures both pressure sensitivity and asymmetric tension–compression behaviour. Strain-gradient effects are incorporated through a non-local plastic variable governed by a Helmholtz-type equation, enabling a straightforward implementation in standard finite-element platforms via user-defined subroutines. The predictive capabilities of the model are assessed by comparing experimental and numerical results of nanoindentation on neat epoxy and micromechanical analyses of FRP microstructures. The additional constitutive parameters are identified using a Composite Bayesian Optimisation strategy based on experimental data. The results demonstrate that the proposed formulation accurately reproduces experimentally observed size effects and mitigates the unrealistic strain localisation typical of classical plasticity [3]. [1] J. Chevalier, P.P. Camanho, F. Lani and T. Pardoen. Multi-scale characterization and modelling of the transverse compression response of unidirectional carbon fibre reinforced epoxy. Composite Structures, 2019. [2] A.R. Melro, P.P. Camanho, F.M. Andrade Pires and S.T. Pinho. Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I – Constitutive modelling. International Journal of Solids and Structures, 2013. [3] I. A. Lopes, A. F. Carvalho Alves, N. Klavzer, T. Pardoen and P.P. Camanho. Pressure-Dependent Strain Gradient Plasticity for Micro-Mechanical Analyses of Fibre-Reinforced Polymers. Composite Structures, 2026.