Hybrid IG-FE method applied to cohesive fracture/contact in particle-filled elastomeric composites Saeed Maleki Jebeli . Mahmoud Musavi Mashhadi . Mostafa Baghani Received: 28 October 2018 / Accepted: 30 April 2019 Ó Springer Nature B.V. 2019 Abstract In this paper, employing a new numerical framework, a 2D investigation is conducted on the effect of fiber-matrix contact/debonding on the stress– strain response of fiber-reinforced elastomeric com- posites. The analysis is carried out in the framework of large deformation/sliding. The main novelty of this work resides in using hybrid IsoGeometric-Finite Element (IG-FE) technique to discretize the domain where interfaces together with a band around them are represented by NURBS patches. These patches are coupled to the surrounding Lagrangian domain thanks to the transition elements. Interfaces’ discontinuity is readily induced through knot insertion capability within IGA. Moreover, contact constraints together with cohesive behavior are incorporated in the numerical model employing a unified mortar frame- work with appropriate definitions of potentials. Two numerical examples are considered within the pro- posed context and results are discussed in terms of stress–strain curves and stress contours. Due to proven higher accuracy of IGA in modeling contact/cohesive interfaces under large deformation and efficient use of NURBS around discontinuities, the proposed numer- ical methodology seems to be an appropriate (yet efficient) candidate to model such kind of highly nonlinear problems. Keywords Fiber-matrix contact/debonding  Hybrid IG-FE discretization  Knot insertion  Isogeometric analysis 1 Introduction Prediction of critical load is a key task in the assessment of the composite materials. So far, a vast array of researches has been conducted to investigate the load bearing capacity of various composite mate- rials. Fiber reinforced elastomeric composites are a relatively new category of composites that have drawn special attention in many fields such as: electronics (Ponnamma et al. 2014), tyre industry (Cho et al. 2005), isolators (Al-Anany and Tait 2017), conveyer belts, solid propellants (Toulemonde et al. 2016b; Matous ˇ and Geubelle 2006a), etc. These composites often undergo large (finite) deformations during their service life. Numerical modeling could be employed to gain insight about various mechanical characteris- tics of this kind of composites, but one should note that this task involves considering different types of nonlinearity in the modeling. Firstly, material nonlin- earity arises mainly from two sources: (1) Nonlinear behavior of matrix material is often represented by S. Maleki Jebeli  M. Musavi Mashhadi  M. Baghani (&) School of Mechanical Engineering, University of Tehran, Tehran, Iran e-mail: baghani@ut.ac.ir 123 Int J Mech Mater Des https://doi.org/10.1007/s10999-019-09459-9