Contents lists available at ScienceDirect Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech Methodology for macro-modeling of bio-based composites with inelastic constituents Liva Pupure * , Janis Varna, Roberts Joffe Division of Materials Science, Lulea University of Technology, S-97187 Luleå, Sweden ARTICLE INFO Keywords: Polymer-matrix composites (PMCs) (A) Creep (B) Non-linear behavior (B) Multiscale modeling (C) Stress relaxation (C) ABSTRACT Methodology for development of a macro-scale model (with strain as an input) for Regenerated Cellulose fiber (RCF) composites with highly non-linear (viscoelastic (VE) and viscoplastic (VP)) constituents is presented and demonstrated. The VE is described by Schapery's models and Zapas' model is used for VP. For a purely VE constituent the model can be identified from stress relaxation in constant strain tests. In the presence of VP the constant strain test does not render VE stress relaxation functions, because part of the applied strain is VP and the VE strain is changing. As an alternative creep and strain recovery tests are suggested to find the plasticity law and also the nonlinear creep compliances to identify the VE model where stress is an input. The incremental form of this model is then inverted and used to simulate the VE relaxation tests and the simulated relaxation functions are used to identify the VE model with VE strain as an input. Models for constituents are used in micromechanics simulations of the composite behavior in arbitrary ramps including the composite VE relaxation test. Using the latter, a macro-model is developed and its validity and accuracy are demonstrated. 1. Introduction Research on natural fiber composites shows that composites and their constituents exhibit inelastic behavior [1,2] mainly due to visco- plastic (VP) and viscoelastic (VE) strain components [3,4]. Composites are tested to identify parameters in generally non-linear material models. The characterization is time consuming and as soon as the composition or the morphology of the material is changed (e.g. volume fractions) the characterization has to be done again. For design pur- poses a “quick” tool for creating material model by tailoring composite properties according to demands of application to be used in optimi- zation is required. This paper presents a methodology for macro-scale composite time- dependent material model development using micromechanics. A par- ticular (simplest) case is described where a) the applied strain depen- dence on time is the input and b) strains in all composite constituents are equal to the macroscopic strain. However, this hypothesis does not limit the suggested strategy. The iso-strain assumption is widely used in elastic micromechanics and laminate theory of composites. For example, in elasticity it leads to the rule-of-mixtures (ROM) for unidirectional (UD) composite long- itudinal modulus and is used for strains in fiber direction in the more sophisticated Concentric Cylinder Assembly model [5,6]. It also leads to ROM for laminate stiffness matrix that can be ex- pressed through stiffness matrices of all layers in global axis and the volume fractions of layers in the laminate. The iso-strain assumption can be applied to linear viscoelastic case [7] provided the material model for the stress dependence on the applied strains is known for each constituent. Generalization to nonlinear viscoelastic analysis of laminates analysis was described in Ref. [8]. The laminate analysis requires experimental information on VE and VP “Poisson's ratios” of the UD composite with rather limited available data. Guedes [8] as- sumed that the Poisson's interaction is elastic with constant ratio, which, of course, is just an approximation [9,10]. The novelty of the present paper is in including VP strains in con- stituents in the multiscale simulation and testing methodology, which is important for the experimentally studied composite containing re- generated cellulose fibers (RCF) with very distinct VP behavior [11]. The nonlinear viscoelastic characterization required for development of material models in a form where stress is expressed as a function of strain (in this paper it is Schapery's formulation [12,13]) usually is performed in constant strain relaxation test. Unfortunately, the VE model identification in relaxation test is not possible in presence of growing VP strains [14]: keeping the applied strain constant the VE strain component is decreasing due to increasing VP strain. In, other words in this test it is not a viscoelastic stress relaxation at fixed VE https://doi.org/10.1016/j.compscitech.2018.05.015 Received 1 March 2018; Received in revised form 4 May 2018; Accepted 6 May 2018 * Corresponding author. E-mail address: Liva.Pupure@ltu.se (L. Pupure). Composites Science and Technology 163 (2018) 41–48 Available online 09 May 2018 0266-3538/ © 2018 Elsevier Ltd. All rights reserved. T