Coupled Systems Mechanics, Vol. 7, No. 2 (2018) 141-162 DOI: https://doi.org/10.12989/csm.2018.7.2.141 141 Copyright © 2018 Techno-Press, Ltd. http://www.techno-press.org/?journal=csm&subpage=8 ISSN: 2234-2184 (Print), 2234-2192 (Online) Material model for load rate sensitivity Ivica Kožar 1a , Adnan Ibrahimbegovic 2a and Tea Rukavina 1,2b 1 University of Rijeka Faculty of Civil Engineering, Radmile Matej č ic ́ 3, 51000 Rijeka, Croatia 2 Sorbonne Universités / Université de Technologie Compiègne, Laboratoire Roberval de Mécanique Centre de Recherche Royallieu, 60200 Compiègne, France (Received June 7, 2017, Revised June 22, 2017, Accepted June 23, 2017) Abstract. This work presents a novel model for analysis of the loading rate influence onto structure response. The model is based on the principles of nonlinear system dynamics, i.e., consists of a system of nonlinear differential equations. In contrast to classical linearized models, this one comprises mass and loading as integral parts of the model. Application of the Kelvin and the Maxwell material models relates the novel formulation to the existing material formulations. All the analysis is performed on a proprietary computer program based on Wolfram Mathematica. This work can be considered as an extended proof of concept for the application of the nonlinear solid model in material response to dynamic loading. Keywords: lattice material model; nonlinear dynamical system; dynamic loading; Kelvin material model; Maxwell material model; sensitivity 1. Introduction In this work, the structure is modeled as a nonlinear dynamical system. Typically, structures are modeled using the finite element method (FEM) and the material model is included into the continuum model, while discrete material models need some additional transformation to be included into FEM (e.g., see Marenic ́ and Ibrahimbegovic (2015) or Do et al. (2015a)). The approach adopted here formulates the structure model as a system of nonlinear differential algebraic equations with the material model integrated into it. As a result, the material model is directly coupled with the structure and there is a direct link between structure behavior and its parameters. Also, loading is a part of the structure description i.e. it is incorporated into differential equations describing the system, and one can determine the sensitivity to various material or loading parameters. This particular aspect is missing from the FEM model describing the nonlinear dynamical system. Advantages of solution of engineering problems by directly solving differential equations have also been recognized in Keivani et al. (2014). Since loading is an integral part of the model, it is important to choose relevant representatives of the realistic loading. In our analysis, we are dealing with two types of loading: impact loading Corresponding author, Professor, E-mail: ivica.kozar@gradri.uniri.hr a Professor, E-mail: adnan.ibrahimbegovic@utc.fr b Ph.D. Student, E-mail: tea.rukavina@gradri.uniri.hr