Vasilina Filonova

Generalized Viscoplasticity Based on Overstress (GVBO) for Large Strain Single-Scale and Multiscale Analyses

A generalized viscoplasticity based on the overstress (GVBO) model that successfully reproduces large strain and strain rate experimental data has been developed. The GVBO model confirmed increased shear resistance of polyurea at very high strain rates \((10^{5}\)–\(10^{6}\,\mathrm{{s}}^{-1})\) observed in the experiments. With the proposed GVBO model, we conducted numerical simulation of fragment simulating projectile impacting polyurea/ high-hard-steel bi-layers at high impact velocities (>1000 m/s). For model validation, two positions of the polymer coating with respect to the steel plate have been considered: the front and back coating, with a front side being a target. Numerical impact simulations utilizing a single-scale GVBO model predicted that a polyurea bi-layer with a front coating increases penetration velocity by about 15.4 % (against 23 % observed in the experiments), while the steel plate with a back coating raises penetration velocity by 7.5 % (as opposed to 8.8 % in the experiment) in comparison to the ballistic limit of the blank steel plate. This minor discrepancy between experimental and simulation results is qualitatively attributed to the space-time multiscale phenomena. We show that a possible anisotropy introduced by material heterogeneity increases resistance of the polyurea layer by partially transforming the pressure wave into a dissipated shear wave. We further demonstrate that dispersion further enhances energy absorption of the polyurea coating.

6 – Computational Simulation, Multi Scale Computations, and Issues Related to Behavioral Aspects of HSREP

We present singlescale and multiscale models of polyurea and high-density polyethylene (HDPE) subjected to high strain rates. The high strain rate polymer behavior is described by a variant of the viscoplasticity model based on overstress (VBO), hereafter referred to as the generalized VBO or GVBO. The singlescale material properties of the GVBO are identified from the experimental data using a combination of global and local inverse methods for various impact loading conditions. The multiscale model of polyurea/HDPE is based on the reduced order homogenization theory, where the unit cell of a polymer is modeled as a heterogeneous material with ellipsoidal inclusions. The reduced order multiscale model has been further enhanced by incorporating dispersive mechanism aimed at capturing reflection and refraction of stress waves at high strain rates that give rise to dispersion and attenuation of waves within the polymer microstructure. We present a one-parameter macroscopic model of distributed damage and dynamic fracture of polymers. Key characteristics of the model include its simplicity and suitability for straightforward and efficient numerical implementation. The damage model can be derived from a micromechanical model of chain elasticity and failure by recourse to optimal scaling methods and fractional strain gradient elasticity. As a result of the optimal scaling analysis, micromechanical parameters can be linked to the material’s critical energy release rate, which constitutes the single material parameter of the macroscopic fracture model. The model can be integrated into numerical simulations of polymeric materials within the framework of material point eigenerosion. The scope and fidelity of the model is demonstrated in an example of application, namely, Taylor-impact experiments of polyurea specimens.

Reduced Order Computational Continua.

INTRODUCTION The paper presents a new multiscale framework that is both mathematically rigorous and practical in the sense that it has been successfully applied in aerospace, automotive and civil engineering industries. The “rigor” aspect of the method is provided by recently developed computational continua (C) formulation (Fish and Kuznetsov, 2009), which is endowed with fine-scale details, introduces no scale separation, makes no assumption about infinitesimality of the fine-scale structure, does not require higher order continuity, introduces no new degrees-of-freedom and is free of higher order boundary conditions. The “practicality” aspect of the proposed method is inherited from the reduced order homogenization (Yuan and Fish, 2009, Fish and Yuan, 2008) approach, which constructs residual free-fields that eliminate the bottleneck of satisfying fine-scale equilibrium equations and is endowed with a hierarchical model improvement capability where the cost of the most inexpensive member of the sequence is comparable to that of semianalytical or phenomenological methods. Blending of the two methods into a single cohesive computational framework, hereafter to be referred to as the Reduced order Computational Continua or simply RC, that inherits the underlying characteristics of its two ingredients, is the main objective of the present manuscript. We conclude the manuscript with a brief summary and discussion of future research directions. In the present manuscript we consider a heterogeneous body formed by a repetition of a fine structure (unit cells) occupying an open, bounded domain 3 ζ Ω ⊂ . The unit cell domain denoted as 3 Θ ⊂ is assumed to be finite, i.e. unlike in the homogenization theories it is not infinitesimally small compared to the coarse-scale domain. The following governing equations on ζ ∈Ω x are stated at the fine-scale of interest ( ) ( ) ( ) ( ) ( ) ( ) ( )