Understanding the thermomechanical behavior of a TATB-based explosive via microstructure-level simulations. Part I: Microcracking and viscoelasticity

International audienceIn view of a better understanding of the thermomechanical behavior of pressed explosives, a Fourier-based computational tool is used to perform numerical homogenization and compare predictions to experimental macroscopic properties. This is first done in a purely thermoelastic context on simplified polycrystalline virtual microstructures, then extended to cracked polycrystalline ones. A further extension is proposed, aiming at predicting the nucleation and propagation of (micro)-cracks. Besides, a mean-field (self-consistent) approach is also followed, providing accurate thermoelastic predictions. It is currently being extended to account for linear (non-ageing) viscoelasticity of the binder. The study of irreversible deformation mechanisms of the TATB crystal, in view of their incorporation in the full-field tool, is the subject of the companion paper

Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem

The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoplastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy (SMA) constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method (FEM) framework

A K-BKZ Formulation for Soft-Tissue Viscoelasticity

A viscoelastic model of the K-BKZ (Kaye 1962; Bernstein et al. 1963) type is developed for isotropic biological tissues, and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. The standard fractional-order viscoelastic (FOV) solid is used to arrive at the overall elastic/viscoelastic structure of the model, while the elastic potential via the K-BKZ hypothesis is used to arrive at the tensorial structure of the model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including a regularized fractional derivative that was determined to be the best. The Akaike information criterion (AIC) is advocated for performing multi-model inference, enabling an objective selection of the best material function from within a candidate set

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

The original publication is available at http://www.springer.comInternational audienceTA Mixed Finite Element (MFE) method for 3D non-steady flow of a viscoelastic compressible fluid is presented. It was used to compute polymer injection flows in a complex mold cavity, which involves moving free surfaces. The flow equations were derived from the Navier-Stokes incompressible equations, and we extended a mixed finite element method for incompressible viscous flow to account for compressibility (using the Tait model) and viscoelasticity (using a Pom-Pom like model). The flow solver uses tetrahedral elements and a mixed velocity/pressure/extra-stress/density formulation, where elastic terms are solved by decoupling our system and density variation is implicitly considered. A new DEVSS-like method is also introduced naturally from the MINI-element formulation. This method has the great advantage of a low memory requirement. At each time slab, once the velocity has been calculated, all evolution equations (free surface and material evolution) are solved by a space-time finite element method. This method is a generalization of the discontinuous Galerkin method, that shows a strong robustness with respect to both re-entrant corners and flow front singularities. Validation tests of the viscoelastic and free surface models implementation are shown, using literature benchmark examples. Results obtained in industrial 3D geometries underline the robustness and the efficiency of the proposed method

An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of cross-linked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach