Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization

Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second-order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second-order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second-order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them

Direct method-based statistical limit analysis of wc-co composites

In this paper, a direct method-based prediction of load-bearing capacity of nonperiodic WC-Co composites is presented. The main goal is to generalize the methodology of limit analysis on periodic heterogeneous media to materials with random microstructures. For such materials, the admissible macroscopic loading domains demonstrate remarkable scatter among RVE models of identical size and constituents but different morphologies. Limit analysis is performed on samples of a group of RVE models converted automatically from scanning electron microscopy (SEM) images. The corresponding admissible loading domains are numerically determined and statistically interpreted. The obtained results for plastic limit loads by direct method are compared with those from conventional incremental analysis

Fe2-homogenization of micromorphic elasto-plastic materials

In this work, a homogenization strategy for a micromorphic–type inelastic material is presented. In the spirit of FE2, a representative volume element is attached to each macroscopic quadrature point. Due to the inherent length scale of the micromorphic continuum, size effects for inelastic behavior are obtained on RVE–level. A focus is placed on the computation of the homogenized algorithmic tangent. It is determined via sensitivity analyses with respect to the boundary conditions imposed on the RVE. Following this procedure, costly single–scale computations with dense meshes can be replaced by a robust homogenization approach with optimal convergence rates

Prediction of the longitudinal tensile strength of polymer matrix composites

A micromechanical model was developed for the prediction of the longitudinal tensile strength of polymer matrix composites. The model considers successive fibre breaks within an infinitely wide Li-long representative volume element (RVE), Li being the so-called ineffective length. An elastic-plastic stress transfer model is used to define Li and fibre strength is described by a Weibull distribution. The composite strength is obtained by solving numerically an equation for the maximum RVE stress. A simplified closed-form solution derived proved to be in very good agreement with the base formulation. Although there is still significant uncertainty over model input data, predictions agreed well with experimental strengths of carbon fibre composites

Computational modelling of void growth in swelled hydrogels

The nature and the large notable distinguishing features of polymeric gels explain their pervasive use as biomaterials in both regenerative medicine and tissue engineering. With regard to their biocompatibility, their ability to withstand large deformation and their significant capacity of solvent absorption, these biomaterials are often selected owing to their versatile mechanical properties and especially the closeness to soft biological tissues, amongst others. A finite-strain theory for the study of the overall behaviour of a porous polymeric gel where microvoids are present is presented. The swollen polymeric gel is modeled as a two-component body composed of two incompressible components, namely, an elastic porous polymer imbibed with a solvant. The chemical equilibrium is assumed to be preponderate at the interface between the porous polymer and the environment where the chemical potential of the solvent is fixed. The initially dry porous polymer undergoes large deformation induced by absorption of a solvent from the environment and mechanical loading. In this paper an attempt is made towards obtaining an estimation of the macroscopic responses of the swollen porous polymer to prescribed proportional loadings. To this end, a two-level representation of the material at hand for which the Representative Volume Element (RVE) imbibed with a solvent is a simple axisymmetric cylinder composed of a homogeneous matrix surrounding a spherical void, is considered. The computational study addresses the situation where the RVE is subjected to prescribed axial and lateral overall stresses under conditions of constant overall stress triaxiality. For fixed values of the Flory-Huggins parameter and the nominal concentration of the solvent, the overall stress-strain behaviour of the RVE model, the influence of the initial porosity, and the prescribed stress triaxiality ratio have been outlined

Changes in lower extremity muscle function after 56 days of bed rest

Preservation of muscle function, known to decline in microgravity and simulation (bed rest), is important for successful spaceflight missions. Hence, there is great interest in developing interventions to prevent musclefunction loss. In this study, 20 males underwent 56 days of bed rest. Ten volunteers were randomized to do resistive vibration exercise (RVE). The other 10 served as controls. RVE consisted of muscle contractions against resistance and concurrent whole-body vibration. Main outcome parameters were maximal isometric plantar-flexion force (IPFF), electromyography (EMG)/force ratio, as well as jumping power and height. Measurements were obtained before and after bed rest, including a morning and evening assessment on the first day of recovery from bed rest. IPFF (-17.1%), jumping peak power (-24.1%), and height (-28.5%) declined (P < 0.05) in the control group. There was a trend to EMG/force ratio decrease (-20%; P < 0.051). RVE preserved IPFF and mitigated the decline of countermovement jump performance (peak power -12.2%; height -14.2%). In both groups, IPFF was reduced between the two measurements of the first day of reambulation. This study indicates that bed rest and countermeasure exercises differentially affect the various functions of skeletal muscle. Moreover, the time course during recovery needs to be considered more thoroughly in future studies, as IPFF declined not only with bed rest but also within the first day of reambulation. RVE was effective in maintaining IPFF but only mitigated the decline in jumping performance. More research is needed to develop countermeasures that maintain muscle strength as well as other muscle functions including power

Modeling of Polymer Clay Nanocomposite for a Multiscale Approach

The mechanical property enhancement of polymer reinforced with nano-thin clay platelets (of high aspect ratio) is associated with a high polymer-filler interfacial area per unit volume. The ideal case of fully separated (exfoliated) platelets is generally difficult to achieve in practice: a typical nanocomposite also contains multilayer stacks of intercalated platelets. Here we use numerical modelling to investigate how the platelet properties affect the overall mechanical properties. The configuration of platelets is modelled using a statistical interpretation of the Representative Volume Element (RVE) approach, in which an ensemble of "sample" heterogeneous material is generated (with periodic boundary conditions). A simple Monte Carlo algorithm is used to place non-intersecting platelets in the RVE according to a specified set of statistical distributions. The effective stiffness of the platelet-matrix system is determined by measuring the stress (using standard Finite Element analysis) produced as a result of applying a small deformation to the boundaries, and averaging over the entire statistical ensemble. In this work we determine the way in which the platelet properties (curvature, filling fraction, stiffness, aspect ratio) and the number of layers in the stack affect the overall stiffness enhancement of the nanocomposite. Thus, we bridge the gap between behaviour on the macroscopic scale with that on the scale of the nano-reinforcement, forming part of a multi-scale modelling framework.Comment: 39 pages, 19 figure