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Summary: This paper presents the construction of a mean‐field homogenization (MFH) surrogate for nonlinear stochastic multiscale analyses of two‐phase composites that allows the material response to be studied up to its failure. The homogenized stochastic behavior of the studied unidirectional composite material is first characterized through full‐field simulations on stochastic volume elements (SVEs) of the material microstructure, permitting to capture the effect of the microstructural geometric uncertainties on the material response. Then, in order to conduct the stochastic nonlinear multiscale simulations, the microscale problem is substituted by a pressure‐dependent MFH reduced order micromechanical model, that is, a MF‐ROM, whose properties are identified by an inverse process from the full‐field SVE realizations. Homogenized stress‐strain curves can be used for the identification process of the nonlinear range, however, a loss of size objectivity is encountered once the strain softening onset is reached. This work addresses this problematic introducing a calibration of the energy release rate obtained with a nonlocal MFH micromechanical model, allowing to scale the variability found on each SVE failure characteristics to the macroscale. The obtained random effective properties are then used as input of a data‐driven stochastic model to generate the complete random fields used to feed the stochastic MF‐ROM. To show the consistency of the methodology, two MF‐ROM constructed from SVEs of two different sizes are successively considered. The performance of the MF‐ROM is then verified against an experimental transverse‐compression test and against full‐field simulations through nonlocal Stochastic Finite Element Method (SFEM) simulations. The implementation of the energy release rate calibration allows to conduct stochastic studies on the failure characteristics of material samples without the need for costly experimental campaigns, paving the way for more complete and affordable virtual testing. [ABSTRACT FROM AUTHOR]

This article introduces a, possibly damage‐enhanced, pressure‐dependent‐based incremental‐secant mean‐field homogenization (MFH) scheme for two‐phase composites. The incremental‐secant formulation consists on a fictitious unloading of the material up to a stress‐free state, in which a residual stress is attained in its phases. Then the secant method is performed in order to compute the mean stress fields of each phase. One of the main advantages of this method is the natural isotropicity of the secant tensors that allows defining the linear‐comparison‐composite (LCC). In this work, we show that this isotropic nature is preserved for a non‐associated pressure dependent plastic flow, making possible the direct definition of the LCC. This model is thus able to represent the physics of real polymeric composites. The MFH scheme is then verified by testing its prediction capabilities in several cases, including cyclic and nonproportional loading involving perfectly elastic phases, elasto‐plastic and damage‐enhanced elasto‐plastic phases in random representative volume elements (RVE) of uni‐directional (UD) composites and of composites reinforced with spherical inclusions. [ABSTRACT FROM AUTHOR]

Shape‐memory elastomer composite (SMEC) sheets, made of a honeycomb structured electrospun poly(ε‐caprolactone) (PCL) fiber mat embedded in a silicone (PDMS) elastomer, fold on themselves upon uniaxial traction. The self‐folding of the composite sheet originates from a bi‐layered structure obtained by a simple one‐step impregnation process. Indeed, the impregnation of a structured PCL fiber mat by oily PDMS in a flat Teflon mold leads, after curing, to an asymmetric composite sheet made of one PDMS flat thin layer on the mold side and one rough PDMS/PCL composite layer on the other side due to specific affinities between the three polymers involved. The self‐folded shape of such structured single sheet obtained upon uniaxial stretching and stress release is controlled by the honeycomb pattern orientation versus stretching direction, by the pattern size and by the applied uniaxial stretching stress. High shape recovery and robust shape memory cycling are also demonstrated by dynamic mechanical analysis. This innovative process based on the mat structuration allows a straightforward one‐step fabrication of shape memory sheets, with a wide scope of tunable self‐folded curvatures exhibiting efficient temperature shape recovery. [ABSTRACT FROM AUTHOR]

The present article introduces an automated procedure to construct geometrical representative volume elements (RVE) of open‐foam cellular materials from computerized tomography (CT) images, with the final aim of generating meshable geometries usable in the finite element method (FEM) used in order to analyse their mechanical behavior. The methodology consists in growing and fitting a set of ellipsoids to each of the foam cells. These ellipsoids are seeded by local maxima of the distance to the struts obtained from computer tomography images. This methodology is thus fully voxel‐based and does not depend on any assumption about statistical distributions of the foam cells. Therefore, it is able to reproduce an accurate geometrical model of the foam's microstructure and its possible irregularities. Moreover, this procedure allows the processing of large 3D data sets that do not fit the random access memory (RAM) by slicing it into smaller independent chunks. The effectiveness of the proposed approach is illustrated by comparing it to FEM simulations for which meshes are obtained from a feature reconstruction approach. Both FEM simulations are then compared with experimental results of uniaxial compressions of an open foam. [ABSTRACT FROM AUTHOR]

This work investigates in detail the Joule resistive heating phenomenon of electroactive shape memory composites (SMC) when an electric current is injected at constant power. The SMC is a covalent poly(ϵ -caprolactone) network filled with 3 wt% of multiwall carbon nanotubes. The resistive heating of the SMC is studied by means of surface temperature measurements, analytical formulas and a coupled 3D thermo-electric numerical model. Analytical expressions are derived for the 2D temperature distribution within a parallelepipedic SMC, either with constant or linearly-dependent electrical resistivity. These analytical expressions can be used to investigate the influence of geometrical and material parameters in the steady-state temperature and its distribution across the sample. The results also allow one to identify the parameters that are crucial for predicting the temperature rise due to resistive heating: the temperature dependence of the resistivity has little effect on the steady-state temperature, whereas the thermal conductivity plays a significant role. The time-dependent temperature is shown to be related to the particular temperature dependence of heat capacity. Furthermore, the presence of external objects (clamps or grips) used during the shape memory cycle must be taken into consideration for a certain temperature to be reached since they result in a lower steady-state temperature and a slower resistive heating phenomenon. With the findings presented in this work, accurate resistive heating can be predicted for a SMC upon the injection of an electric current at constant power. [ABSTRACT FROM AUTHOR]

A coupled electro-thermo-mechanical discontinuous Galerkin (DG) method is developed considering the non-linear interactions of electrical, thermal, and mechanical fields. In order to develop a stable discontinuous Galerkin formulation the governing equations are expressed in terms of energetically conjugated fields gradients and fluxes. Moreover, the DG method is formulated in finite deformations and finite fields variations. The multi-physics DG formulation is shown to satisfy the consistency condition, and the uniqueness and optimal convergence rate properties are derived under the assumption of small deformation. First the numerical properties are verified on a simple numerical example, and then the framework is applied to simulate the response of smart composite materials in which the shape memory effect of the matrix is triggered by the Joule effect. [ABSTRACT FROM AUTHOR]

Modelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect. In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a nonlocal elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality-dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D state, mandatory to incorporate the in-plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction-separation law is then built from the underlying damage model. The method is numerically shown to capture the stress triaxiality effect on the crack initiation and propagation. [ABSTRACT FROM AUTHOR]

This work provides a unified treatment of arbitrary kinds of microscopic boundary conditions usually considered in the multi-scale computational homogenization method for nonlinear multi-physics problems. An efficient procedure is developed to enforce the multi-point linear constraints arising from the microscopic boundary condition either by the direct constraint elimination or by the Lagrange multiplier elimination methods. The macroscopic tangent operators are computed in an efficient way from a multiple right hand sides linear system whose left hand side matrix is the stiffness matrix of the microscopic linearized system at the converged solution. The number of vectors at the right hand side is equal to the number of the macroscopic kinematic variables used to formulate the microscopic boundary condition. As the resolution of the microscopic linearized system often follows a direct factorization procedure, the computation of the macroscopic tangent operators is then performed using this factorized matrix at a reduced computational time. [ABSTRACT FROM AUTHOR]

The cover image is based on the Research Article I Analysis of an open foam generated from computerized tomography scans of physical foam samples i by Christophe Leblanc et al., https://doi.org/10.1002/nme.7008. GLO:BW7/15dec22:nme7164-toc-0001.jpg PHOTO (COLOR): . gl. [Extracted from the article]

Micro-electro-mechanical systems (MEMS) made of polycrystalline silicon are widely used in several engineering fields. The fracture properties of polycrystalline silicon directly affect their reliability. The effect of the orientation of grains on the fracture behaviour of polycrystalline silicon is investigated out of the several factors. This is achieved, firstly, by identifying the statistical variation of the fracture strength and critical strain energy release rate, at the nanoscopic scale, over a thin freestanding polycrystalline silicon film having mesoscopic scale dimensions. The fracture stress and strain at the mesoscopic level are found to be closely matching with uniaxial tension experimental results. Secondly, the polycrystalline silicon film is considered at the continuum MEMS scale, and its fracture behaviour is studied by incorporating the nanoscopic scale effect of grain orientation. The entire modelling and simulation of the thin film is achieved by combining the discontinuous Galerkin method and extrinsic cohesive law describing the fracture process. [ABSTRACT FROM AUTHOR]

Due to its ability to account for discontinuities, the discontinuous Galerkin (DG) method presents two main advantages for modeling crack initiations and propagation. On the one hand, it provides an easy way to insert the cohesive elements during the simulation and therefore avoids the drawbacks inherent to the use of an extrinsic cohesive law. On the other hand, the capture of complex crack path requires very thin meshes, and the recourse to a parallel implementation of DG formulations exhibits a high scalability of the resolution scheme. Recently, the authors developed such a DG-fracture framework for Kirchhoff-Love shells in the linear and non-linear ranges. They proved that this framework dissipates, during the fracture process, an amount of energy equal to the fracture energy of the material and that the model is able to propagate the crack with the right speed. In this paper, novel numerical benchmarks are presented to validate the method in various fracture conditions. The two first ones include an initial notch and study the fracture propagation under two different dynamic loadings (impact and blast). The two other ones focus on the fragmentation of initially unbroken specimens due to uniform expansion, in order to demonstrate the ability of the new framework to model crack initiations. Results are in all cases in agreement with the ones reported in the literature. [ABSTRACT FROM AUTHOR]

Current neuronavigation systems cannot adapt to changing intraoperative conditions over time. To overcome this limitation, we present an experimental end-to-end system capable of updating 3D preoperative images in the presence of brain shift and successive resections. The heart of our system is a nonrigid registration technique using a biomechanical model, driven by the deformations of key surfaces tracked in successive intraoperative images. The biomechanical model is deformed using FEM or XFEM, depending on the type of deformation under consideration, namely, brain shift or resection. We describe the operation of our system on two patient cases, each comprising five intraoperative MR images, and we demonstrate that our approach significantly improves the alignment of nonrigidly registered images. [ABSTRACT FROM AUTHOR]

Stiction, which results from contact between surfaces, is a major failure mode in microelectromechanical systems (MEMS). Indeed, microscopic structures tend to adhere to each other when their surfaces come into contact and when the restoring forces are unable to overcome the interfacial forces. Since incidental contacts cannot be completely excluded and since contacts between moving parts can be part of the normal operation of some types of MEMS, stiction prediction is an important consideration when designing micro- and nanodevices. In this paper, a micro–macro multiscale approach is developed in order to predict possible stiction. At the lower scale, the unloading adhesive contact–distance curves of two interacting rough surfaces are established based on a previously presented model [L. Wu , J. Appl. Phys. 106, 113502, 2009]. In this model, dry conditions are assumed, and only the van der Waals forces as adhesion source are accounted for. The resulting unloading adhesive contact–distance curves are dependent on the material, surface properties such as elastic modulus and surface energy, and rough surface topography parameters (the standard deviation of asperity heights and the asperity density). At the higher scale, a finite element analysis is considered to determine the residual cantilever beam configuration due to the adhesive forces once contact happens. Toward this end, the adhesive contact–distance curve computed previously is integrated on the surface of the finite elements as a contact law. The effects of the design parameters can then be studied for the given material and surface properties.\hfill[2010-0243] [ABSTRACT FROM PUBLISHER]

A virtual test facility (VTF) for studying the three-dimensional dynamic response of solid materials subject to strong shock and detonation waves has been constructed as part of the research program of the Center for Simulating the Dynamic Response of Materials at the California Institute of Technology. The compressible fluid flow is simulated with a Cartesian finite volume method and treating the solid as an embedded moving body, while a Lagrangian finite element scheme is employed to describe the structural response to the hydrodynamic pressure loading. A temporal splitting method is applied to update the position and velocity of the boundary between time steps. The boundary is represented implicitly in the fluid solver with a level set function that is constructed on-the-fly from the unstructured solid surface mesh. Block-structured mesh adaptation with time step refinement in the fluid allows for the efficient consideration of disparate fluid and solid time scales. We detail the design of the employed object-oriented mesh refinement framework AMROC and outline its effective extension for fluid–structure interaction problems. Further, we describe the parallelization of the most important algorithmic components for distributed memory machines and discuss the applied partitioning strategies. As computational examples for typical VTF applications, we present the dynamic deformation of a tantalum cylinder due to the detonation of an interior solid explosive and the impact of an explosion-induced shock wave on a multi-material soft tissue body. [ABSTRACT FROM AUTHOR]