This proposal is concerned with the development of novel methodologies (including identification and validation strategies), stochastic representations and numerical methods in stochastic micromechanical modeling of nonlinear microstructures and imperfect interfaces. For the sake of feasibility, the applications will specifically focus on the modeling of hyperelastic microstructures and materials exhibiting surface effects and containing nano-inhomogeneities (such as nanoreinforcements and nanopores). For the case of nonlinear microstructures, the project aims at developing relevant probabilistic models for quantities of interests at both the microscale and mesoscale. The consideration of the latter turns out to be especially suitable for random nonlinear microstructures (such as living tissues) for which the scale separation, which is usually assumed in nonlinear homogenization, cannot be stated. Random variable and random field models for strain-energy functions will be constructed by invoking the maximum entropy principle and propagated through stochastic nonlinear homogenization techniques. A complete methodology for identifying the proposed representations will be further introduced and validated on a simulated database. Concerning the imperfect interface modeling, one may note that surface effects are usually taken into account by retaining an interface model (such as the widely used membrane-type model) involving several assumptions such as those related to the mechanical description of the membrane. Such arbitrary choices certainly generate model uncertainties which may be critical while propagated to coarsest scales and which may therefore penalize the predictive capabilities of the associated multiscale approaches. In this project, we propose to tackle the issue of model uncertainties in multiscale analysis of random microstructures with nano-heterogeneities by constructing nonparametric probabilistic representations for the homogenized properties. A complementary aspect is the construction of robust random generators, able to simulate random variables taking their values in given subspaces defined by inequality constraints and non-Gaussian random fields. Whereas such random fields can typically be generated making use of point-wise polynomial chaos expansions, the preservation of the statistical dependence is hardly achievable with the currently available techniques. In this proposal, we will subsequently address the construction of new random generators relying on the definition of families of Itô stochastic differential equations. Such generators are intended to depend on a limited number of parameters (independent of the probabilistic dimension), for which tuning guidelines will be provided. The proposed models will clearly go a step beyond what is currently done in deterministic mechanics for such materials and the expected results are in the forefront of the ongoing developments within the scopes of uncertainty quantification and material science. In addition, it worth pointing out that such theoretical derivations are absolutely required in order to support the current new developments of 3D-fields measurements and image processing at the microscale of complex materials.

The goal of BIO ART is to develop new bio-epoxy resins from renewable resources without bisphenol A, which is toxic to humans and the environment. BIO ART’s originality comes from the synergy between green chemistry and emerging technologies (multiscale modeling and artificial neural network) and sustainable application in industry. In contrast to purely experimental or exclusively numerical approaches, BIO ART integrates simulations and experiments at length and time scales ranging from the atomistic level to the engineering scale. The proposed project will contribute to close the four knowledge gaps: i) use of exclusively bio-sourced molecules from abundant resources and natural fillers with competitive mechanical properties, ii) multiscale modeling of epoxy including its macromolecular network topology, iii) optimization of the resin formulation by an artificial neural network framework linking the chemical nature of the molecules to the mechanical properties, and iv) advanced mechanical characterization and processing of fiber-reinforced bio-composites. BIO ART’s consortium consists of four complementary Franco-German partners with recognized skills in the synthesis of bio-polymers and physicochemical characterization (ICMPE/FR), in microstructure generation and surrogate models based on artificial neural networks (MSME/FR) as well as in multiscale modeling of polymers and discrete-to-continuum coupling methods (FAU/DE), and in composite processing and advanced mechanical characterization (UBT/DE). The scientific program is divided into 5 work packages: WP1: Synthesis of bio-sourced epoxy, WP2: Characterization of bio-sourced epoxy, WP3: Multiscale modeling, WP4: Optimization of bio-sourced epoxy formulation by artificial neural network, and WP5: Composite processing and mechanical characterization. The work packages are defined in a way that they can be completed in 3 years by 3 collaborating doctoral researchers, one for experimental part and two for the numerical part. A technician will support the experimental PhD candidate as regards the processing and characterization of the obtained materials. Beyond them, BIO ART’s consortium, which is a well-balanced composition of early career and senior scientists, will actively contribute to achieve the project’s milestones. BIO ART’s methods are up-to-date, are based on recently published results, and benefit from the strong synergies with current projects of the project partners. In particular, the experimental and numerical methods will range from the atomistic scale (molecular structure, synthesis of constituents, molecular dynamics simulations), to the mesoscale (curing process, network characterization, network model), and to the macroscale (fracture properties, continuum mechanical simulations). This methodology will focus on the investigation of the relationship between the structure and the multiscale properties of the obtained materials. This approach will synergistically combine modelling with experimental characterizations, which will allow to address the scientific issues of this project. This multidisciplinary scientific approach will allow BIO ART to respond to a current crucial societal issue, i.e. biosourced polymer materials from circular bio-economy, aimed for sustainable development applications

The subject of this project is the 3D printing (SLS) of PA12/glass beads composite for applications in aerospace industry. The SLS process uses laser sintering of composite powder with polymer matrix containing glass beads. One of the limiting points of polymers composites for their use in aerospace systems is their durability, and more specifically their resistance to failure due to fatigue cracking. The objective of this project will focus on the study of finished products obtained by SLS of composites powders and their resistance to cracking. The objectives of this work are to understand failure mechanisms in these highly heterogeneous materials at two scales, the scale of the microsctructure and the scale of the workpiece, by combining experimental characterization of cracks networks by mechanical testing, 3D imaging by X-rays laboratory microtomography image analysis, and numerical simulations. The identified microstructural damage models will be used to construct a crack propagation model at the scale of the workpieces, and will account for specificities related to the material and the process: the highly heterogeneous nature of the microstructure and its strong anisotropy due to the layered structure obtained by SLS. Then, it will be used to optimize the process parameters and the shapes of products in the design step. Up to now, the damage mechanisms in compounds obtained by SLS 3D printing are not very well understood, even less for products obtained from composite powders. The objectives imply several challenges related to the numerical simulation of complex crack networks in highly heterogeneous materials, the detection of micro cracks by 3D imagery imaging within combined with in situ mechanical testing, the modelling of damage and its identification at both micro and macro scales. The mechanical parameters, including the damage ones, will be characterized at the micro and macro scales by approaches combining tomography within microstructures (damage at the interfaces, damage related to the layered structure of the material) or at the scale of the workpiece, and numerical simulations through inverse approaches. The studied material is obtained from composite powder made of a polymer matrix of PA12 and containing glass beads. The powder is then sintered by laser to obtain 3D workpieces by PRISMADD. This project will allow optimizing the process parameters of the 3D process and the geometries of the workpieces with respect to failure criteria and lightweight. A numerical simulation code working able to capture damage mechanisms at both microscopic and macroscopic scales will be developed, based on the phase field method. This technique allows modelling initiation, propagation and merging of complex 3D crack networks in heterogeneous media. The method will be extended to the behaviour related to the material, characterized by a strongly nonlinear anisotropic behaviour. The tasks will consist into: (a) developing an efficient modeling numerical framework for simulating complex networks of cracks in highly heterogeneous microstructures from voxel models such as those arising from X-rays computed micro tomography imaging (XRµCT) and at the scale of the workpieces; (b) manufacturing by SLS 3D printing samples for a set of controlled process parameters; (c) characterize the strength properties of the new manufactured materials, with both macroscopic experimental mechanical testing and imaging at microscale, based on in situ mechanical testing in imaging devices and full-field kinematic measurement techniques, in 2D (optical observation) and in full 3D (XRµCT) ; (d) proposing microstructural and macroscopic damage models, identifying them by the mentioned experiments, and developing simplified multiscale damage models for bridging micro and macro damage; (e) optimizing the process parameters and the geometries of the produced workpieces with respect to the strength resistance of the produced products.