This paper presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material systems. An example demonstrates the integration of experimental data with a computational database. The statistical approach is based on the probabilistic learning on manifolds recently developed by the authors. This approach leverages intrinsic structure detected through diffusion on graphs with projected stochastic differential equations to generate samples constrained to that structure.

A computationally efficient multiscale-multiphysics model aimed at predicting mechanical response of thermoplastic composites subjected to different levels of moisture was developed. The mathematical model of the coupled moisture-diffusion-mechanical-deformation phenomenon was stated at the microscale, based on the observed experimental data, and then upscaled using a mathematical homogenization approach. A two-way coupling between moisture diffusion and mechanical deformation was introduced by which diffusivity was enhanced by hydrostatic strain, whereas strength and stiffness were assumed to degrade because of moisture ingression, which also gives rise to swelling. The computational complexity of analyzing the two coupled physical processes at multiple scales was reduced via a model reduction scheme for multiple physical processes. The model was validated for 30% by weight filled glass fiber and carbon fiber reinforced thermoplastic composites. The moisture conditioning and uniaxial tension experiments were utilized to identify diffusion and mechanical properties at a fine scale. The identified properties were then used to validate the formulation in the three-point bending test. motor oil, brake fluid, gasoline, and battery acid) has often resulted in overdesign and thus limited their insertion in load bearing components because the overdesigned component may not yield any mass advantages. There are two main reasons for this state of affairs: (1) existence of multiple spatial scales and multiple coupled physical processes, such as thermal, mechanical, and moisture diffusion; and (2) costly environmental degradation experiments that require long time exposure of the test specimens to varied levels of humidity and temperature conditions. Among the various thermoplastic composites, short fiber thermoplastics have been increasingly used in the automotive industry. Their usage is intended to fill the gap in the mechanical properties between continuous-long fiber composites, primarily used as structural members, and unreinforced polymers, used as non-load bearing members. Glass and carbon short fibers are primarily used as reinforcements in polyamides (PA/nylon) or polyphthalamides. The main applications are in body parts, such as door panels, hoods, bonnets, and bumpers, and engine parts including cam covers, engine mounts, fuel tanks, fuel cells, and interior trims including molded seats. These materials are in demand because of their manufacturing ease, versatility, low cost, corrosion resistance, and superior mechanical, thermal, and electrical properties.Polyamides of semi-crystalline composition are known to absorb moisture because of their chemical structure. Experimental studies of PA-6, PA-66, and PA-46 polyamides report an equilibrium moisture content varying in the range from 1.2 to 2.5 wt.% of water at 50% relative humidity (RH) and 23 ı C temperatures and about 8-9 wt.% upon reaching saturation conditions [6][7][8][9]. The moisture is first absorbed in the microcracks and macrocracks/voids, if present, ...

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Summary We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo‐chemo‐mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale‐multiphysics approach. To address the enormous computational complexity involved, a reduced‐order homogenization was originally developed for a single physics problem is employed. The proposed reduced‐order two‐scale thermo‐chemo‐mechanical model has been validated for predicting part distortion beam strength in three‐point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.

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