A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

Following their discovery in the early 1960s, there has been a continuous quest for ways to take advantage of the extraordinary properties of shape memory alloys (SMAs). These intermetallic alloys can be extremely compliant while retaining the strength of metals and can convert thermal energy to mechanical work. The unique properties of SMAs result from a reversible diffussionless solid-to-solid phase transformation from austenite to martensite. The integration of SMAs into composite structures has resulted in many benefits, which include actuation, vibration control, damping, sensing, and self-healing. However, despite substantial research in this area, a comparable adoption of SMA composites by industry has not yet been realized. This discrepancy between academic research and commercial interest is largely associated with the material complexity that includes strong thermomechanical coupling, large inelastic deformations, and variable thermoelastic properties. Nonetheless, as SMAs are becoming increasingly accepted in engineering applications, a similar trend for SMA composites is expected in aerospace, automotive, and energy conversion and storage-related applications. In an effort to aid in this endeavor, a comprehensive overview of advances with regard to SMA composites and devices utilizing them is pursued in this paper. Emphasis is placed on identifying the characteristic responses and properties of these material systems as well as on comparing the various modeling methodologies for describing their response. Furthermore, the paper concludes with a discussion of future research efforts that may have the greatest impact on promoting the development of SMA composites and their implementation in multifunctional structures.

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Review and perspectives: shape memory alloy composite systems

This article focuses on computational multiscale methods for the mechanical response of nonlinear heterogeneous materials. After a short historical note, a brief overview is given of some recent activities in the field, with a particular focus on nonlinear homogenization methods. The two‐scale nonlinear computational homogenization (CH) scheme for mechanics is presented, along with details on representative unit cell aspects and statistics. Model performance is advocated through a decoupled implementation and multiscale schemes based on the nonuniform transformation field analysis. High‐performance parallel multiscale implementations of the CH scheme are addressed in more detail.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119176817.ecm2107

Homogenization methods and multiscale modeling : Nonlinear problems

A generalized coupled viscoplastic–viscodamage–viscohealing theory for glassy polymers

Homogenization of elasto-(visco) plastic composites based on an incremental variational principle

A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites

End-to-End FE-Based Homogenization of Woven Composites

Whereas prediction of elastic properties of woven is a standard in the industry, prediction of their non-linear behavior remains a challenge. Accurate prediction of the non-linear behavior is the key for a successful modeling of woven composites solicited by off-axis loading. Woven composites are represented by interlacing yarns impregnated by a resin matrix. Yarns are made of a resin matrix reinforced by continuous fibers. Homogenization of woven composites therefore requires two levels of homogenization, the one of the yarn and the one of the ply. Finite element (FE) based homogenization at the ply level can be combined with mean-field homogenization at the yarn to predict the mechanical behavior of a single ply. The main difficulty of this approach lies in the generation of representative volume element (RVE) of a single ply. An end-to-end FE based homogenization of woven composites was developed in Digimat®. The developed set of tools allows running finite element simulations on single ply woven RVE with the use of mean-field homogenization at the yarn level. Generated RVEs are meshed with voxels to avoid meshing troubles in resin rich pockets between yarns or close to yarn crossings. The local fiber orientation used in the yarn homogenization is function of the yarn curvature. A fully analytical framework based on mean-field homogenization has also been developed. The particularity of this framework is that it takes yarn curvature into account. The developed tools will be presented and the FE based and mean-field homogenization predictions of linear and non-linear properties will be compared to experimental measurements on plain weave and 5HS carbon epoxy woven composites.

Jean-Sébastien Gerard

Papers

A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites

End-to-End FE-Based Homogenization of Woven Composites

End-to-End FE Based Homogenization of Woven Composites