Polymer composite materials: A comprehensive review

Artificial intelligence, especially machine learning (ML) and deep learning (DL) algorithms, is becoming an important tool in the fields of materials and mechanical engineering, attributed to its power to predict materials properties, design de novo materials and discover new mechanisms beyond intuitions. As the structural complexity of novel materials soars, the material design problem to optimize mechanical behaviors can involve massive design spaces that are intractable for conventional methods. Addressing this challenge, ML models trained from large material datasets that relate structure, properties and function at multiple hierarchical levels have offered new avenues for fast exploration of the design spaces. The performance of a ML-based materials design approach relies on the collection or generation of a large dataset that is properly preprocessed using the domain knowledge of materials science underlying chemical and physical concepts, and a suitable selection of the applied ML model. Recent breakthroughs in ML techniques have created vast opportunities for not only overcoming long-standing mechanics problems but also for developing unprecedented materials design strategies. In this review, we first present a brief introduction of state-of-the-art ML models, algorithms and structures. Then, we discuss the importance of data collection, generation and preprocessing. The applications in mechanical property prediction, materials design and computational methods using ML-based approaches are summarized, followed by perspectives on opportunities and open challenges in this emerging and exciting field.

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Artificial intelligence and machine learning in design of mechanical materials

Higher–order nonlocal gradient elasticity: A consistent variational theory

Nanoporous materials find a wide range of applications spanning diverse disciplines For sufficiently small nanopores, surface effects must be accounted for in calculating homogenized moduli and local stress fields Surface effects are typically simulated using the Gurtin-Murdoch model based on the concept of an infinitesimally thin surface with its own elastic moduli and equilibrium conditions This paper critically reviews the different approaches employed in the calculation of both homogenized moduli and local stress fields of unidirectional nanoporous materials in a wide range of porosity volume fractions, pore sizes and different array types These approaches include classical micromechanics, elasticity-based, finite-element and finite-volume techniques The vehicles for comparison which provide the gold standard are two recently extended homogenization theories with incorporated Gurtin-Murdoch type surfaces The locally-exact homogenization theory is an efficient elasticity-based approach which accurately yields the full set of homogenized moduli and concomitant local stress fields in rectangular, square and hexagonal porosity arrays of unidirectional nanocomposites The theory's excellent stability, quick convergence and rapid execution times enable extensive parametric studies to be conducted efficiently The second homogenization theory is the recently generalized finite-volume direct averaging micromechanics approach This theory provides greater flexibility in simulating the response of nanoporous materials with arbitrarily shaped porosities, and exhibits herein demonstrated greater range of numerical stability relative to the commonly used finite-element method New results are generated aimed at demonstrating the effects of nanopore volume fraction, radii and arrays on homogenized moduli, local stress fields and initial yield surfaces These results highlight the importance of adjacent pore interactions neglected in the classical micromechanics models, which are critically assessed

Homogenization and localization of nanoporous composites - A critical review and new developments

Higher order mixture nonlocal gradient theory of wave propagation

Finite-volume homogenization of elastic/viscoelastic periodic materials

Homogenization and localization of elastic-plastic nanoporous materials with Gurtin-Murdoch interfaces: An assessment of computational approaches

The recently generalized locally-exact homogenization theory is further extended to enable the determination of homogenized moduli and local stress fields in unidirectional nano-composites with surface effects based on the Gurtin-Murdoch model. The excellent stability and quick convergence of the homogenization theory with the concomitant rapid execution times enables repetitive solutions of the unit cell problem with variable geometric and material parameters, thereby enabling extensive parametric studies to be conducted efficiently. The distinguishing feature of the theory is its ability to provide accurate homogenized moduli as well as accurate local stress fields for square, rectangular and hexagonal arrays of nano-inclusions or nano-porosities. The extended elasticity-based computational capability is validated by published results on homogenized moduli and stress concentrations in nanoporous aluminum obtained using classical micromechanics, elasticity-based, semi-analytical and numerical approaches. New results are generated aimed at demonstrating the effects of nanopore arrays on homogenized moduli and local stress fields in a wide range of porosity volume fractions and nanopore radii. These results highlight the importance of adjacent pore interactions either neglected or not directly taken into account in the classical micromechanics models, nor easily captured by numerical techniques.

Homogenized moduli and local stress fields of unidirectional nano-composites

Surface elasticity effects based on the Gurtin-Murdoch model are incorporated for the first time into a finite-volume based homogenization theory to enable analysis of materials with nanoscale cylindrical voids of circular and ellipsoidal cross-section in periodic arrays. In a departure from the previously employed enforcement of traction and displacement continuity conditions in a surface-average sense applied locally to each subvolume of the unit cell, the Young-Laplace equilibrium equations are implemented using a central-difference approach involving adjacent subvolumes, an approach both new to the finite-volume theory as well as necessary. In Part 1, the new computational capability is validated by published results on homogenized moduli, stress concentrations and full-field stress distributions in nanoporous aluminum obtained using elasticity-based and numerical approaches. Notably, numerical problems associated with singular-like stresses and associated instabilities experienced in finite-element solutions (as well as the elasticity solution of an elliptical void in an infinite matrix) are not as pronounced in the proposed approach, enabling determination of surface and full-field stresses in a wider range of pore radii. New results are generated in Part 2 aimed at demonstrating the effects of nanopore array type and aspect ratio of elliptical voids on homogenized moduli and local stress fields in a wide range of porosity volume fractions and radii. These results highlight the importance of adjacent pore interactions neglected in the classical micromechanics models , that remains to be quantified by numerical homogenization techniques.

Qiang Chen

Papers

Homogenization and localization of nanoporous composites - A critical review and new developments

Finite-volume homogenization of elastic/viscoelastic periodic materials

Homogenization and localization of elastic-plastic nanoporous materials with Gurtin-Murdoch interfaces: An assessment of computational approaches

Homogenized moduli and local stress fields of unidirectional nano-composites

Finite-volume homogenization and localization of nanoporous materials with cylindrical voids. Part 1: Theory and validation