Fractional mechanics for composites
Abstract
The main objective of this fundamental research project is to develop and experimentally validatean innovative multiscale and multiphysics nonlocal theoretical framework to track the degradationof composite materials and to predict the formation and propagation of damage. The proposedapproach is expected to largely surpass the performance of traditional techniques, based onempirical and data-fitting methodologies, by embracing a fully mechanistic view of the damageprocess. This research promotes a remarkable paradigm shift in damage mechanics by leveragingthe rapidly growing field of fractional mechanics, that is a reformulation of mechanics via fractionalorder calculus. The implications of using fractional order mathematics to simulate damagemechanics are profound at both mathematical and physical levels. The intrinsic nonlocal, multiscale,and evolutionary nature of the fractional framework can naturally transfer information acrossscales and adapt the underlying structure of the model to the dominant damage mechanisms andphysical processes at the given scale. The result is a framework capable of unprecedented accuracyand computational efficiency without requiring a priori information typical of classical fatigue andfracture mechanics. To achieve these goals, this research will develop innovative theoretical andnumerical tools. At the theoretical level, distributed and variable-order fractional calculus willbe leveraged as the foundation of a physically, mathematically, and thermodynamically consistentformulation of nonlinear mechanics that will lead to a fully mechanistic representation of fatiguein composites. At the numerical level, methods to solve the distributed-variable-order frameworkwill be developed by combining both concepts of multimesh finite elements and machine learning.Finally, the newly developed modeling tools will be extensively validated against experimentalresults available in the literature.Distributed and variable-order fractional calculus isused as the foundation of a formulationthat leads to a fully mechanistic approach to fatigue and damage mechanics in composites. Thisapproach is in stark contrast to currently available methodologies that approach fatigue as an #aposteriori# study based on empirical relations applied to either stress or strain data. The DVOframework approaches the failure problem from a multiscale structural analysis perspective wherethe damage becomes a calculated field quantity, similarly to other classical quantitieslike deformationsand thermo-mechanical stresses. This radical shift of perspective is possible because thefractional approach captures, in a unified and cohesive mathematical framework, many importantmechanisms controlling the damage process across scales. A few examples include the abilityto deliver fully integrated multiscale capabilities, a natural connection between scales without theneedfor complex handshaking algorithms, the ability to adapt the mathematical formulation (hencethe physical response of the system) asdamage evolves. All this can be achieved without #a priori#information on the damage (e.g. type of damage, location of damage initiation, preferentialdirection of propagation). The combination of these unique capabilities leads to a modeling environmentwith high computational efficiency and a degree of accuracy unattainable even with themost recent damage mechanics approaches.The proposed framework is expected to be generally applicable to discrete or continuum levelformulations. Therefore, while this project targets damage mechanics of fibrous composites, thetheoretical and numerical methodologies are directly extendable to other material systems (e.g. ceramiccomposites) and applications (e.g. fluid-dynamics, fluid-structure-interaction, heat transfer,electromagnetism).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 08, 2024
- Source ID
- N000142412480
Entities
People
- Fabio Semperlotti
Organizations
- Office of Naval Research
- Purdue University
- United States Navy