<p>Composite materials have been successfully applied in various industries, such as aerospace, automobile, and wind turbines, etc. Although the material properties of composites are desirable, the behaviors of composites are complicated. Many efforts have been made to model the constitutive behavior and failure of composites, but a complete and validated methodology has not been completely achieved yet. Recently, machine learning techniques have attracted many researchers from the mechanics field, who are seeking to construct surrogate models with machine learning, such as deep neural networks (DNN), to improve the computational speed or employ machine learning to discover unknown governing laws to improve the accuracy. Currently, the majority of studies mainly focus on improving computational speed. Few works focus on applying machine learning to discover unknown governing laws from experimental data.  In this study, we will demonstrate the implementation of machine learning to discover unknown governing laws of composites. Additionally, we will also present an application of machine learning to accelerate the design optimization of a composite rotor blade.</p> <p><br></p> <p>To enable the machine learning model to discover constitutive laws directly from experimental data, we proposed a framework to couple finite element (FE) with DNN to form a fully coupled mechanics system FE-DNN. The proposed framework enables data communication between FE and DNN, which takes advantage of the powerful learning ability of DNN and the versatile problem-solving ability of FE. To implement the framework to composites, we introduced positive definite deep neural network (PDNN) to the framework to form FE-PDNN, which solves the convergence robustness issue of learning the constitutive law of a severely damaged material. In addition, the lamination theory is introduced to the FE-PDNN mechanics system to enable FE-PDNN to discover the lamina constitutive law based on the structural level responses.</p> <p><br></p> <p>We also developed a framework that combines sparse regression with compressed sensing, which leveraging advances in sparsity techniques and machine learning, to discover the failure criterion of composites from experimental data. One advantage of the proposed approach is that this framework does not need Bigdata to train the model. This feature satisfies the current failure data size constraint. Unlike the traditional curve fitting techniques, which results in a solution with nonzero coefficients in all the candidate functions. This framework can identify the most significant features that govern the dataset. Besides, we have conducted a comparison between sparse regression and DNN to show the superiority of sparse regression under limited dataset. Additionally, we used an optimization approach to enforce a constraint to the discovered criterion so that the predicted data to be more conservative than the experimental data. This modification can yield a conservative failure criterion to satisfy the design needs.</p> <p><br></p> <p>Finally, we demonstrated employing machine learning to accelerate the planform design of a composite rotor blade with strength consideration. The composite rotor blade planform design focuses on optimizing planform parameters to achieve higher performance. However, the strength of the material is rarely considered in the planform design, as the physic-based strength analysis is expensive since millions of load cases can be accumulated during the optimization. Ignoring strength analysis may result in the blade working in an unsafe or low safety factor region since composite materials are anisotropic and susceptible to failure. To reduce the computational cost of the blade cross-section strength analysis, we proposed to construct a surrogate model using the artificial neural network (ANN) for beam level failure criterion to replace the physics-based strength analysis. The surrogate model is constructed based on the Timoshenko beam model, where the mapping is between blade loads and the strength ratios of the cross-section. The results showed that the surrogate model constraint using machine learning can achieve the same accuracy as the physics-based simulation while the computing time is significantly reduced. </p>

Two methods using lumped element (lumped parameter) methods to model flexible bodies have been presented. The methods are based on the concept of using a Guyan reduced stiffness matrix to describe the elasticity of a body. The component to be modeled has been divided into two parts using FE software and the mass and inertia tensor for the respective part of the component have been retrieved. The first method has been based on including the elements from the stiffness matrix in compliant constraints. The compliant constraints have been derived and a prototype has been implemented in MATLAB. It has been shown that using compliant constraints and stiffness parameters from a Guyan reduced stiffness matrix it is possible, with highly accurate results, to describe the deformation of a flexible body in multibody simulations. The second method is based on springs and dampers and has been implemented in the simulation environment Dymola. The springs and dampers have been constructed to include coupling elements from a Guyan reduced stiffness matrix. It has been shown that using the proposed method it is possible, with highly accurate results, to describe the static deformation of a flexible body. Further, using dynamic simulations of a full robot manipulator model, it has been shown that it is possible to use the spring-damper model to capture the deformation of the links of a manipulator in dynamic simulations with large translations and rotations.

<p>Li-ion batteries is a system that dynamically couples electrochemistry and mechanics. The electrochemical processes occurring during battery operation induces a wealth of elemental mechanics such as deformation, plasticity, and fracture. Likewise, mechanics influences the electrochemical processes via modulating the thermodynamics of Li reactions and kinetics of ionic transport. These complex interrelated phenomena are far from being well understood and need to be further explored. This thesis studies the couplings between the mechanical phenomena and electrochemical processes in Li-ion batteries using integrated theories and experiments. </p> <p>A continuum model coupling the kinetics of Li diffusion and kinematics of large elasto-plastic deformation is established to investigate the coupling between Li transport and stress evolution in electrodes of Li-ion batteries. Co-evolutions of Li distribution, stress field and deformation in the electrodes with multiple components are obtained. It is found that the Li profile and stress state in a composite electrode are significantly different from <a></a><a>that </a>in a free-standing configuration, mainly due to the regulation from the mechanical interactions between different components. Chemomechanical behaviors of the heterogeneous electrodes in real batteries are further explored. Three-dimensional reconstructed models are employed to investigate the mechanical interactions of the constituents and their influence on the accessible capacity of batteries. </p> <p>Structural disintegration of the state-of-art cathode materials LiNi_xMn_yCo_zO₂ (x+y+z=1, NMC) during electrochemical cycling is experimentally revealed. Microstructural evolution of different marked regimes in electrodes are tracked before and after lithiation cycles. It is found that the decohesion of primary particles constitutes the major mechanical degradation in the NMC materials. Electrochemical impedance spectroscopy (EIS) measurement confirms that the mechanical disintegration of NMC secondary particle causes the electrochemical degradation of the battery. To reveal the reasons for particle disintegration, the dynamic evolution of mechanical properties of NMC during electrochemical cycling is explored by using instrumented nanoindentation. It is found that the elastic modulus, hardness, and interfacial fracture strength of NMC secondary particle significantly depend on the lithiation state and degrade as the electrochemical cycles proceed, which may cause the damage accumulation during battery cycling.</p> <p>Corrosive fracture of electrodes in Li-ion batteries is investigated. Li reaction causes embrittlement of the host material and typically results in a decrease of fracture toughness. The dynamics of crack growth depends on the chemomechanical load, kinetics of Li transport, and the Li embrittlement effect. A theory of coupled diffusion, large deformation, and crack growth is implemented into finite element program and the corrosive fracture of electrodes under concurrent mechanical and chemical load is simulated. The competition between energy release rate and fracture resistance as crack grows during both Li insertion and extraction is examined in detail, and it is found that the corrosive fracture behaviors of the electrodes rely on the chemomechanical load and the supply of Li to the crack tip. The theory is further applied to model corrosive behavior of intergranular cracks in NMC upon Li cycles. The evolving interfacial strength at different states of charge and different cycle numbers measured by in-situ nanoindentation is implemented in the numerical simulation.</p>