Mechanical joints are integral to structures, affecting performance and reliability. Joints provide coupling forces and moments between substructures, and introduce localized compliance and dissipation. Aspects of joint dynamics not fully understood include the nature of the slipping process between contacting interfaces, local impacts at mating surfaces away from the connecting elements, sensitivity of response to roughness of mating surfaces, and contaminants and lubricants which introduce uncertainty into the process of response prediction. The proposed research effort includes new developments in scale representation, efficient fine-scale estimation, and interscale coupling. A major contribution of the proposed work will be a systematic spatial decomposition into large and small scales, where the latter are mathematically injected into the calculations for the former. Another will be the representation of the joint interface as a strong discontinuity, leading to interfacial flux terms that provide a natural mechanism for embedding the constitutive laws in a variationally consistent fashion, and novel experiments yielding the required constitutive behavior of the interface.
These results will be broadly disseminated, through course materials, conference presentations, and publication in archival journals. Integral with the research effort is a plan for education and outreach, targeting middle school students quickly approaching the age where future career decisions are formed, initially through partnership with Jefferson Middle School in Champaign. Classroom demonstrations and experiments addressing fastener technologies will be developed. Undergraduate and graduate students will be recruited; ideally a broad demographic, for research, to construct demonstrations and experiments, and to mentor middle school students during the school year.
Mechanical joints are integral to modern structures, significantly affecting their dynamic response and, ultimately, performance and reliability. Joints provide the coupling forces and moments between connected substructures, and in the process introduce localized compliance and dissipation. Although joints are ubiquitous in practical engineering applications, there are certain aspects of their dynamics that are not fully understood. These aspects include but are not limited to the nature of the slipping process between contacting structural interfaces, the local impacts at mating surfaces at some distance from the connecting elements (i.e., bolts), and the sensitivity of structural response to roughness of the mating surfaces, contaminants and lubricants, and so forth. These difficulties introduce uncertainty into the process of response prediction, resulting in considerable variability from structure to structure, even for nominally identical material properties and geometry. The objective of the project was to develop a multiscale capability that is mathematically robust and computationally economical for the modeling of complex structures containing mechanical joints. A two pronged approach was followed: Basic research in multiscale computational methods as applied to problems with mechanical joints, complemented by carefully designed experiments to provide the physical basis for the development of interfacial constitutive models. The main attributes of the computational and the experimental investigations are presented below. Computational Contributions and Outcomes: A major aim of the computational aspect of this research was to develop a finite element method capable of simulating structures containing mechanical joints by incorporating constitutive models for frictional behavior. The key idea centered on the use of discontinuous Galerkin concepts locally at the interface to derive flux terms that couple the displacements and forces from the two sides of a joint in a weak sense. The resulting integral terms provide a natural avenue to embed models for frictional response in a consistent fashion as opposed to other traditional methods such as using discrete springs. This numerical method does not require additional Lagrange multiplier fields or enrichment of shape functions, thereby reducing the computational overhead and also avoiding the numerical bias associated with master-slave constructs. Alongside the developments for the bolted joints simulations, the numerical techniques were also applied to solve domain coupling problems and nonconforming contact problems. One bottleneck in the traditional finite element method is the nonconforming meshes that arise in substructure modeling when parts of a structure are meshed independently and connected together. The main issues caused by the mismatch of element faces and types along these junctures can be remedied by incorporating the interface flux terms from the discontinuous Galerkin method. The weak enforcement of continuity and equilibrium allows the nonconforming interfaces to be treated seamlessly. Another important component of the interface approach is the stabilized formulation that is derived based on Variational Multiscale ideas. By modeling the fine-scale features that are beyond the resolution capacity of a given finite element mesh, the method enhances the stability of the underlying mixed formulation to accommodate arbitrary element interpolation combinations and improves coarse mesh accuracy for problems involving incompressible materials. In particular, the method has been tested on distorted meshes and on problems with singularities, and has exhibited excellent performance. Additionally, the formulation contains a built-in error estimation module developed by exploiting the presence of numerical scales. Experimental Contributions and Outcomes The experimental part of the research program was aimed at developing and verifying a physics-based constitutive model of a joint. A meso-scale model accounting for crucial joint interface physics was developed by the PIs. This model was extended and verified to be applicable to macroscale joint applications. The experiments to verify the models were conducted by the partial slip tester designed and built by the authors, and further experiments were conducted to show the effect of roughness and lubrication on the joint behavior. The approach for the development of the friction models was based on continuum mechanics formulations at asperity scale and utilized statistical representation of surface roughness to model friction in macroscale applications. The models at each length scale were validated by experiments designed and traced from the literature. These models were incorporated in the variationally-consistent finite element models developed in the computational developments part of the overall effort.
