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Solid Mechanics and Failure

The newest addition to the ME department, Professor Jean-François Molinari, is interested in failure. Not failure of the personal kind, assuredly, but failure analysis of solids that are subjected to a variety of stressful conditions. Materials subjected to tremendous pressure and highly repetitive activities, such as human knee prostheses or high-speed manufacturing tools, exhibit wear and roughening, eventually leading to failure. Satellites confront micrometeorites traveling at speeds of about 4,000 m/s, and damage is inevitable and costly. For such complex problems, in which material deformation is very large, no closed form analytical solutions exist. It is often not practical or even possible to subject an object to various real-world fatigue-inducing conditions in the laboratory. A solution to this problem is Computational Mechanics. Prof. Molinari is an expert in using finite-element computational methods to study different kinds of material failure, including thermal and mechanical fatigue, large deformations, and wear. Ultimately, this kind of modeling could lead to improved design specifications for various engineering applications, by optimizing the overall structure and the composite materials used.

In finite element analysis, the structure to be modeled is subdivided into a finite set of elements of simple shape, say, tetrahedra or cubes. The mechanical, thermal, chemical, or other properties are then approximated at a finite number of nodes defining the elements. Upon applying boundary conditions, mathematical techniques are used to solve very large systems of equations. For dynamic problems the numerical time steps range from the order of nanoseconds, for impact events, to seconds or larger, for fatigue events. This means that the equation solving needs to be repeated a large number of times, and computational efficiency is an important consideration. When a large deformation occurs, the arrangement of nodes and elements, referred to as the “mesh,” becomes distorted. The way the mesh evolves over time tells a “story” of the deformation and the response of the material under scrutiny. Prof. Molinari uses an adaptive mesh, which adjusts itself when areas of significant deformation occur, preventing nodes from crossing over each other and providing finer detail in areas of interest. With the ability to pinpoint and selectively analyze areas that are undergoing relatively more change, the finite element analysis combined with adaptive meshing optimizes the computational resources.

Prof. Molinari uses this model to computationally test different kinds of composite materials, conditions, and geometries in an effort to optimize design parameters. Coating turbine blades with an extra layer of material, for example, protects them from thermal fatigue and wear. The interface characteristics (such as roughness) between the substrate and the coating layer can also be optimized to achieve better fatigue properties. This kind of modeling effort is particularly useful, since by coupling mechanical, thermal, and chemical effects together—a “multiphysics” approach—much can be learned about the characteristics and behavior of newly designed composite materials before they are used in any real applications. Likewise, those interested in designing new materials and structures can turn to these models to determine what kinds of chemical and mechanical properties the material will need if it is to withstand a particular environment.