Drying and/or cooling accompanies many industrial processes such as photographic, magnetic or protective coating; injection molding; and curing of concrete structures. This is always associated with volumetric changes, which sometimes are very large, and with changes in material properties that may not be negligible. Such changes are typically nonuniform in space and are often incompatible with the conditions imposed by the surrounding material such as coated substrate or the casting mold. As a result, stresses almost always develop in drying or cooling materials and, if they are sufficiently high, various defects of the manufactured product may occur. Predicting these stresses and controlling their magnitude is an important goal with various potential applications.
A model has already been developed to describe development of stress and deformation fields in drying viscoelastic materials. Materials with these properties are frequently used in practice, a fact which constitutes an important practical aspect of the project. The model is based on large deformation theory, referring to multiplicative decomposition of the deformation gradient into its elastic and viscous part. The third part of the deformation gradient, representing volumetric changes of the material, is also added in a similar, multiplicative fashion and, through the appropriate constitutive equations, is connected to the variables representing current state of drying or cooling. These variables, in turn, are governed by diffusion-type equations written for the medium that moves as a result of large deformations. Together, this leads to a highly nonlinear system and constitutes one academic side of the project.
Shongtao Dai, Minnesota Department of Transportation, Maplewood, Minnesota
Jason Graves, Graduate Student Researcher
Khalid Obeidat, Graduate Student Researcher
Zourab Tchomakhidze, Graduate Student Researcher
Julie M. Vandenbossche, Graduate Student Researcher
Zhong Zhao, Graduate Student Researcher
The second academic side of the project is development of a numerical technique to solve the resulting system of nonlinear equations and its computer implementation. In this process, the equations have been discretized using the finite element method. The resulting semidiscrete system of equations, describing time evolution of the discrete problem, are integrated in time numerically to solve the problem incremenatlly.
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URL: http://www.msi.umn.edu/about/publications/annualreport/ar2000/depts/IT/CivEng/stolarski.html |
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