Mathematical Sciences: Crack Propagation in Linear and Nonlinear Viscoelastic Material

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8903672 Walton The purpose of this project is to analyze various mathematical models of propagating cracks in linear and nonlinear viscoelastic material. For the linear material models, the principle interest is dynamic crack growth with emphasis given to boundary value problems relevant to composites. The focus of this effort is toward obtaining analytical solutions to initial/boundary value problems incorporating a crack-tip-failure-zone into the model; the fracture criterion utilized is based upon the work input to this failure zone. Various crack-tip constitutive models are studied. For the nonlinear material models, the principal focus is on finite element methods for analyzing crack growth. Initially, quasi-static crack growth and small strains is assumed, the nonlinearity entering through the constitutive equations. Subsequently, dynamic effects and geometric nonlinearity will be considered. The principal goal of this work is the development of finite element simulations for growing cracks in nonlinear viscoelastic material utilizing a fracture criterion based upon incorporation of a crack-tip-failure-zone into the model. Again, various crack-tip constitutive models will be studied.