Mathematical Sciences: Crack Propagation in Linear and Nonlinear Viscoelastic Material

8903672沃尔顿这个项目的目的是分析线性和非线性粘弹性材料中裂纹扩展的各种数学模型。对于线性材料模型，主要关注动态裂纹扩展，重点研究与复合材料相关的边值问题。这项工作的重点是获得包含裂纹尖端失效区的初始/边值问题的解析解；所使用的断裂准则基于对该失效区的功输入。研究了各种裂纹尖端本构模型。对于非线性材料模型，主要集中在分析裂纹扩展的有限元方法上。初始假定裂纹准静态扩展和小应变，非线性通过本构方程进入。随后，将考虑动力效应和几何非线性。这项工作的主要目的是发展有限元模拟的扩展裂纹在非线性粘弹性材料使用断裂准则的基础上纳入裂纹尖端破坏区到模型。再次，将研究各种裂纹尖端本构模型。

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.