Precise Algorithm In Time Domain For Solving Nonlinear Viscoelastic Problems

Numerical solution to nonlinear viscoelastic problems has notable signification boththeoretically and practically.Basically, nonlinear viscoelastic problems can be studied as physically nonlinearproblems or geometrically nonlinear problems. In this paper, physical nonlinearity isdiscussed in two parts, one part is concerned with the field problems of nonlinear viscoelastichomogeneous materials, while the other part predicts equivalent constitutive relation ofinhomogeneous materials in a macroscopically way. Otherwise, geometric nonlinearproblems discussed in this paper are mainly focused on large deformation of viscoelasticmaterials. In view of entirety, stability analysis of viscoelastic structures is also placed in thegeometrical nonlinearity part. This paper studies nonlinear viscoelastic problems withapplication of a self-adaptive precise algorithm in the time domain, main work as follow1. Combining with FEM, a precise numerical model is set up for solving nonlinearviscoelastic static/dynamic problems with integral constitutive, utilizing a two-levelexpansion technique of field variables and integral variables. (Chapter 2)2. Taking advantage of asymptotic homogenized solution and FEM, a precise numericalmodel is established to solve macroscopically equivalent field problems of periodicalviscoelastic materials. (Chapter 3)3. A precise numerical model is set up to analyze the static and dynamic stability ofviscoelastic beam in virtual of FEM. Viscoelastic critical load, maximal critical load andcritical time are work out exactly. (Chapter 4)4. A precise numerical model is established to analyze large deformation of viscoelasticmaterials utilizing FEM, the computation requires no iteration except for the firststep.(Chapter 5)5. Combining a group theory based EFGM, a precise numerical model is set up forviscoelastic problems with cyclic symmetry utilizing a partitioning algorithm which cutcomputational cost effectively. (Chapter 6)6. According to numerical models mentioned above, numerical validation showssatisfactory performance.It is presented that the precise numerical models can convert non-lineardifferential/integral space-time coupled initial-boundary values problems into a series of recursive linear boundary value problems. There will be no requirement of hypothesize oriteration for nonlinear problems. Numerical validation shows satisfactory performance. Theycan be useful tools for numerically solving nonlinear viscoelastic problems.