Set Of Internal State Variables Research Articles

Analysis of composite structures with distributed and localized damage by the finite-element method

A finite-element method of analysis is proposed for the analysis of composite laminates containing transverse cracks. The formulation is particularly simple as the effects of the damage are fully incorporated into the damage vector, which contains the set of internal state variables. Application of the finite-element code is demonstrated through examples of analysis of composite laminates with centrally located holes. Comparison with experimental stress-strain curves show good agreement with the present finite-element results. Furthermore, the finite-element analysis also enables the damage distribution maps to be obtained for each individual layer.

Predicted temperature field in a thermomechanically heated viscoplastic space truss structure

s - surface area This paper focuses on the effect of thermomechanically induced heating on the response of a single member of a space truss structure which behaves viscoplastically. The governing equations are given for a typical truss member, wherein material inelasticity is reflected in constitutive equations via a set of internal state variables, each characterized by a history dependent growth law. The governing equations are coupled in the sense that temperature and displacement are dependent on each other. This difficulty, together with the fact that the inelastic constitutive equations are nonlinear and numerically stiff, requires that a computationally complex semidiscretized finite element spatial technique be utilized to obtain a solution. This procedure, detailed herein, is utilized to predict the response of a typical metallic space ,truss member under vibrational or cyclic loading. Particular interest is placed on the temperature rise in such a member due to hysteretic loss during structural vibrations and in the presence of complex thermal boundary conditions representative of space conditions. Example cases are constructed for a typical cylindrical bar of 6061-T6 aluminum both with and without special coatings. Results indicate that significant, possibly even catastrophic, heating can occur due to thermomechanical coupling.

Nonlinear viscoelasticity and relaxation phenomena of polymer solids

The specific Helmholtz free energy of nonlinear viscoelastic isotropic polymer solids is assumed to be a separable, symmetric function along three orthogonal principal strain directions, i.e.Ψ=ψ(λ1,qn(1))+ψ(λ2,qn(2))+ψ(λ3,qn(3)), where theλr (r=1, 2, 3) are three principal stretch ratios and theqn(r) are a set of internal state variables. It is shown that, by using this postulated form of the free energy function, one can readily characterize the mechanical response of viscoelastic polymer solids.