A nonlinear programming method for plastic limit analysis of polymer composites with a unified physical model

This paper proposes a general methodology for the application of the classical plastic limit analysis to polymer materials with a unified physical model. The classical plastic limit analysis is based on the assumption of a perfectly plastic material model which is mostly expressed by separated elastic/yielding/plastic-flow laws. In order to introduce the unified physical model into the plastic limit analysis, the relation between the incremental and total values of field variables from yielding to plastic flow is analytically obtained. Then, a nonlinear programming method which was early developed by the author for a microstructure with classical material models is further extended, so that the plastic limit state of a polymer microstructure with the unified physical model can be solved in a direct way. The kinematic limit state of polymer composites is formulated as a nonlinear, non-smooth programming problem subject to equality constraints, which can be solved by a generalized direct iterative algorithm. The effectiveness and efficiency of the proposed algorithm are validated through numerical examples. The influence of the temperature dependence of glassy polymers on the macroscopic strength is also numerically investigated. The developed method can serve as a powerful tool for the microstructure design of polymer composites.