考虑Cowper-Symonds黏塑性材料本构的向量式有限元三角形薄壳单元研究

Study on triangular thin-shell element of vector form intrinsic finite element considering Cowper-Symonds viscoplastic constitutive model

薄壳结构的力学行为分析往往涉及显著的材料非线性效应,对爆炸、冲击等高速动力问题还需进一步考虑高应变率效应的影响。基于此,将可同时考虑应变硬化和应变率效应的Cowper-Symonds黏塑性材料本构模型(简称C-S模型)引入向量式有限元三角形薄壳单元,以实现金属薄壳结构的动力非线性分析。推导了C-S模型的弹塑性增量分析步骤,并将其作为单独的计算分析模块引入薄壳结构的向量式有限元分析程序,适用于线弹性、理想弹塑性、双线性弹塑性和率相关C-S模型等4种材料模型条件下的薄壳结构分析。算例分析表明,所编制的向量式有限元程序可以有效实现非线性材料情况下薄壳结构的静、动力分析以及爆炸冲击作用下的非线性动力响应分析,验证了文中C-S模型理论推导和程序的正确、可靠。

Analysis of complex behavior for thin-shell structures often involves significant effect of material nonlinearity. For high-speed dynamic problems such as explosion and impact, the effect of high strain-rate should also be considered. The Cowper-Symonds viscoplastic constitutive model （C-S model） considering both strain hardening effect and strain-rate effect is introduced into the triangular thin-shell element of vector form intrinsic finte element （VFIFE） , so that the dynamic nonlinear analysis of thin metal shells can be realized. The elasto-plastic incremental analysis steps of the C-S model are derived in detail, and the C-S model is introduced into the VFIFE program as a separate calculation module. The program is applicable for the analysis of thin-shell structures with four material models including linear elastic, perfect elasto-plastic, bilinear elasto-plastic and rate-dependent C-S models. Results from numerical examples show that, static analysis, dynamic analysis and nonlinear dynamic analysis under explosion loading for thin-shell structures under the condition of nonlinear material can all be well performed by the developed program, verifying the correctness and reliability of the theoretical derivation and the computer program.