Abstract

A model of non-isothermal viscoelastic-viscoplastic deformation of multidirectionally reinforced flexible plates has been developed. The viscoplastic deformation of isotropic materials of the composition is described by the relations of the flow theory with isotropic hardening, which take into account the dependences of the loading functions on temperature and strain rate intensity. The viscoelastic behavior of the composition components is described by the equations of the Maxwell–Boltzmann model. The weakened resistance of reinforced plates to transverse shifts is modeled by the Ambartsumian bending theory relations, and the geometric nonlinearity is modeled in the Karman approximation. The connection between the thermophysical and mechanical components of the problem of inelastic dynamic deformation of reinforced plates is taken into account. The temperature over the thickness of structures is approximated by a 7th order polynomial. The numerical solution of the formulated nonlinear two-dimensional problem is constructed using an explicit scheme of time steps. The viscoelastic-viscoplastic dynamic behavior of a relatively thin glass-plastic plate is studied with and without allowance for the thermal response in it. The structure is loaded transversely with an air blast wave. It is shown that the failure to take into account the thermal response in a fiberglass plate can significantly distort the calculated fields of residual deformations of the components of its composition, despite the fact that the maximum heating of such a structure does not exceed 10°C. Viscoelastic-plastic calculations, when the sensitivity of the composite materials to the rate of their deformation can be neglected, can reasonably be carried out without taking into account the thermal response of the composite plate, if there are no external heat sources of non-mechanical origin.

中文翻译：

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弯曲钢筋板的非等温粘弹粘塑性变形建模

摘要

建立了多向增强柔性板的非等温粘弹性-粘塑性变形模型。组合物的各向同性材料的粘塑性变形通过流动理论与各向同性硬化的关系来描述，其中考虑了载荷函数对温度和应变速率强度的依赖性。成分组分的粘弹性行为由麦克斯韦-玻尔兹曼模型方程描述。采用安巴楚弯曲理论关系对加强板横向位移的减弱阻力进行建模，并采用卡门近似对几何非线性进行建模。考虑了增强板非弹性动态变形问题的热物理和力学分量之间的联系。结构厚度上的温度由七阶多项式近似。所表述的非线性二维问题的数值解是使用显式的时间步长方案构建的。研究了相对较薄的玻璃塑料板的粘弹性-粘塑性动态行为，考虑或不考虑其中的热响应。该结构受到空气冲击波的横向加载。结果表明，尽管这种结构的最大加热不超过 10°C，但如果不考虑玻璃纤维板的热响应，其成分的残余变形的计算场会显着扭曲。 。当可以忽略复合材料对其变形速率的敏感性时，如果没有非机械的外部热源，可以合理地进行粘弹塑性计算，而不考虑复合材料板的热响应起源。