Mechanical metamaterials provide tailorable functionality based on a careful combination of base material and structural architecture. Truss-based metamaterials, e.g., exploit structural topology and beam geometry to achieve beneficial mechanical and physical properties from stiffness and wave dispersion to strength and toughness. While the focus to date has been primarily on static metamaterial properties or elastic wave motion, 3D-printed polymeric base materials naturally come with significant viscoelasticity, making the effective truss response time- and rate-dependent. Here, we report a theoretical-numerical-experimental study which (i) deploys a linear viscoelastic corotational beam description (capturing finite rotations at small strains), (ii) implements the latter in a finite element framework, (iii) calibrates a generalized Maxwell model based on viscoelastic experiments on 3D-printed polymer samples, (iv) validates the theory and implementation through experimental truss benchmark tests, and (v) introduces a generalized continuum formulation for the efficient simulation of viscoelastic truss metamaterials containing large numbers of structural members. We show that the viscoelastic beam approach, calibrated via tension tests on individual strut samples, performs well when applied to complex truss lattices undergoing time-dependent stress relaxation — as verified by the effective mechanical response and full-field deformation maps. The resulting variational generalized continuum framework uses on-the-fly periodic homogenization based on a representative unit cell and is extended to dynamics by including inertial effects. By comparison to discrete numerical simulations we demonstrate the accuracy of the continuum approach, which is promising for modeling and optimizing 3D-printed truss metamaterials for engineering applications from shock-absorbing structures to rate-dependent architected materials and soft robotics.

机械超材料基于基础材料和结构架构的精心组合提供可定制的功能。例如，基于桁架的超材料利用结构拓扑和梁几何形状来实现从刚度和波色散到强度和韧性的有益机械和物理特性。虽然迄今为止的重点主要是静态超材料特性或弹性波运动，但 3D 打印的聚合物基础材料自然具有显着的粘弹性，使得有效的桁架响应时间和速率相关。在这里，我们报告了一项理论 - 数值 - 实验研究，其中（i）部署线性粘弹性共旋梁描述（捕获小应变下的有限旋转），（ii）在有限元框架中实现后者，(iii) 基于 3D 打印聚合物样品的粘弹性实验校准广义 Maxwell 模型，(iv) 通过实验桁架基准测试验证理论和实现，以及 (v) 引入广义连续介质公式，用于有效模拟粘弹性桁架超材料包含大量结构构件。我们表明，通过对单个支柱样品进行拉伸测试校准的粘弹性梁方法在应用于经历时间相关应力松弛的复杂桁架晶格时表现良好——如有效机械响应和全场变形图所证实的那样。由此产生的变分广义连续体框架使用基于代表性晶胞的动态周期性均匀化，并通过包括惯性效应扩展到动力学。