Analytical investigations to characterize the effective mechanical properties of lattice materials allow an in-depth exploration of the parameter space efficiently following an insightful, yet elegant framework. 2D lattice materials, which have been extensively dealt with in the literature following analytical as well as numerical and experimental approaches, have limitations concerning multi-directional stiffness and Poisson's ratio tunability. The primary objective of this paper is to develop mechanics-based formulations for a more complex analysis of 3D lattices, leading to a physically insightful analytical approach capable of accounting the beam-level mechanics of pre-existing intrinsic stresses along with their interaction with 3D unit cell architecture. We have investigated the in-plane and out-of-plane effective elastic properties to portray the physics behind the deformation of 3D lattices under externally applied far-field normal and shear stresses. The considered effect of beam-level intrinsic stresses therein can be regarded as a consequence of inevitable temperature variation, pre-stress during fabrication, inelastic and non-uniform deformation, manufacturing irregularities etc. Such effects can notably impact the effective elastic properties of lattice materials, quantifying which for 3D honeycombs is the central focus of this work. Further, from the material innovation viewpoint, the intrinsic stresses can be deliberately introduced to expand the microstructural design space for effective elastic property modulation of 3D lattices. This will lead to programming of effective properties as a function of intrinsic stresses without altering the microstructural geometry and lattice density. We have proposed a generic spectral framework of analyzing 3D lattices analytically, wherein the beam-level stiffness matrix including the effect of bending, axial, shear and twisting deformations along with intrinsic stresses can be coupled with the unit cell mechanics for obtaining the effective elastic properties.

中文翻译：

---

具有本征应力的 3D 晶格材料的有效弹性特性：自下而上的光谱表征和本构编程


表征晶格材料有效机械性能的分析研究允许按照一个有洞察力而优雅的框架有效地深入探索参数空间。二维晶格材料在文献中已按照分析以及数值和实验方法进行了广泛处理，但在多向刚度和泊松比可调性方面存在局限性。本文的主要目标是开发基于力学的公式，用于更复杂的 3D 晶格分析，从而形成一种具有物理洞察力的分析方法，能够解释预先存在的内禀应力的梁级力学以及它们与 3D 晶胞架构的相互作用。我们研究了面内和面外的有效弹性特性，以描绘 3D 晶格在外部施加的远场法向应力和剪切应力下变形背后的物理特性。其中梁级内应力的考虑效应可以被视为不可避免的温度变化、制造过程中的预应力、非弹性和非均匀变形、制造不规则性等的结果。这种效应可以显着影响晶格材料的有效弹性特性，量化 3D 蜂窝的弹性特性是本研究的中心重点。此外，从材料创新的角度来看，可以有意引入内禀应力来扩大微观结构设计空间，以实现 3D 晶格的有效弹性特性调制。这将导致在不改变微观结构几何形状和晶格密度的情况下将有效属性编程为内禀应力的函数。 我们提出了一个解析分析 3D 晶格的通用谱框架，其中梁级刚度矩阵（包括弯曲、轴向、剪切和扭曲变形的影响以及内禀应力）可以与晶胞力学耦合以获得有效的弹性特性。