Abstract
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.
Highlights
Architectural design plus base material determine the effective mechanical properties of metamaterials based on, e.g., trusses (Wadley et al, 2008; Meza et al, 2015), plates and shells (Zheng et al, 2018; Bonatti and Mohr, 2019), or spinodal structures (Vidyasagar et al, 2018; Kumar et al, 2020)
We report a theoretical-numerical-experimental study which (i) deploys a linear viscoelastic corotational beam description, (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
The discrete truss is replaced by a continuous body, whose effective mechanical constitutive behavior is obtained from on-the-fly numerical homogenization of a representative unit cell, and whose deformation is solved by a finite element calculation on the macroscale
Summary
Architectural design plus base material determine the effective mechanical properties of metamaterials based on, e.g., trusses (Wadley et al, 2008; Meza et al, 2015), plates and shells (Zheng et al, 2018; Bonatti and Mohr, 2019), or spinodal structures (Vidyasagar et al, 2018; Kumar et al, 2020). The discrete truss is replaced by a continuous body, whose effective mechanical constitutive behavior is obtained from on-the-fly numerical homogenization of a representative unit cell, and whose deformation is solved by a finite element calculation on the macroscale (comparable to FE2). This two-scale model captures finite strains on the macroscale (accommodated by finite rotations of truss members on the microscale), and it applies to stretching- and bending-dominated truss topologies. We compare simulation results of discrete numerical calculations to those of the two-scale generalized continuum approximation for several 3D relaxation and vibration benchmarks, using a selection of bendingand stretching-dominated truss topologies, which demonstrate the homogenization scheme’s accuracy and efficiency as well as its applicability.
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