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An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

Journal Article · · Computer Methods in Applied Mechanics and Engineering

An optimization-based design framework is proposed to tune the response of soft metamaterials involving both geometric instabilities and nonlinear viscoelastic material behavior. Designing the response of soft metamaterials to harness instabilities and undergo large, tailored configuration changes will enable advancements in soft robotics, shock and vibration mitigation, and flexible electronics. In line with the metamaterial concept, the response of these materials is governed to a large extent by the geometric and topological makeup of their small-scale features. However, the link between structure and response is less intuitive for soft metamaterials due to their reliance upon highly nonlinear responses triggered by geometric instabilities. This is further complicated by the effects of viscoelastic relaxation, which recent studies have shown to alter the emergence of instabilities in non-intuitive ways. Here, these effects are accounted for in our framework to achieve various design objectives, including tailored force–displacement response and maximized energy absorption from both geometric and material effects. To fully automate this process, it is essential to have a completely robust equation solver for forward problems involving instabilities and viscoelastic relaxation. We achieve this by casting the search for stable mechanical equilibrium — i.e. the forward problem — as a minimization problem and utilize a trust region algorithm to robustly handle instabilities and follow energetically-favorable equilibrium paths through critical points.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
NA0003525; AC52-07NA27344
OSTI ID:
2498462
Alternate ID(s):
OSTI ID: 2510953
Report Number(s):
SAND-2025-00242J; LLNL-JRNL-2002293
Journal Information:
Computer Methods in Applied Mechanics and Engineering, Vol. 435; ISSN 0045-7825
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (87)

Tailored Buckling Microlattices as Reusable Light-Weight Shock Absorbers journal May 2016
A density‐based boundary evolving method for buckling‐induced design under large deformation journal December 2020
Inflatable soft jumper inspired by shell snapping journal May 2020
On compliance and buckling objective functions in topology optimization of snap-through problems journal August 2012
Tunable Metamaterials for Impact Mitigation journal January 2024
Mechanically‐Guided Structural Designs in Stretchable Inorganic Electronics journal July 2019
Topology optimization approaches: A comparative review journal August 2013
Pattern Transformation Triggered by Deformation journal August 2007
Structural stability and artificial buckling modes in topology optimization journal August 2021
Rapid inverse design of metamaterials based on prescribed mechanical behavior through machine learning journal September 2023
Numerical analysis perspective in structural shape optimization: A review post 2000 journal May 2021
A variational, finite‐deformation constitutive model for piezoelectric materials journal January 2011
The Conjugate Gradient Method and Trust Regions in Large Scale Optimization journal June 1983
Isogeometric shape design optimization: exact geometry and enhanced sensitivity journal May 2008
Three-Dimensional-Printed Multistable Mechanical Metamaterials With a Deterministic Deformation Sequence journal October 2016
Error estimation and adaptive meshing in strongly nonlinear dynamic problems journal April 1999
Relating pore shape to the non-linear response of periodic elastomeric structures journal March 2014
Large deformations and stability in topology optimization journal July 2005
The variational formulation of viscoplastic constitutive updates journal April 1999
Stiffness design of geometrically nonlinear structures using topology optimization journal April 2000
Characteristics of mechanical metamaterials based on buckling elements journal May 2017
On The Construction of Aircraft Conceptual Geometry for High-Fidelity Analysis and Design conference January 2012
Topology optimization of pressure dependent elastoplastic energy absorbing structures with material damage constraints journal October 2017
Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation journal March 2022
Control of Bifurcation Structures using Shape Optimization journal January 2022
Shape optimization of thin walled structures governed by geometrically nonlinear mechanics journal September 2012
Condition number analysis and preconditioning of the finite cell method journal April 2017
Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers journal April 2021
Design Sensitivity Calculations Directly on CAD-based Geometry conference January 2015
Finite strain topology optimization with nonlinear stability constraints journal August 2023
Digital synthesis of free-form multimaterial structures for realization of arbitrary programmed mechanical responses journal March 2022
Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures journal August 2008
The extreme mechanics of viscoelastic metamaterials journal August 2022
Multistable Architected Materials for Trapping Elastic Strain Energy journal June 2015
Topology optimization of energy absorbing structures with maximum damage constraint: TOPOLOGY OPTIMIZATION INELASTIC DAMAGE journal March 2017
Isogeometric shape optimization of smoothed petal auxetics with prescribed nonlinear deformation journal November 2019
Nonlinear shape optimization of flexible mechanical metamaterials journal June 2023
A variational formulation of constitutive models and updates in non-linear finite viscoelasticity
  • Fancello, Eduardo; Ponthot, Jean-Philippe; Stainier, Laurent
  • International Journal for Numerical Methods in Engineering, Vol. 65, Issue 11 https://doi.org/10.1002/nme.1525
journal January 2006
Bistable and Multistable Actuators for Soft Robots: Structures, Materials, and Functionalities journal March 2022
Shape optimal design using B-splines journal August 1984
Towards understanding the role of viscoelasticity in microstructural buckling in soft particulate composites journal August 2023
A gradient-based, parameter-free approach to shape optimization journal February 2011
Structural shape optimization—A survey journal August 1986
Isogeometric sizing and shape optimization of 3D beams and lattice structures at large deformations journal January 2022
Strain rate–dependent mechanical metamaterials journal June 2020
Toward the topology design of mechanisms that exhibit snap-through behavior journal September 2004
Phase transforming cellular materials journal September 2015
Level-set topology optimization with PDE generated conformal meshes journal October 2024
The Engineering Sketch Pad: A Solid-Modeling, Feature-Based, Web-Enabled System for Building Parametric Geometry conference June 2013
Navigating the landscape of nonlinear mechanical metamaterials for advanced programmability journal February 2020
Topology optimization for energy dissipation design of lattice structures through snap-through behavior journal January 2020
A Trust Region Method for Parabolic Boundary Control Problems journal January 1999
Topology optimization of dissipative metamaterials at finite strains based on nonlinear homogenization journal May 2020
Design sensitivity analysis and shape optimization of structural components with hyperelastic material journal June 2000
Second-order computational homogenisation enhanced with non-uniform body forces for non-linear cellular materials and metamaterials journal March 2023
Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization journal August 2017
Numerical methods for the topology optimization of structures that exhibit snap-through
  • Bruns, T. E.; Sigmund, O.; Tortorelli, D. A.
  • International Journal for Numerical Methods in Engineering, Vol. 55, Issue 10 https://doi.org/10.1002/nme.544
journal January 2002
An incremental approach to the solution of snapping and buckling problems journal January 1979
Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials journal January 2013
Adaptive finite element methods for shape optimization of linearly elastic structures journal August 1986
Shape optimization with a level set based mesh evolution method journal December 2014
Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity journal July 1994
Failure resistant topology optimization of structures using nonlocal elastoplastic-damage model journal April 2018
Layout design of a bi-stable cardiovascular stent using topology optimization journal June 2016
A variational Cam-clay theory of plasticity journal July 2004
Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures journal March 2019
Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials journal July 2014
A unified framework for nonlinear path-dependent sensitivity analysis in topology optimization journal March 2018
Programming soft robots with flexible mechanical metamaterials journal April 2019
A theory of finite viscoelasticity and numerical aspects journal September 1998
Simultaneous shape and topology optimization of inflatable soft robots journal February 2024
Negative stiffness honeycombs for recoverable shock isolation journal March 2015
Multistable Shape-Reconfigurable Architected Materials journal July 2016
Viscoelastic Snapping Metamaterials journal September 2019
The effect of topology on the shock dynamics of two-dimensional architected materials journal August 2024
A Heaviside function‐based density representation algorithm for truss‐like buckling‐induced mechanism design journal June 2019
Unstructured grid generation using iterative point insertion and local reconnection journal September 1995
Full analytical sensitivities in NURBS based isogeometric shape optimization journal June 2010
Topology optimization of bistable elastic structures — An application to logic gates journal September 2021
Isogeometric structural shape optimization journal June 2008
A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials journal December 2020
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate journal October 2008
Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization journal May 2019
Soft network composite materials with deterministic and bio-inspired designs journal March 2015
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement journal October 2005
Design of buckling-induced mechanical metamaterials for energy absorption using topology optimization journal April 2018
Global Convergence of a a of Trust-Region Methods for Nonconvex Minimization in Hilbert Space journal January 1988