Fig. 2: Mechanical characterization of CMA structures.

a–d Characterization of the energy-absorbing performance of CMA structures by instrumented indentation tests (IIT). a Schematic of typical stress–strain (\(\sigma - \varepsilon\)) curve of materials in response to compression, with its key features of peak stress \(\sigma _{{\mathrm{pe}}}\), plateau stress \(\sigma _{{\mathrm{pl}}}\), peak force strain \(\varepsilon _{{\mathrm{pe}}}\) and strain threshold \(\varepsilon _{{\mathrm{tr}}}\) marked in the plot. b Engineering stress–strain features of CMA structures with different unit side lengths obtained from IIT at a strain rate of 10⁻¹ s⁻¹. c Calculated engineering stress (plateau stress and peak stress) and energy-absorbing efficiency of CMA structures (represented by unit side length). d Energy absorption diagram showing the amount of absorbed energy per unit volume as a function of stresses at the given strains. e, f FEA simulation of the elastic compressive response of CMA structures based on static loading. e Load-displacement features of CMA structures in the linear elastic regime. The solid lines are simulation predictions. f Calculated and measured spring constants versus structures with different unit side lengths. g–j Dynamic tip–sample impact simulation based on dynamic finite element analysis (FEA). The tips have an initial speed of 20 μm s^-1 in +z direction approaching and impacting the sample surface (see Supplementary Movie 1). g Morphological evolutions of a CMA tip (a = 5 μm) and a solid cone tip during the first 10 ms of the impact. All tips are displayed in a render style of wireframes. h Time-lapse indentation cross-sections and normalized local stress distributions on the sample within the first 10 ms (tips are concealed) by employing the CMA tip and the solid tip as shown in the insets. For comparison, the dashed arrow line indicates the evolution of the indentation level by the CMA tip. i Tip displacement and max interfacial indentation depth over time. j Normalized maximum interfacial stress versus time. Scale bars are 1 μm for g and 100 nm for h. Source data of b–f, i, j are provided as a Source Data file.