The reliability of through-glass via (TGV) interconnects is critical for advanced semiconductor packaging. This work investigates microstructural and mechanical evolution in electroplated TGV–Cu subjected to long-term aging at 250 °C. TGV samples were fabricated via laser-induced etching and double-sided copper electroplating, then aged for up to 1008 h. Nanoindentation revealed region-dependent reductions in hardness (from 2.0–2.5 GPa to below 0.5 GPa) and modulus (from 110–130 GPa to 40–90 GPa), with surface-near regions most affected. The glass substrate maintained stable mechanical properties until microcracks formed after 1008 h. EBSD quantification showed grain-size enlargement from 0.46 µm to 1.86 µm and a concurrent decrease in dislocation density. Molecular dynamics simulations of 3, 4, 5 nm grains corroborated the inverse relationship between grain size and micro-mechanical properties. A hybrid Potts-phase field model further linked grain coarsening to stress relaxation and elastic-energy minimization, revealing that as grains grow, the overall von Mises stress in the structure decreases; high-modulus grains retain relatively higher local stresses, while low-modulus, low-stress grains exhibit faster growth rates. Electrical I–V measurements confirmed stable ohmic behavior, despite a drop in insulation resistance. These integrated experimental and computational insights provide theoretical guidance for optimizing TGV interposer design and ensuring long-term operational reliability in heterogeneous integration technologies. (Figure presented.)

Sintered Cu nanoparticles (Cu NPs) are promising interconnection materials for high-temperature power electronics, yet how their authentic three-dimensional pore architecture governs microscale deformation remains unclear. Here, synchrotron nano-computed tomography (nano-CT) was combined with in-situ micropillar compression, explicit dynamic elastoplastic finite element analysis, and TEM/TKD characterization to interrogate sintered Cu NPs. The nano-CT voxel size was 45 nm, and the reconstructed volume corresponded to a cylinder 16 µm in diameter and 10 µm in height. The average sectional porosity was 12.44%, with a systematic discrepancy between two-dimensional and three-dimensional porosity quantification. During loading, the porosity decreased to 9.55% while the pore aspect ratio increased from 1.82–2.35. Finite element analysis further showed pronounced pore-adjacent stress/strain localization at the elastic–plastic transition, with local stress and equivalent plastic strain reaching 650 MPa and 1.7 × 10⁻², compared with 250 MPa and 1.1 × 10⁻³ in adjacent regions. The GND density increased by 95.9% at a compressive strain of 26%, linking pore-induced strain gradients to dislocation accumulation. These results quantitatively connect authentic three-dimensional pore architecture, local deformation localization, and dislocation-mediated strengthening in sintered Cu NPs. Highlights Synchrotron nano-CT (45 nm voxel size) reconstructed a 16 × 10 µm cylindrical volume of sintered Cu NPs and resolved the authentic 3D pore network. Sectional porosity was 12.44%, and 2D/3D quantification showed a systematic discrepancy, with porosity decreasing to 9.55% and pore aspect ratio increasing from 1.82 to 2.35 during compression. Pore-adjacent localization was quantified at the elastic–plastic transition, with local stress/PEEQ reaching 650 MPa and 1.7 × 10⁻² versus 250 MPa and 1.1 × 10⁻³ in adjacent regions. A 95.9% increase in GND density at 26% compressive strain links pore-induced strain gradients to dislocation accumulation and strain-gradient-driven strengthening.

This study is motivated by a conceptual inconsistency in the physical interpretation of eight-chain hyperelastic theory, which arises from the combined effect of two distinct issues: the use of the marginal projection distribution p_z(|r_z|) as a surrogate for the full probability density of end-to-end distance p_r̄(r̄), and the subsequent reliance on a root mean square (RMS) approximation step in the micro–macro averaging of chain stretch. We first revisit this probabilistic mismatch by reformulating the probability density function of freely-jointed chains (FJCs) in terms of the squared end-to-end vector r², thereby restoring consistency on chain-level statistics. Building on this formulation, the micro–macro mapping averaging of chain conformational free energy is constructed directly in terms of r², leading to a one-step mean-field approximation that avoids RMS averaging. The modified probability transformation is examined by Monte Carlo sampling at the microscopic level. To account for interchain interactions, q-mean statistical description of micro tube confinement was incorporated, leading to the appearance of the general invariant I_q=λ₁^q+λ₂^q+λ₃^q. The resulting continuum constitutive model is assessed against multiaxial experimental data for several polymer networks, including vulcanized natural rubber, Entec Enflex S4035A thermoplastic elastomer, Tetra-PEG, and isoprene rubber vulcanizate. Comparisons with three existing hyperelastic strain energy formulations, the extended eight-chain, extended tube models, and the four-parameter ”comprehensive” model, demonstrate comparable phenomenological accuracy of the current model while providing a clearer and more consistent micro–macro physical interpretation of model parameters. A parametric study further illustrates how the dimensionless parameters n and q govern the shape of the macroscopic stress–strain responses. The present formulation provides a consistent theoretical basis within the scope of hyperelasticity and admits potential extensions toward more complex irreversible phenomena.

This study demonstrates a breakdown analysis of the dynamics of a liquid crystal elastomer (LCE) including quality check, geometric measurement, thermal characterization, and comparison of heat- and light-induced contractions. A blue light-responsive acrylate side chain LCE with 1% azobenzene dye was characterized. From a classical viewpoint, photo-thermal contraction is considered a dominating effect, while direct photo-mechanical deformation can be neglected due to a low dye percentage. However, the findings of this research suggest that a low percentage of azobenzene dye does not necessarily lead to heat-dominating dynamics of LCE. This phenomenon has not yet been quantitatively studied before. The approach reported in this Letter can potentially be used to extract the data to improve the dynamics models of light-driven LCEs.

Some atrial contractile assist devices applied on the heart surface can be regarded as a laminated Liquid crystal elastomer (LCE) plate under steady temperature loads and a contact mechanical force. An exact solution for the deformation of the laminated LCE plate under combined thermal and mechanical loads is derived by solving the three-dimensional (3D) equilibrium equations including heat conduction and thermoelastic theory. The validity of mathematical formula and computer programming is proved by convergence and comparison examples with finite element method (FEM). In order to simplify the complex calculation of exact solution, a back propagation neural network (BPNN) is further trained with a database containing 9504 sets of thermo-mechanical load conditions and their corresponding deformation which is solved by the exact solutions. Then the deformations of LCE plate subject to combined thermo-mechanical load can be predicted by this BP neural network instead of complex numerical calculation. Moreover, it is also applied to inverse the contact mechanical force at the bottom surface of LCE plate with a given deformation and temperature conditions. The results show that: (1) The results from the exact theoretical solution are in consistence with that from FEM but have a higher computational efficiency and stability; (2) The deformation of the laminated plate is more sensitive to the layered thickness of LCE than the variation of the temperature; (3) 3-D elasticity solutions of a laminated LCE plate under the combined thermos-mechanical load can be effectively predicted by a trained BP neural network.