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Elastomeric materials display a complicated set of stretchability and fracture properties that strongly depend on the flaw size, which has long been of interest to engineers and materials scientists. Here, we combine experiments and numerical simulations for a comprehensive understanding of the nonlocal, size-dependent features of fracture in elastomers. We show the size-dependent fracture behavior is quantitatively described through a nonlocal continuum model. The key ingredient of the nonlocal model is the use of an intrinsic length scale associated with a finite fracture process zone, which is inferred from experiments. Of particular importance, our experimental and theoretical approach passes the critical set of capturing key aspects of the size-dependent fracture in elastomers. Applications to a wide range of synthetic elastomers that exhibit moderate (~100%) to extreme stretchability (~1000%) are presented, which is also used to demonstrate the applicability of our approach in elastomeric specimens with complex geometries.

Thermoplastic polyurethanes (TPU) are block copolymeric materials composed of plastomeric "hard" and elastomeric "soft" domains, by which they exhibit highly resilient yet dissipative large deformation features depending on volume fractions and microstructures of the two distinct domains. Here, we develop a new methodology to address the microscopic deformation mechanisms in TPU materials with highly disordered microstructures. We propose new micromechanical models for randomly dispersed (or occluded) as well as randomly continuous hard domains, each within a continuous soft structure as widely found in representative TPU materials over a wide range of volume fractions, v$_{\mathrm{hard}}$ = 26.9% to 52.2%. The micromechanical modeling results are compared to experimental data on the macroscopic large strain behaviors reported previously (Cho et al. 2017). We explore the role of the dispersed vs. continuous nature of the geometric features of the random microstructures on shape recovery and energy dissipation at the microstructural level in this important class of phase-separated copolymeric materials.

Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial PDF of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts using physical models often fail to capture the statistics of structural evolution during material deformation. This study proposes a data-driven statistical reduced-order modeling framework to provide a probabilistic forecast of the deformation process leading to porosity-based ductile damage, with uncertainty quantification. The framework starts with computing the time evolution of the leading moments of specific state variables from full-field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is used to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations show that the model can characterize the time evolution of the non-Gaussian PDF of the von Mises stress and quantify the probability of extreme events. The learning process also reveals that the mean stress interacts with higher-order moments and extreme events in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement shows that the leading four moments are sufficient to characterize the crucial non-Gaussian features throughout the entire deformation history.

A physically-informed continuum crystal plasticity model is presented to elucidate the deformation mechanisms and dislocation evolution in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show our unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10$^{-3}$ s$^{-1}$) to extreme strain rates (5000 s$^{-1}$) and at room temperature and higher (873K) at both single- and polycrystal levels. We also present predictive capabilities of our model for microstructural evolution in the material. To this end, we investigate the effects of dislocation interactions on slip activities, instability and strain-hardening behavior at the single crystal level. Furthermore, ex situ measurements on crystallographic texture evolution and dislocation density growth are carried out for the polycrystal tantalum specimens at increasing strains. Numerical simulation results also support that our modeling framework is capable of capturing the main features of the polycrystal behavior over a wide range of strains, strain rates and temperatures. The theoretical, experimental and numerical results at both single- and polycrystal levels provide critical insight into the underlying physical pictures for micro- and macroscopic responses and their relations in this important class of refractory bcc materials undergoing severe inelastic deformations.

A finite strain nonlinear constitutive model is presented to study the extreme mechanical behavior of a polyurethane-urea well suited for many engineering applications. The micromechanically- and thermodynamically based constitutive model captures salient features in resilience and dissipation in the material at low to high strain rate. The extreme deformation features are further elucidated by laser-induced micro-particle impact tests for the material, where an ultrafast strain rate ($>10^6$ s$^{-1}$) incurs. Numerical simulations for the strongly inhomogeneous deformation events are in good agreement with the experimental data, supporting the predictive capabilities of the constitutive model for the extreme deformation features of the PUU material over at least 9 orders of magnitude in strain rates ($10^{-3}$ to $10^{6}$ s$^{-1}$).

Plastic deformations in body-centered-cubic (BCC) crystals have been of critical importance in diverse engineering and manufacturing contexts across length scales. Numerous experiments and atomistic simulations on BCC crystals reveal that classical crystal plasticity models with the Schmid law are not adequate to account for abnormal plastic deformations often found in these crystals. In this paper, we address a continuum mechanical treatment of anomalous plasticity in BCC crystals exhibiting non-Schmid effects, inspired from atomistic simulations recently reported. Specifically, anomalous features of plastic flows are addressed in conjunction with a single crystal constitutive model involving two non-Schmid projection tensors widely accepted for representing non-glide components of an applied stress tensor. Further, modeling results on a representative BCC single crystal (tantalum) are presented and compared to experimental data at a range of low temperatures to provide physical insight into deformation mechanisms in these crystals with non-Schmid effects., Comment: 33 pages, 8 figures