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The buckling of thin films with natural nonlinearity can provide a useful tool in many applications. In the present paper, the mechanical properties of controllable buckling of thin films are investigated by accounting for both geometric nonlinearity and surface effects at nanoscale. The effects of surface elasticity and residual surface tension on both static and dynamic behaviors of buckled thin films are discussed based on the surface-layer-based model. The dynamic design strategy for buckled thin films as interconnects in flexible electronics is proposed to avoid resonance in a given noise environment based on the above analysis. Further discussion shows that the thermal and piezoelectric effects on mechanical behavior of buckled thin film are equivalent to that of residual surface tension. [ABSTRACT FROM AUTHOR]

The objective of this paper is to model the synergistic bond-degradation mechanisms that may occur at the interface between a fiber-reinforced polymer (FRP) that is adhesively bonded to a substrate and subjected to elevated temperature and humidity. For this purpose, a two-dimensional cohesive-layer constitutive model with a prescribed traction-separation law is constructed from fundamental principles of continuum mechanics and thermodynamics, taking into account strain-dependent, non-Fickian hygrothermal effects as well as diffusion-induced degradation in the cohesive layer. In the interest of solution tractability, a simplified approach is employed where the rate-dependent behavior in the cohesive layer is implemented through the characterization of rate dependence of the maximum stresses and maximum strains in the cohesive layer, rather than through the use of convolution integrals in the free-energy definition. The remainder of the polymeric adhesive outside the cohesive layer is modeled as a nonlinear viscoelastic continuum with time-dependent constitutive behavior. The influence of temperature and moisture concentration on the work-of-separation and on crack growth is derived from first principles. The model is implemented in a test-bed finite element code. Results predicted by the computational model are benchmarked through comparison to experimental data from mixed-mode fracture experiments performed using a moving wedge test. [ABSTRACT FROM AUTHOR]

Data-driven equation identification for dynamical systems has achieved great progress, which for static systems, however, has not kept pace. Unlike dynamical systems, static systems are time invariant, so we cannot capture discrete data along the time stream, which requires identifying governing equations only from scarce data. This work is devoted to this topic, building a data-driven method for extracting the differential-variational equations that govern static behaviors only from scarce, noisy data of responses, loads, as well as the values of system attributes if available. Compared to the differential framework typically adopted in equation identification, the differential-variational framework, due to its spatial integration and variation arbitrariness, brings some advantages, such as high robustness to data noise and low requirements on data amounts. The application, efficacy, and all the aforementioned advantages of this method are demonstrated by four numerical examples, including three continuous systems and one discrete system. [ABSTRACT FROM AUTHOR]

The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied solid mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the three-dimensional (3D) finite element method. The simplified governing equations are in variational form, which is compact and advantageous for data-driven discovery. AI-Timoshenko liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler-Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems. [ABSTRACT FROM AUTHOR]

The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied solid mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the three-dimensional (3D) finite element method. The simplified governing equations are in variational form, which is compact and advantageous for data-driven discovery. AI-Timoshenko liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler-Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems. [ABSTRACT FROM AUTHOR]