A three-dimensional multiscale model of intergranular hydrogen-assisted cracking

We present a three-dimensional model of intergranular hydrogen-embrittlement (HE) that accounts for: (i) the degradation of grain-boundary strength that arises from hydrogen coverage; (ii) grain-boundary diffusion of hydrogen; and (iii) a continuum model of plastic deformation that explicitly resolves the three-dimensional polycrystalline structure of the material. The polycrystalline structure of the specimen along the crack propagation path is resolved explicitly by the computational mesh. The texture of the polycrystal is assumed to be random and the grains are elastically anisotropic and deform plastically by crystallographic slip. We use the impurity-dependent cohesive model in order to account for the embrittling of grain boundaries due to hydrogen coverage. We have carried out three-dimensional finite-element calculations of crack-growth initiation and propagation in AISI 4340 steel double-cantilever specimens in contact with an aggressive environment and compared the predicted initiation times and crack-growth curves with the experimental data. The calculated crack-growth curves exhibit a number of qualitative features that are in keeping with observation, including: an incubation time followed by a well-defined crack-growth initiation transition for sufficiently large loading; the existence of a threshold intensity factor K_(Iscc) below which there is no crack propagation; a subsequent steeply rising part of the curve known as stage I; a plateau, or stage II, characterized by a load-insensitive crack-growth rate; and a limiting stress-intensity factor K_(Ic), or toughness, at which pure mechanical failure occurs. The calculated dependence of the crack-growth initiation time on applied stress-intensity factor exhibits power-law behavior and the corresponding characteristic exponents are in the ball-park of experimental observation. The stage-II calculated crack-growth rates are in good overall agreement with experimental measurements

A physics-based reduced-order model for the dynamic and post-buckling behavior of tensegrity structures and metamaterials

Traditional approaches for modeling the behavior of tensegrity structures have their origin either on form-finding applications or on the desire to capture their quasi-static behavior. As such, they generally assume that (i) bars are perfectly rigid, (ii) cables are linear elastic, and (iii) bars experience pure compression and strings pure tension. In addition, a common design constraint is to assume that the structure would fail whenever any of its bars reaches the corresponding Euler buckling load. In reality, these assumptions tend to break down in the presence of dynamic events. In this work, we develop a physics-based reduced-order model to study aspects related to the dynamic and nonlinear response of tensegrity-based structures. With very few degrees of freedom, our model captures their buckling and post-buckling behavior as well as their dynamic response. We then adopt our model to show how, under dynamic events, buckling of individual members of a tensegrity structure does not necessarily imply structural failure. Finally, we show how through successive reflection operations it is possible to architecture a 3D tensegrity metamaterial, and analyze its response to impacts. Our research suggests that efficient structural design of impact-tolerant tensegrity structures and metamaterials could be achieved by exploiting rather than avoiding the buckling behavior of its compression members.Publicado en: Mecánica Computacional vol. XXXV, no. 1.Facultad de Ingenierí

A physics-based reduced-order model for the dynamic and post-buckling behavior of tensegrity structures and metamaterials

Traditional approaches for modeling the behavior of tensegrity structures have their origin either on form-finding applications or on the desire to capture their quasi-static behavior. As such, they generally assume that (i) bars are perfectly rigid, (ii) cables are linear elastic, and (iii) bars experience pure compression and strings pure tension. In addition, a common design constraint is to assume that the structure would fail whenever any of its bars reaches the corresponding Euler buckling load. In reality, these assumptions tend to break down in the presence of dynamic events. In this work, we develop a physics-based reduced-order model to study aspects related to the dynamic and nonlinear response of tensegrity-based structures. With very few degrees of freedom, our model captures their buckling and post-buckling behavior as well as their dynamic response. We then adopt our model to show how, under dynamic events, buckling of individual members of a tensegrity structure does not necessarily imply structural failure. Finally, we show how through successive reflection operations it is possible to architecture a 3D tensegrity metamaterial, and analyze its response to impacts. Our research suggests that efficient structural design of impact-tolerant tensegrity structures and metamaterials could be achieved by exploiting rather than avoiding the buckling behavior of its compression members.Publicado en: Mecánica Computacional vol. XXXV, no. 1.Facultad de Ingenierí

A physics-based reduced-order model for the dynamic and post-buckling behavior of tensegrity structures and metamaterials

Traditional approaches for modeling the behavior of tensegrity structures have their origin either on form-finding applications or on the desire to capture their quasi-static behavior. As such, they generally assume that (i) bars are perfectly rigid, (ii) cables are linear elastic, and (iii) bars experience pure compression and strings pure tension. In addition, a common design constraint is to assume that the structure would fail whenever any of its bars reaches the corresponding Euler buckling load. In reality, these assumptions tend to break down in the presence of dynamic events. In this work, we develop a physics-based reduced-order model to study aspects related to the dynamic and nonlinear response of tensegrity-based structures. With very few degrees of freedom, our model captures their buckling and post-buckling behavior as well as their dynamic response. We then adopt our model to show how, under dynamic events, buckling of individual members of a tensegrity structure does not necessarily imply structural failure. Finally, we show how through successive reflection operations it is possible to architecture a 3D tensegrity metamaterial, and analyze its response to impacts. Our research suggests that efficient structural design of impact-tolerant tensegrity structures and metamaterials could be achieved by exploiting rather than avoiding the buckling behavior of its compression members.Publicado en: Mecánica Computacional vol. XXXV, no. 1.Facultad de Ingenierí

Symmetry-enforcing neural networks with applications to constitutive modeling

The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art micromechanical modeling and advanced machine learning techniques to homogenize complex microstructures exhibiting non-linear and history dependent behaviors (Logarzo et al., 2021). The resulting homogenized model, termed smart constitutive law (SCL), enables the adoption of microstructurally informed constitutive laws into finite element solvers at a fraction of the computational cost required by traditional concurrent multiscale approaches. In this work, the capabilities of SCLs are expanded via the introduction of a novel methodology that enforces material symmetries at the neuron level, applicable across various neural network architectures. This approach utilizes tensor-based features in neural networks, facilitating the concise and accurate representation of symmetry-preserving operations, and is general enough to be extend to problems beyond constitutive modeling. Details on the construction of these tensor-based neural networks and their application in learning constitutive laws are presented for both elastic and inelastic materials. The superiority of this approach over traditional neural networks is demonstrated in scenarios with limited data and strong symmetries, through comprehensive testing on various materials, including isotropic neo-Hookean materials and tensegrity lattice metamaterials. This work is concluded by a discussion on the potential of this methodology to discover symmetry bases in materials and by an outline of future research directions