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Phononic crystals can be designed to show band gaps—ranges of frequencies whose propagation is strongly attenuated in the material. In essence, their working principle is based on destructive interference of waves reflecting from the periodic arrangement of material interfaces (i.e. , Bragg scattering). Consequently, capturing accurately the behavior at material interfaces requires appropriate numerical modeling and computational design techniques. However, the commonly used density-based representation in popular topology optimization methods results in a diffuse staircased boundary. The heavily refined finite element meshes required to compensate for this boundary description results in exceedingly large and expensive optimization problems. In this paper, we demonstrate the adverse effect of the density-based boundary description. Furthermore, we propose a level set-based topology optimization procedure with an enriched finite element method that shows improved performance when compared to the density-based approach. • Topology optimization of phononic crystal with crisp boundaries is attained. • Efficient computation of design sensitivities allows for gradient-based optimization. • Using less degrees of freedom, band gaps are computed accurately during optimization. [ABSTRACT FROM AUTHOR]

Abstract: We derive Riemann solutions for stick, slip and separation contact modes in a linear elastic material with an isotropic Coulomb friction relation and explore their numerical implementation. The Riemann solutions preserve the characteristic structure of the underlying elastodynamic system and imply dynamic contact conditions that are distinct from the quasi-static conditions used in some numerical models. Nonphysical discontinuities in the standard Coulomb model at stick–slip transitions can cause contact-mode chatter in numerical simulations. We restate the Coulomb relation to remove these artificial discontinuities and eliminate the need for algorithmic remedies. Discontinuous response at abrupt separation-to-contact transitions is physically reasonable, and we propose a regularization scheme to address this case. We implement the Riemann contact solutions within an adaptive spacetime discontinuous Galerkin (SDG) code and report numerical results that demonstrate the model’s efficacy. [Copyright &y& Elsevier]

In predicting failure of a material, small scale material properties are critical, and yet small scale random heterogeneities are difficult to characterize accurately and efficiently. In building fracture models, work has focused on statistical characterization of local random microstructure at small to intermediate scales (termed micro- or mesoscale). Many materials can be characterized as effectively isotropic and homogeneous at a large scale. In contrast, at a micro- or mesoscale, Statistical Volume Elements (SVE) often show significant anisotropy and heterogeneity. Characterizing the properties of SVE presents challenges because modeling choices, such as the length scale, boundary conditions applied, and boundary shape chosen, may introduce modeling bias. Modeling bias must be separated from the actual prediction of anisotropic and heterogeneous characteristics at the SVE level, in order to provide an accurate basis for fracture simulation. Much literature has been devoted to characterizing the size of an RVE in order to effectively homogenize a material, however, there is less study of the effective isotropic limit. The representative size may be different when approaching the homogeneous limit or the isotropic limit. In this work, elastic and strength properties will be evaluated at multiple scales using SVE with square and circular (so-called "regular") geometry. A Voronoi tessellation based geometry, where aggregation of Voronoi cells is achieved using square or circular grids, is studied and compared with regular partitioning methods. Models will be tested on two types of microstructures, one that is isotropic at the macroscale, and one which contains a slight directional bias. Results for different SVE geometries will be compared to demonstrate how SVE modeling choices affect the characterization of anisotropy and heterogeneity at the micro- and mesoscale. • Statistical Volume Elements (SVE) are generated using different edge geometries • SVE elastic and material strength properties are evaluated at multiple scales • SVE edge geometry affects characterization of anisotropy and heterogeneity • Circular SVE edge geometry is preferable to square geometry for capturing anisotropy • SVE boundaries that avoid phase intersections improve modeling accuracy. [ABSTRACT FROM AUTHOR]

Abstract To model the sample-to-sample variations and the effect of microscale inhomogeneities on fracture response, statistical volume elements (SVEs) are employed to homogenize the elastic and fracture properties of ZrB 2 -SiC, a two-phase particulate composite often used as a thermal coating. In the mesoscale analysis, 2D finite element models are generated using a non-iterative, automated mesh generation algorithm named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR). The analysis of SVEs under mixed, traction, and minimal kinematic boundary conditions yields their angle-dependent tensile and shear fracture strengths and elastic stiffnesses. This study shows that homogenized fracture strengths are highly dependent on the SVE size and the particular geometric distribution of inclusions (even for similar volume ratios), whereas elastic properties are mainly a function of the volume fraction. Moreover, mean values of strength and bulk modulus, respectively, decrease and remain almost constant as the SVE size increases. For the macroscale analysis, an isotropic, inhomogeneous field of fracture strength is generated from the homogenization of SVEs. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is subsequently employed for fracture analysis under uniaxial tensile and thermal strain loadings. [ABSTRACT FROM AUTHOR]

Accurate characterization of random heterogeneity in a material microstructure is essential to the accurate characterization of complex fracture patterns that result from random crack nucleation and propagation. It is also important to characterize microstructural behavior at intermediate scales, between the length scale of material heterogeneity and the scale of a Representative Volume Element (RVE). The availability of material property data at multiple scales will ultimately allow adjustment of computational cost and level of accuracy with respect to resolution of complex fracture patterns. Statistical Volume Elements (SVE) may be generated at the mesoscale by partitioning an RVE. SVE provide a probabilistic characterization of material heterogeneity, while also presenting a continuum representation of apparent properties. Appropriate definition of an SVE requires modeling choices, such as partitioning methods and size. An essential modeling assumption is the choice of loading condition used to approximate SVE apparent behavior, since the constitutive properties of an SVE are not necessarily invariant with respect to the boundary condition applied. This work develops a Voronoi tessellation based partitioning scheme applied at various length scales, for heterogeneous materials with various contrast ratios. Results show the variability of failure strength for a given SVE as a function of loading direction. Results of the mesoscale material property analysis are implemented in an asynchronous spacetime discontinuous Galerkin (aSDG) finite element based fracture model. [ABSTRACT FROM AUTHOR]