More Like this

1. Energy minimizing twinning with variable volume fraction, for two nonlinear elastic phases with a single rank-one connection

   https://doi.org/10.1142/S0218202522500397  

   Conti, Sergio ; Kohn, Robert V. ; Misiats, Oleksandr ( July 2022 , Mathematical Models and Methods in Applied Sciences)

   Ball, J. (Ed.)

   In materials that undergo martensitic phase transformation, distinct elastic phases often form layered microstructures — a phenomenon known as twinning. In some settings the volume fractions of the phases vary macroscopically; this has been seen, in particular, in experiments involving the bending of a bar. We study a two-dimensional (2D) model problem of this type, involving two geometrically nonlinear phases with a single rank-one connection. We adopt a variational perspective, focusing on the minimization of elastic plus surface energy. To get started, we show that twinning with variable volume fraction must occur when bending is imposed by a Dirichlet-type boundary condition. We then turn to paper’s main goal, which is to determine how the minimum energy scales with respect to the surface energy density and the transformation strain. Our analysis combines ansatz-based upper bounds with ansatz-free lower bounds. For the upper bounds we consider two very different candidates for the microstructure: one that involves self-similar refinement of its length scale near the boundary, and another based on piecewise-linear approximation with a single length scale. Our lower bounds adapt methods previously introduced by Chan and Conti to address a problem involving twinning with constant volume fraction. The energy minimization problem considered in this paper is not intended to model twinning with variable volume fraction involving two martensite variants; rather, it provides a convenient starting point for the development of a mathematical toolkit for the study of twinning with variable volume fraction. 

   more » « less
2. Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution

   https://doi.org/10.1177/1081286520968149  

   Timofeev, Dmitry ; Barchiesi, Emilio ; Misra, Anil ; Placidi, Luca ( May 2021 , Mathematics and Mechanics of Solids)

   null (Ed.)

   Mechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology. Here, we consider the damage behavior of these materials based upon purely mechanical concepts utilizing energy and variational approach. Granular micromechanics is accounted for through Piola’s ansatz and objective kinematic descriptors obtained for grain-pair relative displacement in granular materials undergoing finite deformations. Karush–Kuhn–Tucker (KKT)-type conditions that provide the evolution equations for grain-pair damage and Euler–Lagrange equations for evolution of grain-pair relative displacement are derived based upon a non-standard (hemivariational) variational approach. The model applicability is illustrated for particular form of grain-pair elastic energy and dissipation functionals through numerical examples. Results show interesting damage-induced anisotropy evolution including the emergence of a type of chiral behavior and formation of finite localization zones. 

   more » « less
3. The effects of boundary and inhomogeneities on the delamination of a bi-layered material system

   https://doi.org/10.1177/10567895231216008  

   Wu, Chunlin ; Yin, Huiming ( November 2023 , International Journal of Damage Mechanics)

   The inclusion-based boundary element method (iBEM) is developed to calculate the elastic fields of a bi-layered composite with inhomogeneities in one layer. The bi-material Green’s function has been applied to obtain the elastic field caused by the domain integral of the source fields on inclusions and the boundary integral of the applied loads on the surface. Using Eshelby’s equivalent inclusion method (EIM), the material mismatch between the particle and matrix phases is simulated with a continuously distributed source field, namely eigenstrain, on inhomogeneities so that the iBEM can calculate the local field. The stress singularity along the interface leads to the delamination of the bimaterials under a certain load. The crack’s energy release rate (  J) is obtained through the J-integral, which predicts the stability of the delamination. When the stiffness of one layer increases, the J-integral increases with a higher gradient, leading to lower stability. Particularly, the effect of the boundary and inhomogeneity on the J-integral is illustrated by changing the crack length and inhomogeneity configuration, which shows the crack is stable at the beginning stage and becomes unstable when the crack tip approaches the boundary; a stiffer inhomogeneity in the neighborhood of a crack tip decreases J and improves the fracture resistance. For the stable cracking phase, the J-integral increases with the volume fraction of inhomogeneity are evaluated. The model is applied to a dual-glass solar module with air bubbles in the encapsulant layer. The stress distribution is evaluated with the iBEM, and the J-integral is evaluated to predict the delamination process with the energy release rate, which shows that the bubbles significantly increase the J-integral. The effect of the bubble size, location, and number on the J-integral is also investigated. The present method provides a powerful tool for the design and analysis of layered materials and structures.

    

   more » « less
4. Deformation of the Juan de Fuca Plate Beneath the Central Cascadia Continental Margin (44°-45°N) in Response to an Upper Plate Load

   https://doi.org/10.3389/esss.2023.10085  

   Tréhu, Anne M. ; Davenport, Kathy ; Kenyon, Christopher B. ; Carbotte, Suzanne M. ; Nabelek, John L. ; Toomey, Douglas R. ; Wilcock, William S. ( November 2023 , Earth Science, Systems and Society)

   Palin, Richard (Ed.)

   A 3D crustal model for the central Cascadia continental shelf and Coast Range between 44°N and 45°N shows that the crystalline crust of the forearc wedge beneath the coastline is characterized by a NW-trending, vertical slab of high-velocity rock interpreted to represent the dike complex that fed the Yachats Basalt, which was intruded into the forearc approximately 37 million years ago. A spatial correlation is observed between downward deflection of the crust of the subducting Juan de Fuca plate, inferred from inversion of PmP arrivals to image the Moho surface, and the high velocity (and consequently high density) anomaly underlying the Yachats Basalt. Apparent subsequent rebound of the subducting plate at greater depth suggests a primarily elastic response of the subducting plate to this load. Calculations for a range of plausible values for the magnitude of the load and the width and depth of the depression indicate that the effective elastic thickness of the subducted Juan de Fuca plate is < 6 km. Although our simple analytical models do not include partial support of the load of the slab by the adjacent upper plate crust or time dependence to account for the motion of the slab beneath the load, incorporation of those effects should decrease rather than increase the apparent strength of the subducted plate. We conclude that the subducted Juan de Fuca plate beneath the central Oregon margin is elastically thin and has the potential to store elastic strain energy before rupturing. Our model of a well-defined, focused and static upper plate load that locally deforms the subducted plate within the nominally seismogenic or transitional part of the Cascadia plate boundary may be unique in providing a relatively straightforward scenario for estimating the mechanical properties of the subducted Juan de Fuca plate. We extrapolate from these results to speculate that elastic deformation of the subducting plate may contribute to the low level of seismicity throughout much of the Cascadia forearc in the inter-seismic period between great earthquakes but note that our local results do not preclude faulting or elasto-plastic deformation of a thin and weak plate as it subducts. These results also suggest that the subducting plate should deform in response to larger scale variations in upper plate thickness and density.

    

   more » « less
5. Multiscale Modeling of Composite Materials under Volumetric and Interfacial Damage: Achieving Adaptive Model Order Reduction

   https://doi.org/10.2514/6.2023-0138  

   Lin, Min ; Brandyberry, David ; Zhang, Xiang ( January 2023 , AIAA SCITECH 2023 Forum)

   In this manuscript, we present a multiscale Adaptive Reduced-Order Modeling (AROM) framework to efficiently simulate the response of heterogeneous composite microstructures under interfacial and volumetric damage. This framework builds on the eigendeformation-based reduced-order homogenization model (EHM), which is based on the transformation field analysis (TFA) and operates in the context of computational homogenization with a focus on model order reduction of the microscale problem. EHM pre-computes certain microstructure information by solving a series of linear elastic problems defined over the fully resolved microstructure (i.e., concentration tensors, interaction tensors) and approximates the microscale problem using a much smaller basis spanned over subdomains (also called parts) of the microstructure. Using this reduced basis, and prescribed spatial variation of inelastic response fields over the parts, the microscale problem leads to a set of algebraic equations with part-wise responses as unknowns, instead of node-wise displacements as in finite element analysis. The volumetric and interfacial influence functions are calculated by using the Interface enriched Generalized Finite Element Method (IGFEM) to compute the coefficient tensors, in which the finite element discretization does not need to conform to the material interfaces. AROM takes advantage of pre-computed coefficient tensors associated with the finest ROM and efficiently computes the coefficient tensors of a series of gradually coarsening ROMs. During the multiscale analysis stage, the simulation starts with a coarse ROM which can capture the initial elastic response well. As the loading continues and response in certain parts of the microstructure starts to localize, the analysis adaptively switches to the next level of refined ROM to better capture those local responses. The performance of AROM is evaluated by comparing the results with regular EHM (no adaptive refinement) and IGFEM under different loading conditions and failure modes for various 2D and 3D microstructures. The proposed AROM provides an efficient way to model history-dependent nonlinear responses for composite materials under localized interface failure and phase damage. 

   more » « less