This manuscript provides a novel reduced-order multiscale modeling methodology for failure analysis of heterogeneous materials. The proposed methodology is based on the computational homogenization method for bridging multiple spatial scales and the eigendeformation-based model reduction method to incorporate failure in the microconstituents and interfaces. This computationally-efficient modeling methodology leads to symmetric reduced-order algebraic systems for evaluation of the microscale boundary value problem. The order and coarse graining for the reduced-order system are systematically identified by a novel model development strategy. Verification studies reveal that the proposed methodology efficiently and accurately models the failure response. The proposed approach eliminates the spurious residual stress effect observed in reduced-order models, which pollutes the post-failure stress field at the macroscale.
This manuscript presents a multiscale modeling methodology for failure analysis of composites subjected to cyclic loading conditions. Computational homogenization theory with multiple spatial and temporal scales is employed to devise the proposed methodology. Multiple spatial scales address the disparity between the length scale of material heterogeneities and the overall structure, whereas multiple temporal scales with almost periodic fields address the disparity between the load period and overall life under cyclic loading. The computational complexity of the multiscale modeling approach is reduced by employing a meso-mechanical model based on eigendeformation based homogenization with symmetric coefficients in the space domain, and an adaptive time stepping strategy based on a quadratic multistep method with error control in the time domain. The proposed methodology is employed to simulate the response of graphite fiber-reinforced epoxy composites. Model parameters are calibrated using a suite of experiments conducted on unidirectionally reinforced specimens subjected to monotonic and cyclic loading. The calibrated model is employed to predict damage progression in quasi-isotropic specimens. The capabilities of the model are validated using acoustic emission testing.
SUMMARYThis manuscript presents an accelerated time domain homogenization methodology for prediction of material and structural failure under fatigue loading. The methodology is based on mathematical homogenization theory applied to the time domain. The method addresses the computational challenge associated with the scale disparity between the characteristic fatigue load period and the overall fatigue life. Cycle sensitive continuum damage mechanics modeling is used to describe the progressive damage accumulation under fatigue loading. The original initial boundary value problem is decomposed into coupled fast and slow time scale problems. A quasilinear approximation to the fast time scale problem is introduced to efficiently evaluate the response under a fatigue load cycle. The effect of the new time integrator on the thermodynamic consistency of the resulting system of discrete equations is demonstrated for a general class of continuum damage mechanics models. The proposed method is numerically verified based on a scalar damage model and a spatially multiscale damage model used for predicting fatigue life of composite materials. The proposed accelerated time integrator is shown to have reasonable accuracy and is orders of magnitude more computationally efficient when compared with previously proposed time homogenization methods.
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