We present a new eigendeformation-based reduced order homogenization approach for simulating progressive degradation and failure in brittle composite materials. A new reduced model basis construction strategy is proposed, where the bases are based on numerically calculated "failure paths" within the material microstructure subjected to a pre-selected set of load configurations. The failure paths are allowed to overlap, leading to a slight deviation from orthonormality of the basis functions of the reduced order model. In order to alleviate the spurious post failure residual stresses, we propose a new hierarchical failure path update approach, where the influence functions are adaptively updated to incorporate compatible eigenstrains as microstructural failures are detected. The reduced order modeling approach is verified against particulate composite microstructures with ordered and random configurations. The proposed approach leads to significant improvements in accuracy, while maintaining a low model order.
Summary Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra‐high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it will run inside the reproducing kernel particle method (RKPM)‐based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and lastly projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. To ensure arbitrary mesh geometry for which the homogenized stress‐strain curves are derived, a size scaling law is incorporated into the homogenized tensile damage evolution law. This ensures energy‐bridging equivalence of the microscopic cell to the homogenized medium irrespective of arbitrary mesh geometry. Results of numerical investigations will be compared with results of penetration experiments.
This manuscript presents a new methodology for the identification of optimal reduced order models for the inelastic and failure response of heterogeneous materials. The proposed methodology employs the eigendeformation-based reduced order homogenization approach. The identification of the optimal reduced order model is posed as an integer optimization problem and the genetic algorithm method is used to evaluate the optimization problem. A second optimization problem is posed to ensure that the errors associated with the optimal reduced order model are minimized through scaling of the failure parameters. The performance and capabilities of the optimal reduced order models identified based on the proposed approach are demonstrated by comparing model predictions with the computational homogenization method with full resolution of the material microstructure. Numerical simulations conducted using unidirectional reinforced matrix microstructures reveal that the reduced order models accurately describe the response characteristics of the composite material for a wide range of loading regimes.
Many continuum damage mechanics models for cementitious materials are typically phenomenological in design. Recent work has shown that a physics-based multiscale approach to modeling damage is efficient and effective. In order to use a multiscale approach, appropriate experimental data are necessary to model the microscale calculations that will then inform the continuum-scale calculations. This work uses the multiscale approach and experimentally determines the parameters necessary to model the microscale calculations. Notched three-point beam experiments were performed to determine the fracture energy of the ultra-high performance concrete known as Cor-Tuf. The fracture energy is then used by a simplified microscale calculation to determine a physics-based damage evolution equation that can be used in continuum-scale calculations. A meshfree method is used to show the usefulness of the newly determined damage evolution equation. Both a quasi-static application and a dynamic application are shown as examples. DISCLAIMER: The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. All product names and trademarks cited are the property of their respective owners. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.
Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra‐high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it runs inside the reproducing kernel particle method (RKPM)‐based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. Results of numerical investigations will be compared with results of penetration experiments.
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