查看更多>>摘要：In recent years, the phase field method has been widely used in the simulation of fatigue crack propagation. However, fine mesh and cyclic simulation cycle by cycle significantly increase the computational cost of phase field simulation, which poses challenges in simulating the entire process of fatigue crack propagation. This paper proposes a cycle jump method considering the effect of plasticity at the crack tip, enabling accelerated simulations of fatigue crack propagation in elasto-plastic materials. In this method, fatigue crack propagation is accelerated through cycle jump prediction of displacement field and phase field variables, while the plastic strain accumulation at the crack tip is considered by the prediction of displacement field variables. An adaptive algorithm is developed to automatically adjust the cycle jump size based on the phase field evolution. The effectiveness of the proposed method is verified by several numerical examples. The results show that the proposed method ensures computational accuracy while significantly enhancing efficiency.
Centofanti, EdoardoHuynh, Ngoc Mai MonicaPavarino, Luca F.Scacchi, Simone...
1.1-1.15页
查看更多>>摘要：In this paper, we develop and numerically study algebraic multigrid (AMG) preconditioners for the cardiac EMI (Extracellular space, cell Membrane, and Intracellular space) model, a recent and biophysically detailed framework for cardiac electrophysiology. The EMI model addresses the limitations of traditional homogenized cardiac models and leverages contemporary computational power to enable high-resolution simulations at the cellular scale. Using a composite Discontinuous Galerkin (DG) discretization, we introduce an AMG-EMI solver for the three dimensional EMI model. Our investigation includes the AMG-EMI scalability performance, both weak and strong, and evaluates its numerical robustness under ischemic conditions, addressing the challenges of heterogeneous media. Numerical tests exploit state-of-the-art pre-exascale supercomputers with hybrid CPU-GPU architectures. The results indicate better scalability performance of the AMG-EMI solver on CPUs compared to GPUs. However, the best solution times achieved using GPUs are up to 40x faster than those obtained on CPUs.
El Masri, SamirCansiz, BarisStorm, JohannesKaliske, Michael...
1.1-1.18页
查看更多>>摘要：The finite element method (FEM) and its associated field have mainly been developed for adiabatic and closed systems. Nonetheless, open systems, which allow for the exchange of energy and mass with the surroundings, have gained increasing interest in applications where mass change occurs. For solving open systems two approaches can be undertaken. The first is the local approach, which incorporates mass change as an internal variable at the material level, while the second is the global approach, which treats mass change as an additional degree of freedom (DOF), solving the mass and momentum balance equations simultaneously. Although the global approach has been already developed, it has not yet incorporated a kinematic split of the deformation gradient. This split is necessary for modeling large strain deformations volume change (e.g. soft tissues). Hence, this study proposes a monolithic coupled mass-mechanical framework with a multiplicative split of the deformation gradient. The deformation gradient is multiplicatively split into mass-changing and mechanical components, with the mass-changing part accommodating orthotropic deformation and constraints enforcing density preservation. The study presents the complete finite element method from the kinematic foundations through to the discretization process. A sensitivity analysis is conducted to study the effects of various factors on the deformation and mass change. Moreover, a numerical example demonstrating the framework's application to a general mass change problem is also conducted. The results show that the proposed framework effectively models mass-changing phenomena, offering a tool for future research in the field of open systems.
查看更多>>摘要：In this paper, an implicit cell-based material point method (MPM) with particle boundaries is proposed to effectively solve large deformation static problems. The volume integrals of the incremental weak form based on an updated Lagrangian approach are evaluated at integration points defined by equally sub-dividing grid cells, which eliminates the cell-crossing error and reduces the integration error in solving problems with particles not aligned with a background grid. A level set function based on the particle volume is used to define a particle boundary. The number of integration points of the boundary grid cells intersected by the particle boundary is increased to more accurately perform the numerical integration of the incremental weak form over the boundary grid cells. The present method is applied to solve contact problems of two bodies discretized by particles. Contact between particles is detected using the level set values at the integration points of the boundary grid cells. The surface integral of the contact weak form is replaced by a volume integral in the contact penetration domain. Numerical results show that large deformation contact problems can be effectively solved by the implicit cell-based MPM with particle boundaries.
查看更多>>摘要：This work proposes a novel Isogeometric Analysis (IGA) extension of the assumed natural strain (ANS) method to alleviate locking phenomena in solid beams, which are modeled as 3D elements accounting for displacement degrees of freedom solely and designed such that accurate analyses can be generally obtained using only one element to discretize the structure's crosssection. ANS methods substitute covariant compatible strains that cause locking in solid beams, when, e.g., constrained to be thin, with a so-called assumed strain field. Namely, the compatible strains are interpolated at suitable locations, termed tying points, and the assumed strains are then derived using an ad hoc element-based extrapolation. This local operation involves, in principle, the inversion of extrapolation matrices; yet, these quantities can be computed at once and in closed form, using a linear extrapolation in the quadratic case, without needing any inversion operation. The introduced IGA ANS technique, specifically tailored to mitigate membrane and shear locking, given the superior geometric approximation provided by the adopted IGA framework, as well as the high regularity of the utilized computer-aided design basis functions, is also able to naturally alleviate thickness and curvature-thickness locking phenomena and its effectiveness is proven through extensive numerical testing.
查看更多>>摘要：We develop a strain gradient elastodynamics model for heterogeneous materials based on the two-scale asymptotic homogenization theory. Utilizing only the first-order cell functions, the present model is more concise and more computationally efficient than previous works with high-order truncations. Furthermore, we rigorously prove that the coefficient tensors, including the homogenized elasticity tensor, the strain gradient stiffness tensor, and the micro-inertial tensor are symmetric positive definite, thereby establishing the well-posedness of the strain gradient elastodynamics model, i.e., the existence and uniqueness of solutions. Numerical simulations are performed to confirm the theoretical findings and illustrate the characteristics of the present model in comparison with classical elastodynamics model (without strain gradient terms) and strain gradient models with higher-order truncations. The results indicate that the strain gradient model derived based on the first-order truncation can achieve an optimal balance between accuracy and computational cost.
查看更多>>摘要：3D swept volume, enabled by advancements in additive manufacturing, present new opportunities for lightweight and functional optimization. However, efficient design methodologies for conformal filling gradient lattice structures (CFGLSs) remain scarce. This paper proposes a modified level set function (MLSF) that matches lattice structures to the geometry of 3D swept volume. Furthermore, a multiscale isogeometric topology optimization (MITO) approach is used to adaptively optimize the distribution of graded lattices, ensuring optimal integration. A surrogate constitutive model is developed using polynomial interpolation in conjunction with the MLSF and the homogenization method. Incorporating the surrogate constitutive model into the MITO, the relative density distribution of the swept volume is obtained. Continuous CFGLSs are generated using the updated MLSF method, with the equivalent density distribution guiding the simultaneous optimization of both the micro-scale lattice geometry and its macro-scale distribution. The proposed approach is validated through the design, fabrication, and experimental evaluation of semi-circular specimens and engineering rudders, exhibiting its effectiveness and practicality.
Li, BinZhang, RanranZur, Krzysztof KamilRabczuk, Timon...
1.1-1.20页
查看更多>>摘要：Flexoelectricity is an electromechanical coupling phenomenon in which electric polarization is generated in response to strain gradients. This effect is size-dependent and becomes increasingly significant at micro-and nanoscale dimensions. While heterogeneous flexoelectric materials demonstrate enhanced electromechanical properties, their effective application in nanotechnology requires robust homogenization methods. In this study, we propose a novel second-order computational homogenization framework for flexoelectricity, which combines isogeometric analysis and the finite cell method. Key innovations include the introduction of high-order periodic boundary conditions and homogenized high-order stresses, which ensure consistent multiscale analysis. Periodic boundary conditions are applied using penalty methods, and perturbation analysis is employed to efficiently compute equivalent material coefficients. The effectiveness of the proposed method is validated through numerical examples, demonstrating its ability to generate piezoelectric effects in flexoelectric microstructured materials.
查看更多>>摘要：In this paper, a decoupled, linearized, unconditionally stable, and fully discrete numerical scheme is presented for simulating two-phase ferrofluid flows. This scheme is constructed by introducing two scalar auxiliary variables. It is based on the backward Euler scheme with variable time step and mixed finite element discretization. Nonlinear terms are treated explicitly to simplify the computational process. Meanwhile, without any restriction on time step, we show the stability of the proposed scheme. Finally, numerical examples are presented to check the accuracy and efficiency of the proposed scheme.
查看更多>>摘要：This study is dedicated to the multi-material topology optimization formulation (MMTO) for finite strain nonlocal elastoplasticity. The subloading surface model is newly incorporated into the primal problem to achieve the gradual change of the deformation process from pure elastic to material-specific plastic hardening. The stress-strain relationship of the model is a smooth continuous function, which is beneficial for elastoplastic topology optimization since the resulting continuous tangent is used in the adjoint problem to determine the sensitivity. Also, the nonlocal plastic modeling is introduced to resolve mesh-dependency issues in the evolution of plastic deformation. In addition, in order to maintain computational stability and to avoid unrealistic plastic deformation occurring in voids (ersatz material), the concept of interpolating energy densities is introduced, by which linearly elastic material is chosen to represent voids. The continuous adjoint method is employed to derive the governing equations and sensitivity of the adjoint problem, and the resulting equations are valid at any position, boundary, or time in the continuum without relying on any discretization. An arbitrary number of design variables can be considered for multiple materials in the optimization problem, and by referring to the derived sensitivity, the multiple reaction-diffusion equations are solved to update the material distribution and configuration. The first numerical example demonstrates the "oscillation of deformation states" caused by the conventional plastic model and shows how the subloading surface model effectively resolves this issue, achieving stable optimization processes. Also, the second example presents the unconventional deformation magnitude-dependent stiffness maximization problems with multiple materials, in which the optimal designs are realized by referring to the same elastic but different plastic material properties.
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