Computational Mechanics最新文献

The energy is a crucial factor in dynamical contact analysis. And the complexity of real-world surface morphologies characterized by roughness, poses a considerable challenge for accurately predicting their dynamic contact behaviors. Hence, it is meaningful to explore the influence of surface roughness on energy dissipation. In this study, the two-dimensional geometry with randomly rough surface is reconstructed based on Karhunen–Loève expansion and isogeometric collocation method. And a contact algorithm is tailored for dynamic frictional contact problems by incorporating the Bi-potential method into isogeometric analysis. Numerical results show that roughness factors such as the correlation length and square roughness of the randomly rough surface significantly affect the maximum ratio of real contact area to the normal contact area and the rate of energy dissipation. This work could provide a reference for future research on the dynamic contact between rough surfaces.

As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also output parameters, e.g., stresses, fluctuate. For the estimation of those fluctuations it is imperative to incoporate randomness into engineering simulations. Unfortunately, incorporating uncertain parameters into the modeling and simulation of inelastic materials is often computationally expensive, as many individual simulations may have to be performed. The promise of the proposed method is simple: using extended material models to include stochasticity reduces the number of needed simulations to one. This single computation is cheap, i.e., it has a comparable numerical effort as a single standard simulation. The extended material models are easily derived from standard deterministic material models and account for the effect of uncertainty by an extended set of deterministic material parameters. The time-dependent and stochastic aspects of the material behavior are separated, such that only the deterministic time-dependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during post-processing. The feasibility of this approach is demonstrated for three different and highly non-linear material models: viscous damage, viscous phase transformations and elasto-viscoplasticity. A comparison to the Monte Carlo method showcases that the method is indeed able to provide reliable estimates of the expectation and variance of internal variables and stress at a minimal fraction of the computation cost.

In recent times, immersed methods such as the finite cell method have been increasingly employed in structural mechanics to address complex-shaped problems. However, when dealing with heterogeneous microstructures, the FCM faces several challenges. Weak discontinuities occur at the interfaces between the different materials, resulting in kinks in the displacements and jumps in the strain and stress fields. Furthermore, the morphology of such composites is often described by 3D images, such as ones derived from X-ray computed tomography. These images lead to a non-smooth geometry description and thus, singularities in the stresses arise. In order to overcome these problems, several strategies are presented in this work. To capture the weak discontinuities at the material interfaces, the FCM is combined with local enrichment. Moreover, the L(^2)-projection is extended and applied to heterogeneous microstructures, transforming the 3D images into smooth level-set functions. All of the proposed approaches are applied to numerical examples. Finally, an application of cemented granular material is investigated using three versions of the FCM and is verified against the finite element method. The results show that the proposed methods are suitable for simulating heterogeneous materials starting from CT scans.

Moving boundaries and interfaces are commonly encountered in fluid flow simulations. For instance, fluid–structure interaction simulations require the formulation of the problem in moving and/or deformable domains, making the mesh distortion an issue of concern when it is required to guarantee the accuracy of the numerical model predictions. In addition, traditional elasticity-based mesh motion methods accumulate permanent mesh distortions when cyclic motions occur. In this work, we exploit a biologically-inspired framework for the mesh optimization at the same time it is moved to solve cyclic and nearly cyclic domain motions. Our work is in the framework introduced in Takizawa et al. (Comput Mech 65:1567–1591, 2020) under the name“low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state”. This mesh optimization/motion method is inspired by the mechanobiology of soft tissues, particularly those present in arterial walls, which feature an outstanding capacity to adapt to various mechanical stimuli through adaptive mechanisms such as growth and remodeling. This method adopts different reference configurations for each constituent, namely ground substance and fibers. Considering the optimization features of the adopted framework, it performs straightforwardly for cyclic motion with no cycle-to-cycle mesh distortion accumulation. Numerical experiments in both 2D and 3D using simplicial finite element meshes subjected to cyclic loads are reported. The results indicate that BIMO performance is better than the linear-elasticity mesh moving method in all test cases the two methods are compared.

The high computational efficiency of the Koiter reduced-order methods for structural buckling analysis has been extensively validated; however the high-order strain energy variations in constructing reduced-order models is still time-consuming, especially when involving the fully nonlinear kinematics. This paper presents a reduced-order method with the hybrid-stress formulation for geometrically nonlinear buckling analysis. A solid-shell element with Green-Lagrange kinematics is developed for three-dimensional analysis of thin-walled structures, in which the numerical locking is eliminated by the assumed natural strain method and the hybrid-stress formulation. The fourth-order strain energy variation is avoided using the two-field variational principle, leading to a significantly lower computational cost in construction of the reduced-order model. The numerical accuracy of the reduced-order model is not degraded, because the third-order approximation to equilibrium equations is recovered by condensing the stress. Numerical examples demonstrate that although the fourth-order strain energy variation is not involved, the advantage in path-following analysis using large step sizes is not only unaffected, but also enhanced in some cases with respect to the displacement based reduced-order method. The small computational extra-cost for the hybrid-stress formulation is largely compensated by the reduced-order analysis.

A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress–strain-strain rate responses in both training and testing regimes and improve prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted meshes, immersed boundary methods instead embed the computational domain in a structured background grid. Interpolation-based immersed boundary methods augment existing finite element software to non-invasively implement immersed boundary capabilities through extraction. Extraction interpolates the structured background basis as a linear combination of Lagrange polynomials defined on a foreground mesh, creating an interpolated basis that can be easily integrated by existing methods. This work extends the interpolation-based immersed isogeometric method to multi-material and multi-physics problems. Beginning from level-set descriptions of domain geometries, Heaviside enrichment is implemented to accommodate discontinuities in state variable fields across material interfaces. Adaptive refinement with truncated hierarchically refined B-splines (THB-splines) is used to both improve interface geometry representations and to resolve large solution gradients near interfaces. Multi-physics problems typically involve coupled fields where each field has unique discretization requirements. This work presents a novel discretization method for coupled problems through the application of extraction, using a single foreground mesh for all fields. Numerical examples illustrate optimal convergence rates for this method in both 2D and 3D, for partial differential equations representing heat conduction, linear elasticity, and a coupled thermo-mechanical problem. The utility of this method is demonstrated through image-based analysis of a composite sample, where in addition to circumventing typical meshing difficulties, this method reduces the required degrees of freedom when compared to classical boundary-fitted finite element methods.

Aiming to address the challenge of inaccurately describing the curve boundary of the complex design domain in traditional finite element mesh, this paper proposes an improved polygon mesh generation and polygon scaled boundary finite element method (PSBFEM) using non-uniform rational B-spline (NURBS) boundary. In the improved mesh generation scheme, the domain boundary will be accurately described using NURBS curves. Within this framework, a NURBS updating strategy is proposed, allowing the NURBS curve information on the boundary to be updated as the mesh changes. By employing point inversion and knot insertion, additional control points are introduced to ensure that some coincide with the nodes of the elements, thereby guaranteeing the accuracy of subsequent analyses. The boundary elements can be discretized into NURBS elements and conventional elements using SBFEM, whose physical fields are respectively constructed using NURBS basis functions and Lagrange shape functions in the circumferential direction. In the radial direction, by transforming a system of partial differential equations into a system of ordinary differential equations, which can be analytically solved without fundamental solutions. Furthermore, the internal elements can be solved directly with the traditional polygon SBFEM. The numerical examples demonstrate that the proposed method can achieve a high-quality polygon mesh with NURBS updating. Moreover, it effectively solves the corresponding polygon elements and significantly improves the accuracy of the displacement and stress solutions compared to the traditional polygon SBFEM.

In this article, we combine a Fast Fourier Transform based computational approach and a supervised machine learning strategy to discover models for the anisotropic effective viscosity of shear-thinning fiber suspensions. Using the Fast Fourier Transform based computational approach, we study the effects of the fiber orientation state and the imposed macroscopic shear rate tensor on the effective viscosity for a broad range of shear rates of engineering process interest. We visualize the effective viscosity in three dimensions and find that the anisotropy of the effective viscosity and its shear rate dependence vary strongly with the fiber orientation state. Combining the results of this work with insights from literature, we formulate four requirements a model of the effective viscosity should satisfy for shear-thinning fiber suspensions with a Cross-type matrix fluid. Furthermore, we introduce four model candidates with differing numbers of parameters and different theoretical motivations, and use supervised machine learning techniques for non-convex optimization to identify parameter sets for the model candidates. By doing so, we leverage the flexibility of automatic differentiation and the robustness of gradient based, supervised machine learning. Finally, we identify the most suitable model by comparing the prediction accuracy of the model candidates on the fiber orientation triangle, and find that multiple models predict the anisotropic shear-thinning behavior to engineering accuracy over a broad range of shear rates.