Computer Methods in Applied Mechanics and Engineering最新文献

The thermal conductivity of materials dictates their functionality and reliability, especially for materials with complex microstructural topologies, such as woven composites. In this paper, we develop a physics-informed machine-learning architecture built specifically for solving thermal conductivity problems. Originally developed for mechanical problems, we extend and develop a deep material network (DMN) that incorporates (i) principles from thermal homogenization directly into the network architecture in which nodes propagate heat flux and temperature gradient (as opposed to stress and strain in the original ‘mechanical’ DMN) and (ii) nodal rotations to capture the topological complexity of the materials’ microstructure. The result is a ‘thermal’ DMN better suited for thermal conductivity problems than the ‘mechanical’ deep material network. We demonstrate the ability of this ‘thermal’ DMN to act as an accurate reduced order model with a significantly smaller number of degrees of freedom on two different woven microstructures examples. Our results show that the ‘thermal’ DMN can not only accurately predict the averaged effective thermal conductivity of these complex weaved composite structures but also the distribution of local heat flux and temperature gradients. Based on these performances, we show how this ‘thermal’ DMN can be exercised for rapid uncertainty and sensitivity analyses to assess microstructure effects and variability of the properties of the composite’s constituents, a task that would be otherwise computationally prohibitive with direct numerical simulations. Based on its architecture, the ‘thermal’ DMN opens possibilities for multiscale, multiphysics simulations for a heterogeneous structure, especially when coupled with its mechanical counterpart.

A maximum energy dissipation-based incremental approach (MEDIA) is proposed to overcome limit points, e.g. strong snap-backs, in the fracture analysis of quasi-brittle materials. An optimisation step is applied using an expression proposed to compute the change of dissipated energy within the discretised body when moving from one state of equilibrium to another. This expression is developed at the integration point level and uses a binary pathway vector to define all the possible solutions within that step. Due to the unique way the problem is cast, a genetic algorithm is deployed to identify the solution leading to the highest energy dissipation while following applicable thermodynamic constraints. The resulting analysis is non-iterative and purely incremental. MEDIA is particularly applicable in combination with discrete crack models. In this case, meshes are relatively coarse and each crack can be individually handled to maintain the computational cost independent of the discretisation. The equations are also cast in a direct inverse method that avoids explicitly solving the inversion of the stiffness matrices for each chromosome in the genetic optimisation. Problems having multiple snap-back effects and non-proportional loading, as well as lightly and highly reinforced concrete beams, are used to assess the suitability and efficiency of the proposed method. In contrast with other available techniques, MEDIA is shown to follow the adopted constitutive models without any energy loss due to the solution-finding process while providing adequate structural responses.

A plasticity formulation for the Hybrid Virtual Element Method (HVEM) is presented. The main features include the use of an energy norm for the VE projection, a high-order divergence-free interpolation for stresses and a piecewise constant interpolation for plastic multipliers within element subdomains. The HVEM does not require any stabilization term, unlike classical VEM formulations which are affected by the choice of stabilization parameters. The algorithmic tangent matrix is derived consistently and analytically. A standard strain-driven formulation and a Backward-Euler time integration scheme are adopted. The return mapping process for the stress evaluation is formulated at the element level to preserve the stress interpolation as plasticity evolves. Even though general constitutive laws can be readily considered, to test the robustness of HVEM, an elastic-perfectly plastic behavior is adopted. In such a case, the return mapping process is efficiently solved using a Sequential Quadratic Programming Algorithm. The solution is free from volumetric locking and from spurious hardening effects that are observed in stabilized VEM. The numerical results confirm the accuracy of HVEM for rough meshes and high rate of convergence in recovering the collapse load.

We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time integration algorithm, but still requires a system matrix inversion due to the use of a consistent mass matrix. Moreover, in that work, the efficiency was also limited by an iterative solution scheme needed due to the presence of a nonlinear term in the time-discretized rotational balance equation. In the present paper, we address these limitations and propose a novel fully explicit formulation able to preserve high-order accuracy in space. This is done by extending a predictor–multicorrector approach, originally proposed for standard elastodynamics, to the case of the rotational dynamics of geometrically exact beams. The procedure relies on decoupling the Neumann boundary conditions and on a rearrangement and rescaling of the mass matrix. We demonstrate that an additional gain in terms of computational cost is obtained by properly removing the angular velocity-dependent nonlinear term in the rotational balance equation without any significant loss in terms of accuracy. The high-order spatial accuracy and the improved efficiency of the proposed formulation compared to the existing one are demonstrated through some numerical experiments covering different combinations of boundary conditions.

A critical look and review of the so-called generalized single-step time integration method by Zhang (CMAME, 418(2024), 116503) is proved and demonstrated to be not new, but identical to and within the existing GS4-II computational framework. The following are addressed: (1) Firstly, it is claimed that 16 parameters were introduced (somewhat misleading as evident in what follows) to obtain a more generalized single-step mathematical formulation. We show that 4 conditions are made redundant with minimum consistency requirements, and thus, the framework is not new and is identical to the original version of the GS4-II computational framework with 12 parameters. (2) Then, the overshooting behavior is revisited, and the analysis, missteps, and information are clarified and corrected in this paper, which is significant. (3) Next, the time shift phenomenon is also revisited to show the recovery of the order of time accuracy in the acceleration, which is misunderstood in much of the existing literature. (4) Lastly, each design in the so-called newly proposed schemes already exists and is found in the GS4-II computational framework. In particular, via GS4-II we additionally prove and demonstrate that the so-called “Optimal Equivalent Single-step with Single parameter (OESS)” scheme by Zhang (CMAME, 418(2024), 116503) is nothing but identical to the existing Three-Parameters Optimal/Generalized-$\alpha$ method within the GS4-II framework for physically undamped problems. Furthermore, it is noteworthy to point out that also within the GS4-II framework, for physically damped problems, U0/U0${}^{\ast }$, TPO/G-$\alpha$, and OESS all share the same undesired overshooting deficiency in comparison to V0/V0${}^{\ast }$. Numerical examples validate the issues identified about the accuracy and overshooting analysis.

We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational formulation involving spaces with at most $H^1$-smoothness, so that conforming discretizations require at most $C^0$-continuity. The method is demonstrated on arbitrary order $C^1$-splines.