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• Phase-field virtual modelling method (PFVM) is proposed for dynamic fracture in elasto-plastic materials. • Full-field uncertainties of PFVM enable reliable tracking of non-deterministic cracks. • The exceptional capability of PFVM in complex 3D conditions is demonstrated. • PFVM is validated in practical cases with both precision and efficiency. In modern engineering, dynamic fracture failure because of unexpected load or human faults may lead to catastrophic disasters. Preventive structure design and real-time maintain suggestions based on accurate numerical simulation are critical, especially when plasticity develops. It remains a challenge to efficiently model dynamic crack propagation in elasto-plastic materials while the uncertain factors in service life may significantly increase the difficulty. In this paper, a phase-field virtual modelling method (PFVM), based on the features of the novel extended support vector regression (X-SVR) method, is proposed to tackle this non-deterministic problem. The phase field method is adopted for its outstanding performance in complex fracture problems, which provides solid reference data for the virtual model's training and verification. The PFM application to dynamic elasto-plastic fracture problems is validated in two practical engineering examples. The integrated virtual modelling technique is then proven capable of instantly providing precise crack propagation prediction under multiple complex uncertainties, making up-to-date numerical dynamic fracture simulation achievable and affordable. The proposed PFVM method can minimize the contradiction between accurate modelling and high computational cost and can be utilized in various extensions like sensitivity analysis or design optimization. [ABSTRACT FROM AUTHOR]

Continuum damage models are often employed to represent cracking in quasi-brittle materials (e.g. , concrete, masonry and some rocks). From a numerical perspective, these models yield mesh-dependent results at the structural scale without regularization. Standard regularization techniques are prone, however, to some well-known drawbacks. To address these limitations, non-local models with evolving interactions have been proposed. Inspired by the analogy between non-local interactions and wave propagation time in a damaged domain, the eikonal non-local regularization introduces evolving non-local interactions through a damage-dependent metric field. The contribution of the paper involves coupling for the first time the gradient-enhanced version of the eikonal non-local formulation with a second-order anisotropic damage constitutive model. Such an aspect is essential when modeling quasi-brittle materials, since the material response is anisotropic and associated with various well-established behaviors, including the dissymmetry between tension and compression and unilateral effect. The manuscript provides a detailed overview of the formulation, numerical solution methods, and test cases, demonstrating some important features of these models. Attention is focused not only on the regularization properties of the formulation but also on its capability to naturally represent the transition from damage to fracture. • Damage is supposed to deform the space in which non-local interactions are computed. • The Helmholtz problem is modified using a damage-dependent Riemannian metric. • A second-order tensorial anisotropic damage model is considered. • Anisotropic non-local interactions evolve depending on anisotropic damage. • Numerical simulations are shown to illustrate mesh convergence and damage re-localization. [ABSTRACT FROM AUTHOR]

This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation. In contrast with the standard incremental approach, which solves the (non-linear and computationally intensive) mechanical balance equations at every time step, the proposed PGD approach allows the mechanical balance equations to be solved exclusively for the small-time intra-cyclic response, while the large-time inter-cyclic response is described by simple scalar algebraic equations. Numerical simulations exhibiting complex cyclic responses, including a 2D problem and an application to a monopile foundation, demonstrate that PGD solutions with a limited number of space–time degrees of freedom may be obtained numerically, only requiring a few modes to accurately capture the reference response. [ABSTRACT FROM AUTHOR]

Surrogate models based on machine learning methods have become an important part of modern engineering to replace costly computer simulations. The data used for creating a surrogate model are essential for the model accuracy and often restricted due to cost and time constraints. Adaptive sampling strategies have been shown to reduce the number of samples needed to create an accurate model. This paper proposes a new sampling strategy for global fit called Gradient and Uncertainty Enhanced Sequential Sampling (GUESS). The acquisition function uses two terms: the predictive posterior uncertainty of the surrogate model for exploration of unseen regions and a weighted approximation of the second and higher-order Taylor expansion values for exploitation. Although various sampling strategies have been proposed so far, the selection of a suitable method is not trivial. Therefore, we compared our proposed strategy to 9 adaptive sampling strategies for global surrogate modeling, based on 26 different 1 to 8-dimensional deterministic benchmarks functions. Results show that GUESS achieved on average the highest sample efficiency compared to other surrogate-based strategies on the tested examples. An ablation study considering the behavior of GUESS in higher dimensions and the importance of surrogate choice is also presented. • We study adaptive sampling strategies for global surrogate modeling. • We present a novel strategy using gradient information and predicted uncertainty. • A benchmark study comparing 9 strategies is conducted. • A metric to measure the overall performance and sample-efficiency is proposed. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical simulation of initiation and propagation of mixed mode fracture in rocks. A bond-level energy-based peridynamic model is developed by introducing a dilatation function to capture both volumetric and deviatoric deformations. We proceed to define the nonlocal stresses to obtain the isotropic and deviatoric forces commensurate with the deformations. We then come up with a new failure model to link computational peridynamics with some phenomenological failure criteria, which is highly relevant for both brittle and quasi-brittle rocks. Finally, several numerical examples of mixed-mode fractures are presented to show the performance of our model. [ABSTRACT FROM AUTHOR]

The objective of this article is the modeling and the numerical simulation of the response of elastoplastic structures to impacts. To this end, a numerical method is proposed that takes into account one-sided contact (Signorini condition) and impact phenomena together with plasticity in a monolithic solver, while accounting for the non-smooth character of the dynamics. The formulation of the plasticity and the contact laws are based on inclusions into normal cones of convex sets, or equivalently, variational inequalities following the pioneering work of Moreau (1974) and Halphen and Nguyen (1975), who introduced the assumptions of normal dissipation and of generalized standard materials (GSM) in the framework of associated plasticity with strain hardening. The proposed time–stepping method is an extension of the Jean and Moreau (1987) scheme for nonsmooth dynamics. The discrete energy balance shows that spurious numerical damping can be suppressed and that the scheme is in practice unconditionally stable. Furthermore, the finite-dimensional variational inequality at each time–step is well–posed and can be solved by optimization methods for convex quadratic programs, providing an interesting alternative to the return mapping algorithm coupled with a dedicated frictional contact method. The paper is completed by illustrative numerical examples of impacts on steel structures consisting of beams. • Formulation in a single variational inequality of the elastoplastic and contact laws • A Moreau-Jean type time–stepping method consistent with the nonsmooth dynamics • formulation of a convex quadratic program with well-posedness results • A discrete energy balance that ensures that the scheme is practically stable. • Simulation of multi-criteria elasto-plastic flow rules with contact constraints. • Application to impact on structures made of beams. [ABSTRACT FROM AUTHOR]

In this paper the numerical simulation of the interaction between Oldroyd-B viscoelastic fluid flows and hyperelastic solids is approached. The algorithm employed is a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially. A Galerkin finite element approach has been employed for the numerical approximation of the solid, while the flow equations are approximated using a stabilized finite element method based on the Variational Multi-Scale approach to overcome the instabilities of the Galerkin method. To be able to deal with flows with dominant elasticity, a log-conformation reformulation of the constitutive equation can be employed; here this approach is extended to Fluid–Structure Interaction problems. Several numerical examples are presented and discussed to assess the robustness of the proposed scheme and its applicability to problems with viscoelastic fluids in which elasticity is dominant interacting with hyperelastic solids. [ABSTRACT FROM AUTHOR]

Direct FE 2 , recently proposed by Tan et al. (2020), is a concurrent multilevel modeling approach, which homogenizes a representative volume element (RVE) to a Cauchy continuum but calls for only a single finite element analysis. In this paper, the method is extended to homogenization towards a micromorphic continuum. It allows us to capture the deformation of composites with soft inclusions in the absence of scale separation and the size effects therein. Besides the displacement field, additional morphic fields are employed at the macroscale to characterize the micro-scale heterogeneity. Compared with the classical FE 2 approach, the only effort in the development of the Direct FE 2 is to formulate the macro–micro transition as kinematic constraints between the macro and micro DOFs, that are implemented through multi-point constraints (MPC) in Abaqus®. Automatically, the MPCs enable the micro–macro transition in an energetically consistent way and correlate the microscopic traction back to the macroscopic nodal internal force. The performance of the novel Direct FE 2 modeling is benchmarked with three representative numerical simulations, where a better predictive capability than the classical one is demonstrated in situations without a clear separation of scales. [ABSTRACT FROM AUTHOR]

In this paper, we consider the mathematical modeling and numerical approximation for the fluid-surfactant phase field model coupled with the Navier–Stokes equations on surfaces. Taking account of the effect of the curvature and fluid flows, we first propose the incompressible Navier–Stokes fluid-surfactant phase field model on surfaces. Then, by introducing two power-type scalar auxiliary variables in the phase field equations for the potential energy terms and an exponential-type one in the momentum equation with respect to the inertial term, we transform the proposed model to an equivalent form. Furthermore, with the help of the derived three scalar auxiliary variables (3-SAV) equations, via utilizing the pressure correction method and implicit–explicit techniques in a proper sequence to eliminate the influence of the skew-symmetric loss in the surface finite element method, and applying stabilized methods for the convective and diffusion terms in the phase field and momentum equations according to the feature of the velocity field on surfaces respectively, we construct a linearized and decoupled fully discrete scheme, in which only some linear equations need to be solved at each time step. The unconditional energy stability of the fully discrete scheme is also proved. Finally, we show some numerical examples to verify the rationality of the model and the efficiency of the scheme, and discuss the influence of the geometric curvature and fluid flows on the system. • Taking account of the geometric curvature and fluid flow, we propose a NS-FSPF model. • The combination of an exponential-type SAV and the PC method is proposed. • The stabilized method is utilized to weakly enforce the tangential condition. • The implicit–explicit technique is used to decouple and linearize the 3-SAV system. • The unconditional energy stability of the proposed scheme is derived. [ABSTRACT FROM AUTHOR]