Computational Mechanics最新文献

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach, which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties and secondary variables such as stresses and strains. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method with respect to noise and model uncertainty and its great potential to enable the effective identification of patient-specific, heterogeneous physical properties, e.g. tissue stiffness properties. In particular, we demonstrate the capability of PINNs to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.

Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture plays a critical role. In this paper, we introduce a novel computational approach for modeling fracture in slender beams subjected to large deformations. We adopt a state-of-the-art geometrically exact Kirchhoff beam formulation to describe the finite deformations of beams in three-dimensions. We develop a discontinuous Galerkin finite element discretization of the beam governing equations, incorporating discontinuities in the position and tangent degrees of freedom at the inter-element boundaries of the finite elements. Before fracture initiation, we enforce compatibility of nodal positions and tangents weakly, via the exchange of variationally-consistent forces and moments at the interfaces between adjacent elements. At the onset of fracture, these forces and moments transition to cohesive laws modeling interface failure. We conduct a series of numerical tests to verify our computational framework against a set of benchmarks and we demonstrate its ability to capture the tensile and bending fracture modes in beams exhibiting large deformations. Finally, we present the validation of our framework against fracture experiments of dry spaghetti rods subjected to sudden relaxation of curvature.

The aim of this paper is to propose a fast FEM strategy for simulating molten metal deposition geometry during additive manufacturing for studying the influence of the sequence of deposition on the geometry. The approach is inspired by the algorithm initially proposed by Feulvarch et al. (Eur J Mech A 89:104290, 2021) for coatings. In this article, the membrane finite element is notably improved and extended for simulating of a large stack of deposits in order to study the building of 3D geometries. A constant vertical evolution rate of the surface tension is introduced to adjust the geometry of the free surface of the molten pool which depends on the hydrodynamics of the liquid phase. The simulation is very fast because it is carried out on a 2D mesh composed of linear triangles that corresponds to the sole free surface of the liquid phase at each time step. Moreover, the implicit nonlinear algorithm developed has the advantage of avoiding matrix systems resolution (reduced RAM memory, efficient parallel computing). In addition, a simple and robust remeshing procedure is detailed in order to avoid too large distortions of the triangular elements during the ’inflating’ stage of the workpiece. Its interest lies in the fact that it does not require any field projection typically employed in remeshing procedures, as the geometry serves as the only historical data required to resume FEM computations following each remeshing step. Examples are proposed to clearly evidence the efficiency and robustness of the method developed in terms of geometry and CPU time.

In metal single crystals, the observed formation of deformation banding pattern has been explained by greater latent hardening of slip systems than their self-hardening, which promotes spatial segregation of plastic slips and lamination towards single-slip domains. Numerical studies focusing on the formation of deformation bands usually involved initial imperfections, boundary-induced heterogeneity, or the postulate of minimal global energy expenditure which additionally promoted non-uniformity of deformation. This article analyses the case when no such mechanism enforcing locally non-uniform deformation is implemented in the finite element (FE) method, while the global system of equations of incremental equilibrium is solved in a standard way. The new finding in this paper is that the deformation banding pattern can appear spontaneously in FE simulations of homogeneous single crystals even in the absence of any mechanism favouring deformation banding in the numerical code. This has been demonstrated in several examples in the small strain formalism using a plane-strain model in which the twelve fcc slip systems are reduced to three effective plastic slip mechanisms. Incremental slips are determined at the Gauss-point level either by incremental work minimization in the rate-independent case or by rate-dependent regularization. In the rate-independent approach, the trust-region algorithm is developed for the selection of active slip systems with the help of the augmented Lagrangian method. Conditions under which a banding pattern appears spontaneously or is suppressed are discussed. In particular, a critical rate sensitivity exponent is identified.

In this work, we present a finite deformation, fully coupled thermomechanical crystal plasticity framework. The model includes temperature dependence in the kinematic formulation, constitutive law and governing equilibrium equations. For demonstration, we employ the model to study the evolution and formation of residual stresses, residual statistically stored dislocation density and residual lattice rotation due solely to solid state thermal cycling. The calculations reveal the development of microplasticity within the microstructure provided that the temperature change in the thermal cycle is sufficiently large. They also show, for the first time, that the thermal cycling generates an internally evolving strain rate, where the contributions of mechanical strain and plasticity depend on temperature change. The calculations suggest a strong connection between the maximum temperature of a given cycle and the magnitude of the residual stresses generated after the cycle. A pronounced influence of elastic anisotropy on the heterogeneity of the residual stress distribution is also demonstrated here. Finally, we calculate lattice rotation obtained from thermal cycling ranging from (pm 0.4^{circ }) and show the relation between changes in predominant slip systems with short range intragranular lattice rotation gradients. The model can benefit metal process design, especially where large strains and/or large temperature changes are involved, such as bulk forming and additive manufacturing.

This study explores reduced-order modeling for analyzing time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in which the chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and solved using the finite element method. We employ proper orthogonal decomposition as a model order reduction approach. The reduced-order model performance is tested through a benchmark problem on hydrogel swelling and a case study simulating co-axial printing. Then, we embed the reduced-order model into an optimization loop to efficiently identify the coupled problem’s material parameters using full-field data. Finally, a study is conducted on the uncertainty propagation of the material parameter.

This paper presents a new stabilised Element-Free Galerkin (EFG) method tailored for large strain transient solid dynamics. The method employs a mixed formulation that combines the Total Lagrangian conservation laws for linear momentum with an additional set of geometric strain measures. The main aim of this paper is to adapt the well-established Streamline Upwind Petrov–Galerkin (SUPG) stabilisation methodology to the context of EFG, presenting three key contributions. Firstly, a variational consistent EFG computational framework is introduced, emphasising behaviours associated with nearly incompressible materials. Secondly, the suppression of non-physical numerical artefacts, such as zero-energy modes and locking, through a well-established stabilisation procedure. Thirdly, the stability of the SUPG formulation is demonstrated using the time rate of Hamiltonian of the system, ensuring non-negative entropy production throughout the entire simulation. To assess the stability, robustness and performance of the proposed algorithm, several benchmark examples in the context of isothermal hyperelasticity and large strain plasticity are examined. Results show that the proposed algorithm effectively addresses spurious modes, including hour-glassing and spurious pressure fluctuations commonly observed in classical displacement-based EFG frameworks.

The formation of branches in bacterial colonies is influenced by both chemical interactions (reactions) and the movement of substances through space (diffusion). These colonies can exhibit a variety of fascinating branching patterns due to the interplay of nutrient transport, bacterial growth, and chemotaxis. To understand this complex process, researchers have developed several mathematical models based on solving reaction-diffusion equations. In this letter, we introduce an innovative application of the lattice Boltzmann method to investigate the diverse morphological patterns observed in bacterial colonies. This method is concise, compact, and easy to implement. Our study demonstrates its effectiveness in accurately predicting various types of bacterial colony patterns, offering a new tool to obtain insights into the dynamics of bacterial growth and pattern formation.

In this paper, a penalty-based cell vertex finite volume method (P-CV-FVM) is proposed for the computation of two-dimensional contact problems. The deformation of objects during contact is described using the Total Lagrangian momentum equation. The governing equations are discretized using the cell vertex finite volume method. The control volume is constructed around each grid node to facilitate the efficient and accurate calculation of contact stress using penalty functions. By analyzing a classic contact example, the appropriate range of scaling factors in the penalty function method is obtained. Multiple contact problems are calculated and the results are compared with those from the finite element method (FEM). The results indicate that a stable and accurate solution can only be obtained with a scaling factor range of 10³–10¹² under this method. In addition, the mesh convergence of this method is better than that of FEM, and it meets the computational accuracy of Hertz contact and frictional contact problems.

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.