Computational Mechanics最新文献

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.

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.