Neural network based material description of uncured rubber for use in finite element simulation

The finite element method (FEM) is widely used for structural analysis in engineering. In order to predict the behaviour of structures realistically, it is important to understand and to describe the material behaviour. Therefore, extensive material tests have to be conducted. For highly inelastic materials, such as uncured rubber, the characterisation of the behaviour requires a quite complex rheology. Rheological models are used to describe time-dependent mechanical material behaviour (stress-strain-time dependencies). The mapping of the real material behaviour by such models is only possible with restrictions. However, the evaluation of these models at each integration point within the FEM needs time consuming internal iterations in most cases. In order to describe the material behaviour without model restrictions and to reduce computational cost, the aim of this work is the development of a procedure which enables structural analyses without a specific constitutive material model. In this paper, a neural network is used in order to describe uncured rubber behaviour as a model-free approach

Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain

SummaryIn the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack‐tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ‐limit proof, thus the existence of (local) minimizers is guaranteed by the Γ‐convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker‐Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate‐dependent three‐surface smooth yield function that requires hardening and hardening‐rate parameters. The independent evolution of viscoplasticity in different microplanes induces anisotropy in the mechanical response. The sound performance of the model is illustrated via numerical examples for both rate‐independent and rate‐dependent plasticity

A large deformation and thermomechanically coupled interface approach

Interfaces are formed e.g. by the contact surface of different materials of heterogeneous solids or by crack flanks within damaged bodies. Since the combination of temperature evolution and mechanical loadings influences significantly the deformation and thermal behavior of interfacial layers, these failure layers are thermally and mechanically described in the presented approach in a fully coupled sense. Thermomechanical interface descriptions can be used for prediction of crack propagation and, as soon as a designated failure layer exists, to predict the thermomechanical behavior of the observed solid. The presented interface approach for finite deformation introduces a consistent framework derived from principle thermodynamical laws

Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have shown that when designing loss functions for many engineering problems, using first-order derivatives and combining equations from both strong and weak forms can lead to much better accuracy, especially when there are heterogeneity and variable jumps in the domain. This new approach is called the mixed formulation for PINNs, which takes ideas from the mixed finite element method. In this method, the PDE is reformulated as a system of equations where the primary unknowns are the fluxes or gradients of the solution, and the secondary unknowns are the solution itself. In this work, we propose applying the mixed formulation to solve multi-physical problems, specifically a stationary thermo-mechanically coupled system of equations. Additionally, we discuss both sequential and fully coupled unsupervised training and compare their accuracy and computational cost. To improve the accuracy of the network, we incorporate hard boundary constraints to ensure valid predictions. We then investigate how different optimizers and architectures affect accuracy and efficiency. Finally, we introduce a simple approach for parametric learning that is similar to transfer learning. This approach combines data and physics to address the limitations of PINNs regarding computational cost and improves the network's ability to predict the response of the system for unseen cases. The outcomes of this work will be useful for many other engineering applications where deep learning is employed on multiple coupled systems of equations for fast and reliable computations

Numerical representation of fracture patterns and post-fracture load-bearing performance of thermally prestressed glass with polymer foil

Glass can be thermally prestressed to enhance its load-bearing performance and tensile strength for civil engineering constructions. In such applications, the glass is thermally treated (internal stress state) and polymer foils/interlayers are applied to generate a laminate with a higher resistance to bending (out-of-plane loading) in case of fracture. In this contribution, a thermally prestressed glass panel with polymer foil as a backsheet is investigated as a special configuration of safety glass. In its post-fracture state, the polymer foil still provides a minimum structural integrity. Commonly, the post-fracture load-bearing performance of such polymer-glass assemblies is experimentally assessed by large scale tests related to high costs and testing time. In this research, an approach is presented to numerically assess the post-fracture load-bearing performance (bending) of such a fractured glass panel. The approach is based on A) digital image processing of the fracture pattern of three glass samples, B) the generation of a quadtree finite element (FE) mesh, C) the use of prismatic polyhedral FE to efficiently represent glass fragments in the quadtree FE mesh and D) cohesive elements with a nonlinear traction-separation law (TSL) for finite separation to represent the structural effect of the polymer foil during the post-fracture state

Fast and Reliable Reduced-Order Models for Cardiac Electrophysiology

Mathematical models of the human heart are increasingly playing a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The aim is to aid medical practitioners diagnose and treat the many ailments affecting the heart. Towards this, modelling cardiac electrophysiology is crucial as the heart's electrical activity underlies the contraction mechanism and the resulting pumping action. The governing equations and the constitutive laws describing the electrical activity in the heart are coupled, nonlinear, and involve a fast moving wave front, which is generally solved by the finite element method. The simulation of this complex system as part of a virtual heart model is challenging due to the necessity of fine spatial and temporal resolution of the domain. Therefore, efficient surrogate models are needed to predict the dynamics under varying parameters and inputs. In this work, we develop an adaptive, projection-based surrogate model for cardiac electrophysiology. We introduce an a posteriori error estimator that can accurately and efficiently quantify the accuracy of the surrogate model. Using the error estimator, we systematically update our surrogate model through a greedy search of the parameter space. Furthermore, using the error estimator, the parameter search space is dynamically updated such that the most relevant samples get chosen at every iteration. The proposed adaptive surrogate modelling technique is tested on three benchmark models to illustrate its efficiency, accuracy, and ability of generalization.Comment: 28 pages, 17 figures, 1 tabl

Investigations on the physical and mechanical behaviour of sycamore maple ( Acer pseudoplatanus L.)

Physical and mechanical properties of sycamore maple (Acer pseudoplatanus L.) were extensively investigated as basis for three-dimensional material modelling for structural simulations (e.g., with finite element method) based on this species. The physical properties of swelling, water absorption, water vapour resistance and thermal conductivity were tested and the mechanical properties of tensile, bending and compression strength and of Young's modulus (static and dynamic) as well as of Poisson's ratio, shear strength, shear modulus and fracture toughness were determined. The tests were carried out for most of the features depending on moisture content and also in all three anatomical main directions: longitudinal, radial and tangentia

Static and dynamic tensile shear test of glued lap wooden joint with four different types of adhesives.

Investigations of quasi-static and fatigue failure in glued wooden joints subjected to tensile shear loading are presented. Lap joints of beech wood (Fagus sylvatica L.) connected with four different types of adhesives, i.e. polyurethane (PUR), melamine urea formaldehyde (MUF), bone glue and fish glue, were experimentally tested until the specimens failed. The average shear strengths obtained from the quasi-static test ranged from 12.2 to 13.4 MPa. These results do not indicate any influence of the different adhesive types. The influence of the adhesives is only visible from the results of the fatigue tests, which were carried out under different stress excitation levels between 45% and 75% of the shear strength. Specimens bound with ductile adhesive (PUR) showed a slightly higher number of cycles to failure (Nf) at low-stress levels and lower Nf at high-stress levels in comparison to more brittle adhesives (MUF, fish glue). In general, the performances of animal glues and MUF were similar in both quasi-static and fatigue loading under dry conditions. Keywords: bone glue, fatigue test, fish glue, glued wood lap joint, melamine urea formaldehyde (MUF), polyurethane (PUR), tensile shear tes

Modelling of polymorphic uncertainty in the mesoscopic scale of reinforced concrete structures

The realistic modelling of structures is essential for their numerical simulations and is mainly characterized by the mechanical model and the consideration of the available data at hand by an adequate uncertainty model. The key idea in this contribution is the consideration of polymorphic uncertainty at the numerical structural analysis and the mechanical modelling for reinforced concrete structures, which are characterized by a combination of heterogeneous concrete and different types of reinforcement (e.g. steel bars or carbon fibres mats). Typically, the reinforcement is denoted by another length scale, compared to the overall structure size. The formulation and development of a computational homogenization approach, considering the different homogeneous and heterogeneous characteristics of a macroscopic structure, is essential for a precise numerical computation. In recent years, focal point of research was on structural analysis considering uncertain material or geometry parameters. Probabilistic approaches are dominating the uncertainty consideration currently, although they are connected with certain disadvantages and limits. In this contribution, a generalized uncertainty model is utilized in order to take variability, impression and incompleteness in to account. That allows a separated evaluation of the influence for each uncertainty source on the results. Therefore, polymorphic uncertainty models are applied and developed by combining and extending aleatoric and epistemic uncertainty, resulting e.g. in the formulation of the uncertainty model fuzzy p-box or fuzzy probability based randomness. The information of the different length scales is considered to be uncertain, e.g. the geometry or the material properties of a representative volume element (RVE) at the mesoscale. Subsequently, the uncertainty of the behaviour of a macro structure is derived from uncertain results on the meso structure. Since the computational effort of such investigations is tremendous, highly developed meta-models (recurrent neural networks) are applied in order to replace the uncertain RVE responses

Experimental and Numerical Investigation of Tire Tread Wear on Block Level

Tread wear appears as a consequence of friction, which mainly depends on surface charac-teristics, contact pressure, slip velocity, temperature and dissipative material properties of the tread material itself. The subsequent description introduces a wear model as a function of the frictional energy rate. A post-processing as well as an adaptive re-meshing algorithm are implemented into a finite element code in order to predict wear loss in terms of mass. The geometry of block models is generated by image processing tools using photographs of the rubber samples in the laboratory. In addition, the worn block shape after the wear test is compared to simulation results