Nonlinear Material Model Research Articles

Numerical investigation of crack initiation on rail surfaces considering laminar plasma quenching technology

To recognize the crack initiation life of a corrugated rail surface after quenching, the explicit finite element model referring to real condition is developed for precise frictional rolling contact solutions considering selective quenching. This takes rail profile evolution and the nonlinear material model used for quenching effect into account. Then the simulation results combined with the fatigue model is integrated for the crack initiation life after quenching, the crack initiation on edge of quenching region is mainly caused by the wheel-rail impact induced by irregularities, which is formed by discontinuous material characteristic between quenching and matrix material. Based on this, the most critically susceptible position to crack and number of cycles are predicted, the simulated results are verified through comparison with quenching rail in service.

Topology optimization considering the Drucker–Prager criterion with a surrogate nonlinear elastic constitutive model

We address material nonlinear topology optimization problems considering the Drucker–Prager strength criterion by means of a surrogate nonlinear elastic model. The nonlinear material model is based on a generalized J2 deformation theory of plasticity. From an algorithmic viewpoint, we consider the topology optimization problem subjected to prescribed energy, which leads to robust convergence in nonlinear problems. The objective function of the optimization problem consists of maximizing the strain energy of the system in equilibrium subjected to a volume constraint. The sensitivity analysis is quite effective and efficient in the sense that there is no extra adjoint equation. In addition, the nonlinear structural equilibrium problem is solved through direct minimization of the structural strain energy using Newton’s method with an inexact line search strategy. Four numerical examples demonstrate features of the proposed nonlinear topology optimization framework considering the Drucker–Prager strength criterion.

On the Adoption of Global/Local Approaches for the Thermomechanical Analysis and Design of Liquid Rocket Engines

Large Liquid Rocket Engines for Aerospace applications usually need to be cooled regeneratively since they are characterized by high pressure levels and heat flux with the presence, in the inner structure, of very high thermal gradients—thus necessitating the adoption of elastic-plastic nonlinear material models to study the thermomechanical behavior of the chamber and its service life. Tackling such nonlinearity makes the finite element analyses computationally intensive, particularly so when dealing with three-dimensional models. In these instances, it is highly recommended to adopt optimized numerical approaches that can save computation time while maintaining high levels of accuracy. The aim of the present paper is to implement an iterative coupling technique between two finite element models, a Global linear model and a Local nonlinear one, in the framework of a Global/Local procedure, to improve the accuracy of the numerical simulations. Both conformal and non-conformal meshes at the interface between the Global and the Local models have been considered. The results show that, even with a very few iterations, significant accuracy improvements are achieved.

Mesoscale Modeling of a Masonry Building Subjected to Earthquake Loading

Masonry structures constitute an important part of the built environment and architectural heritage in seismic areas. A large number of these old structures showed inadequate performance and suffered substantial damage under past earthquakes. Realistic numerical models are required for accurate response predictions and for addressing the implementation of effective strengthening solutions. A comprehensive mesoscale modeling strategy explicitly allowing for masonry bond is presented in this paper. It is based on advanced nonlinear material models for interface elements simulating cracks in mortar joints and brick/block units under cyclic loading. Moreover, domain decomposition and mesh tying techniques are used to enhance computational efficiency in detailed nonlinear simulations. The potential of this approach is shown with reference to a case study of a full-scale unreinforced masonry building previously tested in laboratory under pseudodynamic loading. The results obtained confirm that the proposed modeling strategy for brick/block-masonry structures leads to accurate representations of the seismic response of three-dimensional (3D) building structures, both at the local and global levels. The numerical-experimental comparisons show that this detailed modeling approach enables remarkably accurate predictions of the actual dynamic characteristics, along with the main resisting mechanisms and crack patterns.

3D finite element models from serial section histology of skeletal muscle tissue – The role of micro-architecture on mechanical behaviour

In this contribution we create three-dimensional (3D) finite element models from a series of histological sections of porcine skeletal muscle tissue. Image registration is performed on the stained sections by affinely aligning them using auxiliary markers, followed by image segmentation to determine muscle fibres and the extracellular matrix in each section, with particular regard to the continuity of the fibres through the stack. With this information, 3D virtual tissue samples are reconstructed, discretised, and associated with appropriate non-linear elastic anisotropic material models. While the gross anatomy is directly obtained from the images, the local directions of anisotropy were determined by the use of an analogy with steady state diffusion. The influence of the number of histological sections considered for reconstruction on the numerically simulated mechanical response of the virtual tissue samples is then studied. The results show that muscle tissue is fairly heterogeneous along the fascicles, and that transverse isotropy is inadequate in describing their material symmetry at the typical length scale of a fascicle. Numerical simulations of different load cases suggest that ignoring the undulations of fibres and their non-uniform cross-sections only moderately affects the passive response of the tissue in tensile and compressive modes, but can become crucial when predicting the response to generic loads and activation.

Learning Elastic Constitutive Material and Damping Models

AbstractCommonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized models of deformable materials from example surface trajectories. The key idea is to iteratively improve a correction to a nominal model of the elastic and damping properties of the object, which allows new forward simulations with the learned correction to more accurately predict the behavior of a given soft object. Space‐time optimization is employed to identify gentle control forces with which we extract necessary data for model inference and to finally encapsulate the material correction into a compact parametric form. Furthermore, a patch based position constraint is proposed to tackle the challenge of handling incomplete and noisy observations arising in real‐world examples. We demonstrate the effectiveness of our method with a set of synthetic examples, as well with data captured from real world homogeneous elastic objects.

Nonlinear material modelling for fibre-based progressive collapse analysis of RC framed buildings

The choice of the most suitable constitutive models for fibre-based progressive collapse analysis of reinforced concrete (RC) structures is still an open issue, mainly because nonlinear material modelling has never been treated as a variable involved in the assessment problem so far. To support analysts in selecting which models could be more representative of the actual inelastic material response for progressive collapse analysis of RC framed buildings, this paper presents a numerical investigation where fibre modelling was integrated with different combinations of stress–strain relationships for concrete and reinforcing steel. A series of pushdown simulations of a two-bay perimeter frame mock-up were then carried out to assess the gravity load capacity under downward displacement. Analysis results are compared with available experimental test data for performance quantification of numerical models, which is based upon an experimental-to-numerical load capacity ratio and overall statistical parameters. Sensitivity to the material modelling approach, load eccentricity and boundary conditions is evaluated, involving strain indicators that can be used in performance-based robustness assessment of RC framed buildings. Finally, a number of parametric analyses are presented to show how the load capacity is influenced by capacity model properties, such as material strengths, beam span length, and span length ratio of asymmetric frames.

3D-Printed Strain Sensors: Electro-Mechanical Simulation and Design Analysis Using Nonlinear Material Model and Experimental Investigation

This work is driven by the continuous improvement in additive manufacturing and the growing interest in developing flexible strain sensors with complex designs and structures. Characterization and analysis require not only understanding the mechanical behavior of the sensor but also the electrical behavior and the coupled electromechanical behavior. Traditionally, this coupled electromechanical behavior is determined using simplified approaches to establish a relationship between the electrical domain and mechanical domain. This work presents an experimental and numerical platform to characterize strain sensors and serves as a tool for design guidelines for these sensors. A nonlinear finite element COMSOL model is developed and validated against experiment. At 38% strain level the sensitivity is increased by 7% when the thickness,t, of the sensor decreased from t = 1.4 mm to t = 0.6 mm. A sensor with triangular embedded channels exhibits improved performance compared to square, hexagonal, and octagonal cross-sectional shapes. Three common channel patterns are examined including spiral, vertical serpentine, and horizontal serpentine patterns. Three commonly used materials for fabricating strain sensors are investigated including PDMS, EcoFlex, and NinjaFlex. At 35% strain level, a sensor with NinjaFlex substrate exhibits, approximately, 6% improvement in sensitivity, compared to a sensor with EcoFlex substrate.

Determination of the Properties of the Rubber Mounted Under the Agricultural Tractor Rollover Protective Structure Cabin Using a Hyperelastic Tensile Test and Finite Element Analysis

This study was carried out to determine the properties of materials used in the rubber mounted under the agricultural tractor rollover protective structure cabin. The natural rubber specimens were subjected to a hyperelastic uniaxial, biaxial, and planar tensile test, and a volumetric compression test for each of the four shore hardness types. The validity of the properties was assessed using ABAQUS, a commercial finite element analysis program. As a result of measuring the stress-strain curve with five repetitions of loading-unloading within each strain range, it was observed in all test results that the stress gradually eased from the initial level as the number of load iterations and strain intervals increased. The nominal tensile stress was shown in the order of uniaxial, planar, and biaxial tensile test. The nonlinear material models were similar to the tensile test results, and the Ogden 3rd model showed the best performance.

Nonlinear analysis of lightweight aggregate concrete columns

The paper presents a numerical analysis of deformability and load-bearing capacity of lightweight aggregate concrete (LWAC) elements subjected to bending with axial force. The nonlinear material model of LWAC presented in Eurocode 2 (EC2) was assumed. Several different densities and compressive strengths of concrete were taken into account. The investigations included the comparison of the sectional capacity and the behaviour of slender elements made with normal and lightweight aggregate concrete. It was observed that density-dependent mechanical properties of concrete affect the obtained values of the maximum axial force and the bending moment despite the same mean compressive strength. In every case, the capacity of the RLWAC section was lower than the one of normal weight, which was caused by a linear characteristic of the LWAC. Other important factors were the modulus of elasticity and the ultimate strain of concrete. LWAC with the higher density and the lower ultimate strain gave greater stiffness to slender columns but reduced the cross-sectional capacity. It was concluded that the elastic modulus and the peak strain of LWAC which are applied in columns calculations should be verified experimentally.

Material response and failure of highly deformable carbon fiber composite shells

Very thin carbon fiber composite shells can withstand large bending curvatures without failure. The resulting high tensile and compressive strains require accurate modeling of the fiber-dominated non-linear effects to predict the mechanical response. To date, no universal modeling technique can precisely capture the behavior of such structures. In this work, successful representation of composite’s response was achieved by utilizing single fiber tension and compression experimental data, implemented to extend a basal-plane-realignment based non-linear carbon fiber material model. Numerical techniques were adopted to model the bending behavior of unidirectional carbon fiber composites that was recorded in a comprehensive experimental campaign. Observations show that high material non-linearity leads to a non-negligible neutral-axis shift and drastic reduction of bending modulus due to compressive softening. Tensile fiber failure is the driving mechanism in thin shells flexure allowing for elastic compressive strains of up to 3% without micro-buckling. As a result, a remarkable flexibility in thin shells is realized. With increasing thickness, the elastic flexibility is reduced as the failure-driving mode switches to compressive micro-buckling.

Adaptive multi-material topology optimization with hyperelastic materials under large deformations: A virtual element approach

We introduce a general multi-material topology optimization framework for large deformation problems that effectively handles an arbitrary number of candidate hyperelastic materials and addresses three major associated challenges: material interpolation, excessive distortion of low-density elements, and computational efficiency. To account for many nonlinear elastic materials, we propose a material interpolation scheme that, instead of interpolating multiple material parameters (such as Young’s modulus), interpolates multiple nonlinear stored-energy functions. To circumvent convergence difficulties caused by excessive distortions of low-density elements under large deformations, an energy interpolation scheme is revisited to account for multiple candidate hyperelastic materials. Computational efficiency is addressed from both structural analysis and optimization perspectives. To solve the nonlinear state equations efficiently, we employ the lower-order Virtual Element Method in conjunction with tailored adaptive mesh refinement and coarsening strategies. To efficiently update the design variables of the multi-material system, we exploit the separable nature and improve the ZPR (Zhang–Paulino–Ramos) update scheme to account for positive sensitivities and update the design variables associated with each volume constraint in parallel. Four design examples with three types of nonlinear material models demonstrate the efficiency and effectiveness of the proposed framework.

Modeling of the elastic properties of compressed expanded graphite - A material used in spiral wound gaskets

The paper presents the method of modeling the elastic deformations of expanded graphite, a material used as flexible filling in spiral wound gaskets. Five methods (from A to E) were proposed, by means of which the mean values of the effective elasticmodulus were determined on the basis of the experimentally determined stress-strain characteristics of expanded graphite. The values determined in this way constituted the data set into the isotropic material model, reflecting the elastic properties of the expanded graphite tape in the numerical spiral wound gasket model. A different way of modeling the graphite's elastic properties using the numerical model was method F, in which a nonlinear hyperelastic material model proposed by Blatz-Ko was adapted. The basic purpose of the numerical calculations was to determine both the compression curve of the gasket and the stress distribution in the gasket's windings. The obtained numerical results of the gasket's compression were compared with the experimental test, which allowed the assumptions of the numerical models to be validated. The best way to reflect the elastic behavior of expanded graphite in the gasket's numerical model turned out to be the nonlinear material model presented in method F.

A membrane theory for circular graphene sheets, based on a hyperelastic material model for large deformations

Large deflections relevant for suspended circular graphene sheets with simply supported boundaries are computed by a theory for 2D membranes subjected to several types of vertical axisymmetric forces, based on the principle of virtual power (PVP). Corresponding stress–strain relations are provided in the form of a nonlinear hyperelastic material model for graphene. When approximating the deflections through Fourier series, the PVP yields a nonlinear algebraic system of equations, which is solved by the iterative Newton–Raphson procedure. The new computational efficient method is validated through comparison of the numerical results it provides, with predictions obtained from experimental nanoindentaion measurements.

Architectural woven polyester fabrics: examination of possible classification of stiffness values in correlation with strength values

ABSTRACT Down to the present day, the determination of stiffness parameters for architectural fabrics, mainly used as coated woven fabrics, is a field of intense discussion. Designers and material producers are affected by an existing uncertainty. The present contribution investigates the possibility to provide tables of tensile stiffness parameters for specific materials in which tensile stiffness values are given dependent on the material’s tensile strength. The focus is on PVC-coated polyester fabrics as the most commonly used material for textile architecture. Materials of four different producers have been tested experimentally. Furthermore, from each material producer products of different strength classes have been considered in the test series. To achieve a general statement on the possibility of material classification according to their tensile stiffness, material parameters of two different material formulations have been investigated: (1) for a simplified but widely applied linear-elastic material model based on a standardized test and evaluation method and (2) for a recently developed more advanced orthotropic hyperelastic nonlinear material model. The tensile stiffness parameters are statistically evaluated and compared. In order to achieve a required basis, standardized and project-specific biaxial test procedures are presented and analysed in combination with established evaluation procedures. A tabulation of tensile stiffness parameters would be of great help for design engineers and material producers. The results of the present work will lead to a possible classified tabulation of the investigated materials in a meaningful manner.

Numerical stress analysis for single-lap adhesive joint under thermo-mechanical load using non-linear material

A comprehensive stress analysis by means of Finite Element Method (FEM) for single-lap joint subjected to thermal and mechanical loads is presented in this paper. Simulation is used to predict the effect of residual thermal stresses (caused by difference of temperature of use and elevated temperature during the assembly of the joint) on stress distribution within adhesive layer. The residual thermal stresses are assigned to joint members as initial condition before the mechanical load is applied. The FEM model employs linear and nonlinear material model and accounts for geometrical nonlinearity. It is confirmed that the difference between the manufacturing and the ambient temperature results in high residual thermal stresses, especially in axial and lateral directions of the joint. The calculation of total stress as superposition of thermal and mechanical stresses works only for linear materials. Moreover, simultaneous application of temperature and mechanical load (applied strain in case of displacement controlled test) in FEM produces inaccurate results, since in real situation the strain is applied to already thermally loaded structure. It is also found that the residual thermal stresses may reduce the peel and shear stress concentration in the adhesive at the ends of overlap and the shear stress within the overlap.

Stochastic finite element method for non-linear material models

Abstract We present a formulation for the extension of the stochastic finite element method with non-linear material models. Stress and stiffness fields, as well as displacements at each degree of freedom, are modeled as random processes and are expanded along the Polynomial Chaos (PC). PC terms of displacements are solved incrementally under load control by performing stochastic Galerkin projections on the equilibrium equation. PC terms of stress and stiffness are updated between each load increment from the resulting strains inside each elements, which follow a stochastic constitutive algorithm that performs stochastic Galerkin projections on the local level. The proposed approach is similar to the traditional deterministic non-linear finite element method and is consistent with the linear stochastic finite element method. The PC terms of stiffness are directly updated between increments of loading, and the stochastic tangent stiffness matrix is reconstructed at each increment. We illustrate the method to solve for the distribution of displacements caused by gravity loading in an earth dam with uncertain shear modulus and shear strength. The method gives similar results and, for the same level of accuracy, is computationally faster than the classical Monte-Carlo approach by several orders of magnitude.

Design of the hybrid FRP/concrete structures for bridge constructions

The current paper deals with the analysis of the hybrid FRP/concrete structures for bridge constructions. The glass fiber composite structure connected with the reinforced concrete was analyzed numerically. The detailed analysis of the material properties was conducted and then used in the design process of the final construction. The different loading conditions were investigated taking into account nonlinear concrete material model. The preliminary parametric optimization was applied including the different distance between bridge supports and different support shapes. Besides, the influence of two different effects of the concrete shrinkage on the strength properties of the hybrid structure was verified.

Effect of geometric dimensions and material models of the periodontal ligament in orthodontic tooth movement.

The aim of the present work was set to explore the role of root diameter, root length, and thickness of periodontal ligament (PDL) and its material properties (linear and non-linear elastic material models) on the stress and strain distribution, tooth displacement and centre of resistance (CR) location. Both the bone and the tooth were considered as rigid bodies, and the PDL was modelled as a paraboloid with different geometric dimensions and material properties. To achieve this goal, a horizontal force of 1 N was applied in the CR location and the stress and strain distribution and tooth displacement were quantified. Locations of CR were estimated through iterative finite element procedure. It was predicted that the position of CR is in the range of 34%-39% of the root length, slightly higher than one-third of the root length reported in the literature. The geometrical dimensions of the PDL had no significant effect on the position of CR, especially in the non-linear material model of the PDL, while the initial displacement of the tooth was found to be highly dependent on the geometrical and mechanical properties of the PDL. The simplified PDL modelling approach with non-linear material behaviour can be suggested for the estimation of initial tooth movement for individual clinical applications without the use of advanced 3D scans.

How to implement user-defined fiber-reinforced hyperelastic materials in finite element software

Finite element modeling is often used in biomechanical engineering to evaluate medical devices, treatments and diagnostic tools. Using an adequate material model that describes the mechanical behavior of biological tissues is essential for a reliable outcome of the simulation. Pre-programmed material models for biological tissues are available in many finite element software packages. However, since these pre-programmed models are presented to the user as a black box, without the possibility to modify the material description, many researchers turn to implementing their own material formulations. This is a complex undertaking, requiring extensive knowledge while documentation is limited.This paper provides a detailed description, at the level of the biomedical engineer, of the implementation of a nonlinear hyperelastic material model using user subroutines in Abaqus®, in casuUANISOHYPER_INV and UMAT. The Gasser-Ogden-Holzapfel material model is used as an example, resulting in four implementation variations: the built-in implementation, a UANISOHYPER_INV formulation, a UMAT with analytical tangent stiffness formulation and a UMAT with numerical tangent stiffness formulation. In addition, three different element formulations are used: a continuum compressible, a continuum incompressible and a plane stress incompressible. All cases are thoroughly verified by applying a series of deformations on a single cube element and by simulating an extension-inflation experiment with non-homogeneous deformations and multiple elements. In these test cases, stresses, displacements, reaction forces, the required number of iterations and the total CPU time were compared.The results show that the four implementation variations are very similar, with total relative errors between 10−3 and 10−15, number of iterations that varied by maximum one iteration, and a comparable CPU time. In addition to this detailed overview, the user subroutines are added as supplementary material to this tutorial, which can be used as the ideal starting point for biomechanical engineers to implement their own material models at different levels of complexity.