More Like this

1. Convergence Characteristics of Geometrically Accurate Spatial Finite Elements

   https://doi.org/10.1115/1.4048731  

   Tinsley, Brian; Shabana, Ahmed A. (January 2021, Journal of Computational and Nonlinear Dynamics)

   null (Ed.)

   Abstract The convergence characteristics of three geometrically accurate spatial finite elements (FEs) are examined in this study using an eigenvalue analysis. The spatial beam, plate, and solid elements considered in this investigation are suited for both structural and multibody system (MBS) applications. These spatial elements are based on geometry derived from the kinematic description of the absolute nodal coordinate formulation (ANCF). In order to allow for an accurate reference-configuration geometry description, the element shape functions are formulated using constant geometry coefficients defined using the position-vector gradients in the reference configuration. The change in the position-vector gradients is used to define a velocity transformation matrix that leads to constant element inertia and stiffness matrices in the case of infinitesimal rotations. In contrast to conventional structural finite elements, the elements considered in this study can be used to describe the initial geometry with the same degree of accuracy as B-spline and nonuniform rational B-spline (NURBS) representations, widely used in the computer-aided design (CAD). An eigenvalue analysis is performed to evaluate the element convergence characteristics in the case of different geometries, including straight, tapered, and curved configurations. The frequencies obtained are compared with those obtained using a commercial FE software and analytical solutions. The stiffness matrix is obtained using both the general continuum mechanics (GCM) approach and the newly proposed strain split method (SSM) in order to investigate its effectiveness as a locking alleviation technique. 

   more » « less
2. Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

   https://doi.org/10.1016/j.compgeo.2025.107743  

   Alsardi, Abdelrahman; Yerro, Alba; Long, Christopher Curtis (February 2026, Computers and Geotechnics)

   Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications. 

   more » « less
3. Thermo‐hydro‐mechanical modeling of unsaturated soils using isogeometric analysis: Model development and application to strain localization simulation

   https://doi.org/10.1002/nag.3015  

   Shahrokhabadi, Shahriar; Cao, Toan Duc; Vahedifard, Farshid (November 2019, International Journal for Numerical and Analytical Methods in Geomechanics)

   Summary This study presents a thermo‐hydro‐mechanical (THM) model of unsaturated soils using isogeometric analysis (IGA). The framework employs Bézier extraction to connect IGA to the conventional finite element analysis (FEA), featuring the current study as one of the first attempts to develop an IGA‐FEA framework for solving THM problems in unsaturated soils. IGA offers higher levels of interelement continuity making it an attractive method for solving highly nonlinear problems. The governing equations of linear momentum, mass, and energy balance are coupled based on the averaging procedure within the hybrid mixture theory. The Drucker‐Prager yield surface is used to limit the modified effective stress where the model follows small strain, quasi‐static loading conditions. Temperature dependency of the surface tension is implemented in the soil‐water retention curve. Nonuniform rational B‐splines (NURBS) basis functions are used in the standard Galerkin method and weak formulations of the balance equations. Displacement, capillary pressure, gas pressure, and temperature are four independent quantities that are approximated by NURBS in spatial discretization. The framework is used to simulate strain localization in an undrained dense sand subjected to plane strain biaxial compression under different temperatures and displacement velocities. Results show that an increase in the displacement rate leads to reduction in the equivalent plastic strain while an increase in the temperature leads to an increase in the equivalent plastic strain. The findings suggest that the proposed IGA‐based framework offers a viable alternative for solving THM problems in unsaturated soils. 

   more » « less
4. Conversion of explicit microplane model with boundaries to a constitutive subroutine for implicit finite element programs

   https://doi.org/10.1002/nme.6590  

   Nguyen, Hoang T.; Caner, Ferhun C.; Bažant, Zdeněk P. (December 2020, International Journal for Numerical Methods in Engineering)

   Abstract Whereas various simplistic microplane models of limited applicability, defined by stress–strain curves on the microplane, can function as either explicit or implicit, the explicit‐to‐implicit conversion of realistic versatile microplane models for plain or fiber‐reinforced concrete, shale and composites has remained a challenge for quarter century. The reason is that these realistic models use microplane stress–strain boundaries defined by inequalities. Here, we show how the conversion can be easily achieved on the microplane level and then transferred to a tangent stiffness tensor or an inelastic stiffness tensor to be used in Newton–Raphson iterations within a loading step. To ensure convergence, a minor adjustment in the M7 algorithm is introduced to achieve continuity. Power‐law convergence, almost quadratic in most cases, is also demonstrated. Seven examples of crack‐band finite element simulations of challenging laboratory tests document nearly identical implicit and explicit results, as well as good match of test data. Three of them, including the vertex effect in compression‐torsion tests, pure Mode II shear fracture, and the “gap test” of the crack‐parallel compression effect on Mode I load‐deflection curve, have not been reproduced by other models before. The coding of implicit M7 subroutine, usable in, for example, UMAT of ABAQUS, is posted for a free download. 

   more » « less
5. Locking treatment of penalty-based gradient-enhanced damage formulation for failure of compressible and nearly incompressible hyperelastic materials

   https://doi.org/10.1007/s00466-023-02314-x  

   Valverde-González, A.; Reinoso, J.; Dortdivanlioglu, B.; Paggi, M. (March 2023, Computational Mechanics)

   Abstract Soft materials are of major interest for biomechanics applications due to their high deformability and susceptibility to experience damage events under different loading scenarios. The present study is concerned with modelling damage evolution processes in these nonlinear materials whose structural responses are prone to locking when low-order kinematic interpolation is employed in the context of nonlinear Finite Element schemes. For this reason, a pair of gradient-enhanced continuum damage schemes are proposed with the aim of tackling mechanical failure problems in applications that exhibit shear and volumetric locking. In particular, we present the consistent formulation and the assessment of the corresponding performance of (i) a mixed displacement-enhanced assumed strain employing a total Lagrangian formulation, and (ii) a three-field mixed displacement-pressure-Jacobian formulation. The novel and formulations are consistently derived and numerically implemented, providing a satisfactory agreement with respect to built-in elements handling the treatment of shear and volumetric locking, respectively, in conjunction to the modelling damage phenomena via the use of a penalty-based gradient-enhanced formulation. This performance is examined via several numerical applications. Furthermore, the final example justifies the need for a formulation combining both mixed FE approaches to simulate problems encompassing both locking issues (shear and volumetric locking), which can be performed using a combination of the and herein proposed. 

   more » « less