Osman Gültekin, Ahmad Moeineddin, Barış Cansız, Krunoslav Sveric, Axel Linke, Michael Kaliske
{"title":"A Physics-Informed Neural Network Model for the Anisotropic Hyperelasticity of the Human Passive Myocardium","authors":"Osman Gültekin, Ahmad Moeineddin, Barış Cansız, Krunoslav Sveric, Axel Linke, Michael Kaliske","doi":"10.1002/nme.70067","DOIUrl":"https://doi.org/10.1002/nme.70067","url":null,"abstract":"<p>In this article, we present a model of Physics-informed Neural Networks (PINNs) for predicting the anisotropic hyperelastic behavior of the human passive myocardium. PINNs adhere to the governing equations and the boundary conditions by integrating physical laws into the neural network architecture. They are used for forward and inverse simulations under non-standard, complex geometries and loading conditions. The first example features a plane strain shear test, a common protocol in soft tissue mechanics, where we provide a comprehensive comparison of three different total loss functions—namely, the minimization of the PDEs, the total potential energy, or a combination of both—for forward problems as a surrogate to finite element analysis (FEA). The second example deals with a patient-specific geometry of basal myocardium—obtained from cardiac magnetic resonance imaging—for forward and inverse analyses. Key findings reveal that apart from the accurately predicted primary fields, that is, displacements, the inverse design also provides a true estimate of the anisotropic material parameters from ground truth data obtained from experiments or FEA. Limitations remain in the performance of PINNs for forward simulations of the 2D basal myocardium, particularly with respect to computational demands and sensitivity to network architecture and hyperparameters. Despite challenges in accurately predicting secondary fields, for example, stresses, PINNs demonstrate their potential for inverse simulations, particularly in identifying anisotropic constitutive parameters that can be used in the case of noisy or incomplete datasets in future biomechanical applications.</p>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 14","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nme.70067","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144598670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spacetime Wavelet Method for the Solution of Nonlinear Partial Differential Equations","authors":"Cody D. Cochran, Karel Matouš","doi":"10.1002/nme.70076","DOIUrl":"https://doi.org/10.1002/nme.70076","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in both the spatial and temporal dimensions simultaneously. We also propose a novel wavelet-based recursive algorithm to reduce the system sensitivity stemming from steep initial and/or boundary conditions. The resulting nonlinear equations are solved using the Newton–Raphson method. We parallelize the construction of the tangent operator along with the solution of the system of algebraic equations. We perform rigorous verification studies using the nonlinear Burgers' equation. The application of the method is demonstrated by solving the Sod shock tube problem using the Navier–Stokes equations. The numerical results of the method reveal high-order convergence rates for the function as well as its spatial and temporal derivatives. We solve multiscale problems with steep gradients in both the spatial and temporal directions with a priori error estimates.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 13","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144582272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Enriched \u0000 \u0000 \u0000 \u0000 C\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 Finite Elements for Crack Problems in Simplified Strain Gradient Elasticity","authors":"Yury Solyaev, Vasiliy Dobryanskiy","doi":"10.1002/nme.70081","DOIUrl":"https://doi.org/10.1002/nme.70081","url":null,"abstract":"<div>\u0000 \u0000 <p>We present a new type of triangular <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> finite element developed for plane strain crack problems within the framework of simplified strain gradient elasticity (SGE). The finite element space incorporates a conventional fifth-degree polynomial interpolation originally developed for plate bending problems and later adopted for SGE. Enrichment is performed by adding near-field analytic SGE solutions for crack problems, preserving <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}^1 $$</annotation>\u0000 </semantics></math> continuity of interpolation at the mesh nodes. This allows us an accurate representation of strain and stress fields near the crack tip and enables direct calculation of the amplitude factors of the SGE asymptotic solution, along with the corresponding value of the J-integral (energy release rate). The improved convergence of the proposed formulation is demonstrated for mode I and mode II problems. Size effects on the amplitude factors and the J-integral are also evaluated. It is found that the amplitude factors of the SGE asymptotic solution exhibit a linear dependence on crack size for relatively large cracks.</p>\u0000 </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 13","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144573620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}