MAP123-EPF: A mechanistic-based data-driven approach for numerical elastoplastic modeling at finite strain

Highlights

• A data-driven mechanism-based approach is proposed for elastoplastic materials undergoing finite strains.

• The basic ingredients of classical plasticity such as yielding surface and objective stress rate are not employed.

• BVP problems are solved to illustrate the effectiveness and accuracy of the method.

Abstract

Direct numerical simulation based on experimental stress–strain data without explicit constitutive models is an active research topic. In this paper, a mechanistic-based, data-driven computational framework is proposed for elastoplastic materials undergoing finite strain. Harnessing the physical insights from the existing model-based plasticity theory, multiplicative decomposition of deformation gradient and the coaxial relationship between the logarithmic trial elastic strain and the true stress is employed to perform stress-update, driven by two sets of the specifically measured one dimensional (1D) stress–strain data. The proposed approach, called MAP123-EPF, is used to solve several Boundary-Value Problems (BVPs) involving elastoplastic materials undergoing finite strains. Numerical results indicate that the proposed approach can predict the response of isotropic elastoplastic materials (characterized by the classical J2 plasticity model and the associative Drucker–Prager model) with good accuracy using numerically/experimentally generated data. The proposed approach circumvents the need for the several basic ingredients of a traditional finite strain computational plasticity model, such as an explicit yielding function, a hardening law and an appropriate objective stress rate. Demonstrative examples are shown and strengths and limitations of the proposed approach are discussed.

Introduction

Most metals and polymers used for engineering applications are broadly classified as elastoplastic materials and are capable of undergoing large strains. Constitutive models for elastoplastic materials undergoing finite strain have received tremendous research attention, including such seminal works as Rice [1], Moran et al. [2], and Besseling and Van Der Giessen [3]. The numerical implementation of these constitutive models can be found in [4], [5], [6], and are summarized in classical books such as Simo and Hughes [7], Belytschko et al. [8] and the references cited therein.

The data-driven material modeling approach has allowed measurement data to be used for directly solving the Boundary Value Problems (BVPs) involving complex material behavior. The data-driven approach does not require the construction of the analytical functions necessary for the conventional constitutive relationships. This approach is beneficial for finite strain problems as the superposition principle is not applicable. The analysis of newly designed material can also benefit from the data-driven approach to help overcome the knowledge limitations about their mechanical behavior and internal deformation mechanisms.

The research on data-driven modeling approaches for elastoplastic material behaviors has blossomed in recent years. For example, through the use of clustering technique in machine learning, a two-scale, data-driven approach called Self-consistent Clustering Analysis (SCA) was developed to predict the elastoplastic behavior of materials with complex microstructures. SCA greatly reduces the computational costs and avoids the issue of the curse of dimensionality [9], [10], [11], [12], [13]. The SCA development inspired Cheng et al. [14] and Tang et al. [15] to propose the so called FEM-Cluster based Analysis (FCA) and Virtual Clustering Analysis (VCA) approaches, respectively. Harnessing the reinforcement learning technique, Wang et al. [16] proposed a multi-agent meta-modeling approach capable of generating data, knowledge, and models to make predictions on constitutive responses of elastoplastic materials. The prediction of history-dependent laws including yield surface and hardening for general stress states using recurrent neural networks is demonstrated [17]. Unlike most current works on data-driven modeling that stay in a purely computational domain, Bessa et al. [18] showed a data-driven discovery of a new material including experimental validation further. These works relied on a representative volume element (RVE) where the constituents of the material are described by a conventional elastoplastic constitutive law (e.g., J2 plasticity). These models required a large amount of data, which can be generated under different loading paths through off-line computations. On the other hand, the pure model-free approach proposed [19] totally avoided the conventional constitutive laws. Their method was capable of dealing with nonlinear elastic material and has recently been extended to elastoplastic materials [20]. The current form of the pure, model-free data-driven approach may greatly increase the computational cost, especially for three dimensional problems. In addition, it cannot be easily implemented under the current strain-driven finite element framework. Furthermore, all these works are confined to the small deformation regime.

In this paper, a data-driven modeling approach called MAP123-EPF is developed for elastoplastic material undergoing finite strain. Previous data-driven modeling approaches have been developed for three dimensional elastic and small-strain elastoplastic materials [21], [22], [23], [24]. Similar to those works, MAP123-EPF is a mechanics-based data-driven paradigm which is not completely model-free. The prominent feature of the proposed MAP123-EPF is that the basic concepts in classical plasticity theory, such as material yielding and hardening, are preserved, but the construction of explicit yielding surface function and hardening law are totally avoided. This is achieved by employing two sets of 1D experimental data (i.e., spherical strain vs. spherical stress and effective strain vs. effective stress), harnessing the multiplicative decomposition of the deformation gradient and the co-rotational relationship between the Cauchy stress and the trial left Cauchy–Green tensor. The proposed approach is compatible with the strain-driven numerical simulation schemes implemented in many current commercial softwares. It also circumvents the classical return mapping process for stress update and the subtle issue of choosing appropriate objective stress rates. The proposed MAP123-EPF approach has also been employed to solve BVPs under different loading cases. It is found that the results compare well with the results from direct numerical simulations based on the reference conventional constitutive models and physical experiments.

The paper is organized as follows. In Section 2, the framework of the proposed mechanistic-based data-driven computational plasticity approach at finite strain is established. The data generation procedure is described and the theoretical aspects of the approach are also discussed. The numerical implementation details are then presented in Section 3. Section 4 shows the results of several problems solved using the proposed approach and discusses its accuracy. Concluding remarks are presented in Section 5, along with a discussion of the pros and cons of the proposed MAP123-EPF approach.