@article{63676,
  abstract     = {{<jats:sec>
                    <jats:title>Purpose</jats:title>
                    <jats:p>The purpose of this paper is to develop new methods of error representation to improve the accuracy and numerical efficiency of a posteriori and goal-oriented adaptive framework of elastoplasticity with Prandtl–Reuss type material laws.</jats:p>
                  </jats:sec>
                  <jats:sec>
                    <jats:title>Design/methodology/approach</jats:title>
                    <jats:p>To obtain new methods of error representation for a posteriori and goal-oriented error estimators, weak forms of primal and dual problems are investigated starting with the initial boundary value problem (IBVP). Then, we approximate both problems using temporal discretization. Additionally, we introduce a secant form considering the nonlinearity of elasto-plastic constitutive equations, which is approximated by a tangent form. Finally, we obtain numerical primal and dual solutions and their corresponding error approximations of discretized primal and dual problems, allowing to build several goal-oriented a posteriori error estimators on temporal and spatial adaptive refinement by inserting primal solutions, dual solutions and their error approximations as arguments in residuals of both weak forms as well as in the secant form of the bilinear residual.</jats:p>
                  </jats:sec>
                  <jats:sec>
                    <jats:title>Findings</jats:title>
                    <jats:p>An elasto-plastic material is investigated in a framework of goal-oriented error estimator by using separately several methods of error representation to deal with either temporal or spatial adaptive refinement, as well as with both refinements leading to an effective reduction of computational effort. Specifically, new error representations based on goal-oriented error estimators are presented and obtained from primal and dual residuals, which use only primal solutions or only dual solutions or a combination of primal and dual solutions as arguments. Error representations obtained from primal residuals and evaluated using only primal arguments do not require the formulation of a dual problem.</jats:p>
                  </jats:sec>
                  <jats:sec>
                    <jats:title>Research limitations/implications</jats:title>
                    <jats:p>The effectiveness of the different proposed methods is illustrated by an example of a perforated sheet for adaptive spatial refinement where new mesh adaptation methods of error representation are compared against existing mesh adaptation methods such as uniform mesh refinement, mesh refinement based on gradient indicators and adjoint-based methods in literature. The framework generates a balanced mesh consisting of fine, medium and coarse elements for accurate results, avoiding a numerically costly simulation with only fine elements.</jats:p>
                  </jats:sec>
                  <jats:sec>
                    <jats:title>Originality/value</jats:title>
                    <jats:p>All new proposed methods of error representation successfully estimate actual errors during mesh adaptivity. Furthermore, the proposed methods of error representation allow us to obtain significant reduction and equidistribution of spatial error at the end of the mesh adaptivity process. Their application to a framework of goal-oriented error estimation due to time and mesh adaptivity remains an open issue.</jats:p>
                  </jats:sec>}},
  author       = {{Tchomgue Simeu, Arnold and Caylak, Ismail and Ostwald, Richard}},
  issn         = {{0264-4401}},
  journal      = {{Engineering Computations}},
  pages        = {{1--40}},
  publisher    = {{Emerald}},
  title        = {{{Error representations for goal-oriented                    <i>a posteriori</i>                    error estimation in elasto-plasticity with applications to mesh adaptivity}}},
  doi          = {{10.1108/ec-12-2023-0975}},
  year         = {{2026}},
}

@article{45427,
  abstract     = {{<jats:p>In this work a gradient‐based optimization method is applied in order to determine material parameters for a viscoplastic model with dynamic yield surface coupled to damage as presented in 1997. To this end a sensitivity analysis consistent with the integration scheme presented previously is performed in a systematic manner, both for strain and stress controlled experiments. The algorithm is tested in two numerical examples: first, simulated data are used, in order to re‐obtain parameters for the case of damage under monotonic loading. In the second example material parameters are obtained based on experimental data for lcf‐testing of an austenetic stainless steel, thus showing a very good agreement with respect to hardening, rate and damage effects.</jats:p>}},
  author       = {{Mahnken, Rolf and Johansson, Magnus and Runesson, Kenneth}},
  issn         = {{0264-4401}},
  journal      = {{Engineering Computations}},
  keywords     = {{Computational Theory and Mathematics, Computer Science Applications, General Engineering, Software}},
  number       = {{7}},
  pages        = {{925--955}},
  publisher    = {{Emerald}},
  title        = {{{Parameter estimation for a viscoplastic damage model using a gradient‐based optimization algorithm}}},
  doi          = {{10.1108/02644409810236920}},
  volume       = {{15}},
  year         = {{2002}},
}