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1 // Copyright (c) 2017-2026, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
4 // SPDX-License-Identifier: BSD-2-Clause
21 CeedScalar E; // Young's Modulus member
25 // -----------------------------------------------------------------------------
27 // -----------------------------------------------------------------------------
39 const CeedScalar E = context->E; in ElasResidual_Linear() local
40 const CeedScalar nu = context->nu; in ElasResidual_Linear()
50 // -- Qdata in ElasResidual_Linear()
59 // dXdx = (dx/dX)^(-1) in ElasResidual_Linear()
69 // Compute Strain : e (epsilon) in ElasResidual_Linear()
70 // e = 1/2 (grad u + (grad u)^T) in ElasResidual_Linear()
72 const CeedScalar e[3][3] = { in ElasResidual_Linear() local
90 // [1-nu nu nu ] in ElasResidual_Linear()
91 // [ nu 1-nu nu ] in ElasResidual_Linear()
92 // [ nu nu 1-nu ] in ElasResidual_Linear()
93 // S = E/((1+nu)*(1-2*nu)) [ (1-2*nu)/2 ] in ElasResidual_Linear()
94 // [ (1-2*nu)/2 ] in ElasResidual_Linear()
95 // [ (1-2*nu)/2 ] in ElasResidual_Linear()
98 const CeedScalar ss = E / ((1 + nu) * (1 - 2 * nu)); in ElasResidual_Linear()
99 const CeedScalar sigma00 = ss * ((1 - nu) * e[0][0] + nu * e[1][1] + nu * e[2][2]), in ElasResidual_Linear()
100 sigma11 = ss * (nu * e[0][0] + (1 - nu) * e[1][1] + nu * e[2][2]), in ElasResidual_Linear()
101 …sigma22 = ss * (nu * e[0][0] + nu * e[1][1] + (1 - nu) * e[2][2]), sigma12 = ss * (1 - 2 * nu) * e… in ElasResidual_Linear()
102 … sigma02 = ss * (1 - 2 * nu) * e[0][2] * 0.5, sigma01 = ss * (1 - 2 * nu) * e[0][1] * 0.5; in ElasResidual_Linear()
121 // -----------------------------------------------------------------------------
123 // -----------------------------------------------------------------------------
136 const CeedScalar E = context->E; in ElasJacobian_Linear() local
137 const CeedScalar nu = context->nu; in ElasJacobian_Linear()
147 // -- Qdata in ElasJacobian_Linear()
156 // dXdx = (dx/dX)^(-1) in ElasJacobian_Linear()
166 // Compute Strain : e (epsilon) in ElasJacobian_Linear()
167 // e = 1/2 (grad u + (grad u)^T) in ElasJacobian_Linear()
185 // [1-nu nu nu ] in ElasJacobian_Linear()
186 // [ nu 1-nu nu ] in ElasJacobian_Linear()
187 // [ nu nu 1-nu ] in ElasJacobian_Linear()
188 // S = E/((1+nu)*(1-2*nu)) [ (1-2*nu)/2 ] in ElasJacobian_Linear()
189 // [ (1-2*nu)/2 ] in ElasJacobian_Linear()
190 // [ (1-2*nu)/2 ] in ElasJacobian_Linear()
193 const CeedScalar ss = E / ((1 + nu) * (1 - 2 * nu)); in ElasJacobian_Linear()
194 const CeedScalar dsigma00 = ss * ((1 - nu) * de[0][0] + nu * de[1][1] + nu * de[2][2]), in ElasJacobian_Linear()
195 dsigma11 = ss * (nu * de[0][0] + (1 - nu) * de[1][1] + nu * de[2][2]), in ElasJacobian_Linear()
196 …dsigma22 = ss * (nu * de[0][0] + nu * de[1][1] + (1 - nu) * de[2][2]), dsigma12 = ss * (1 - 2 * nu… in ElasJacobian_Linear()
197 … dsigma02 = ss * (1 - 2 * nu) * de[0][2] / 2, dsigma01 = ss * (1 - 2 * nu) * de[0][1] / 2; in ElasJacobian_Linear()
216 // -----------------------------------------------------------------------------
218 // -----------------------------------------------------------------------------
228 const CeedScalar E = context->E; in ElasEnergy_Linear() local
229 const CeedScalar nu = context->nu; in ElasEnergy_Linear()
232 const CeedScalar TwoMu = E / (1 + nu); in ElasEnergy_Linear()
234 const CeedScalar Kbulk = E / (3 * (1 - 2 * nu)); // Bulk Modulus in ElasEnergy_Linear()
235 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasEnergy_Linear()
245 // -- Qdata in ElasEnergy_Linear()
254 // dXdx = (dx/dX)^(-1) in ElasEnergy_Linear()
264 // Compute Strain : e (epsilon) in ElasEnergy_Linear()
265 // e = 1/2 (grad u + (grad u)^T) in ElasEnergy_Linear()
267 const CeedScalar e[3][3] = { in ElasEnergy_Linear() local
274 const CeedScalar strain_vol = e[0][0] + e[1][1] + e[2][2]; in ElasEnergy_Linear()
276 … strain_vol * strain_vol / 2. + strain_vol * mu + (e[0][1] * e[0][1] + e[0][2] * e[0][2] + e[1][2]… in ElasEnergy_Linear()
283 // -----------------------------------------------------------------------------
285 // -----------------------------------------------------------------------------
296 const CeedScalar E = context->E; in ElasDiagnostic_Linear() local
297 const CeedScalar nu = context->nu; in ElasDiagnostic_Linear()
300 const CeedScalar TwoMu = E / (1 + nu); in ElasDiagnostic_Linear()
302 const CeedScalar Kbulk = E / (3 * (1 - 2 * nu)); // Bulk Modulus in ElasDiagnostic_Linear()
303 const CeedScalar lambda = (3 * Kbulk - TwoMu) / 3; in ElasDiagnostic_Linear()
313 // -- Qdata in ElasDiagnostic_Linear()
321 // dXdx = (dx/dX)^(-1) in ElasDiagnostic_Linear()
331 // Compute Strain : e (epsilon) in ElasDiagnostic_Linear()
332 // e = 1/2 (grad u + (grad u)^T) in ElasDiagnostic_Linear()
334 const CeedScalar e[3][3] = { in ElasDiagnostic_Linear() local
346 const CeedScalar strain_vol = e[0][0] + e[1][1] + e[2][2]; in ElasDiagnostic_Linear()
347 diagnostic[3][i] = -lambda * strain_vol; in ElasDiagnostic_Linear()
353 for (CeedInt m = 0; m < 3; m++) diagnostic[5][i] += e[j][m] * e[m][j]; in ElasDiagnostic_Linear()
359 … strain_vol * strain_vol / 2. + strain_vol * mu + (e[0][1] * e[0][1] + e[0][2] * e[0][2] + e[1][2]… in ElasDiagnostic_Linear()
364 // -----------------------------------------------------------------------------