KOKO\Mimi
401 lines
18 KiB
C++
401 lines
18 KiB
C++
#include "fesa/elements/hex8_element.h"
|
|
|
|
#include <gtest/gtest.h>
|
|
|
|
#include <cmath>
|
|
#include <cstdint>
|
|
#include <cstring>
|
|
#include <limits>
|
|
#include <random>
|
|
#include <vector>
|
|
|
|
#include "fesa/materials/isotropic_linear_elastic_material.h"
|
|
#include "../../../src/fesa/math/high_low_arithmetic.h"
|
|
#include "../../../src/fesa/elements/hex8_geometry.h"
|
|
#include "../../../src/fesa/elements/hex8_pair_arithmetic.h"
|
|
#include "../math/high_low_arithmetic_original.h"
|
|
|
|
namespace {
|
|
using fesa::math_internal::HighLow;
|
|
using fesa::math_internal::Subtract;
|
|
|
|
std::uint64_t PairBits(double value) {
|
|
std::uint64_t bits = 0;
|
|
std::memcpy(&bits, &value, sizeof(bits));
|
|
return bits;
|
|
}
|
|
|
|
void ExpectOriginalProduct(HighLow left, HighLow right) {
|
|
const auto actual = fesa::hex8_internal::MultiplyPair(left, right);
|
|
const auto expected = fesa::high_low_original::Multiply(
|
|
{left.high, left.low}, {right.high, right.low});
|
|
EXPECT_EQ(PairBits(actual.high), PairBits(expected.high));
|
|
EXPECT_EQ(PairBits(actual.low), PairBits(expected.low));
|
|
const auto actual_sum = fesa::hex8_internal::AddPair(left, right);
|
|
const auto expected_sum = fesa::high_low_original::Add(
|
|
{left.high, left.low}, {right.high, right.low});
|
|
EXPECT_EQ(PairBits(actual_sum.high), PairBits(expected_sum.high));
|
|
EXPECT_EQ(PairBits(actual_sum.low), PairBits(expected_sum.low));
|
|
}
|
|
|
|
TEST(Hex8HighLow, ScalarCrossProductShortcutMatchesOriginalBits) {
|
|
ASSERT_TRUE(fesa::math_internal::ArithmeticEnvironmentSupported());
|
|
const double minimum = std::numeric_limits<double>::denorm_min();
|
|
const double maximum = std::numeric_limits<double>::max();
|
|
const double infinity = std::numeric_limits<double>::infinity();
|
|
const double nan = std::numeric_limits<double>::quiet_NaN();
|
|
std::vector<HighLow> pairs{{}, {-0.0, 0.0}, {0.0, -0.0}, {-0.0, -0.0},
|
|
{1, -0.0}, {-1, -0.0}, {1, 1}, {0, minimum}, {infinity, 0},
|
|
{0, infinity}, {nan, 0}, {0, nan}, {maximum}, {-maximum},
|
|
{minimum}, {-minimum}, {std::numeric_limits<double>::min()},
|
|
{0.5}, {std::nextafter(0.5, 1.0)},
|
|
{1, std::ldexp(1.0, -53)},
|
|
{std::nextafter(1.0, 2.0), -std::ldexp(1.0, -53)}};
|
|
for (const auto left : pairs)
|
|
for (const auto right : pairs) ExpectOriginalProduct(left, right);
|
|
for (int exponent = -1074; exponent <= 1023; ++exponent) {
|
|
const double value = std::ldexp(1.0, exponent);
|
|
for (double sign : {-1.0, 1.0})
|
|
for (const auto right : pairs) {
|
|
ExpectOriginalProduct(HighLow{sign * value}, right);
|
|
ExpectOriginalProduct(right, HighLow{sign * value});
|
|
}
|
|
}
|
|
std::mt19937_64 random(0x48e81234U);
|
|
for (int sample = 0; sample < 12000; ++sample) {
|
|
double left = 0;
|
|
double right = 0;
|
|
const auto left_bits = random();
|
|
const auto right_bits = random();
|
|
std::memcpy(&left, &left_bits, sizeof(left));
|
|
std::memcpy(&right, &right_bits, sizeof(right));
|
|
const auto pair = fesa::math_internal::TwoSum(left, right);
|
|
ExpectOriginalProduct(pair, HighLow{});
|
|
ExpectOriginalProduct(HighLow{}, pair);
|
|
ExpectOriginalProduct(pair, HighLow{right});
|
|
ExpectOriginalProduct(HighLow{right}, pair);
|
|
ExpectOriginalProduct(pair, pair);
|
|
}
|
|
}
|
|
|
|
fesa::Hex8Element UnitBrick(double offset = 0, double nu = 0) {
|
|
fesa::ElementDofLayout layout;
|
|
layout.node_indices = {0, 1, 2, 3, 4, 5, 6, 7};
|
|
layout.components_per_node = {fesa::DofComponent::kUx,
|
|
fesa::DofComponent::kUy,
|
|
fesa::DofComponent::kUz};
|
|
fesa::Hex8Element::Coordinates coordinates{{{0, 0, 0}, {1, 0, 0},
|
|
{1, 1, 0}, {0, 1, 0},
|
|
{0, 0, 1}, {1, 0, 1},
|
|
{1, 1, 1}, {0, 1, 1}}};
|
|
for (auto& x : coordinates) x[0] += offset;
|
|
fesa::IsotropicLinearElasticMaterial material("test", 12, nu, {});
|
|
return fesa::Hex8Element::Create(0, layout, coordinates, material, 2).Value();
|
|
}
|
|
|
|
TEST(Hex8HighLow, LowOnlyAffineStrainSurvivesUniformHighTranslation) {
|
|
auto brick = UnitBrick();
|
|
fesa::Vector high(24), low(24);
|
|
const double strain = std::ldexp(1.0, -60);
|
|
for (std::size_t a = 0; a < 8; ++a) high[3 * a] = 1;
|
|
for (auto a : {1, 2, 5, 6}) low[3 * a] = strain;
|
|
const auto response = brick.EvaluateLinearHighLow(high, low);
|
|
ASSERT_TRUE(response.HasValue());
|
|
for (std::size_t a = 0; a < 8; ++a) {
|
|
const bool positive = a == 1 || a == 2 || a == 5 || a == 6;
|
|
EXPECT_NEAR(response.Value().high.internal_force[3 * a],
|
|
(positive ? 3 : -3) * strain, 1e-13 * strain);
|
|
}
|
|
EXPECT_NEAR(response.Value().high.strain_energy, 6 * strain * strain,
|
|
1e-13 * strain * strain);
|
|
for (const auto& row : response.Value().high.points)
|
|
EXPECT_NEAR(row.strain[0], strain, 1e-13 * strain);
|
|
}
|
|
|
|
TEST(Hex8HighLow, NonlinearLowGradientProducesSecondOrderForce) {
|
|
auto brick = UnitBrick();
|
|
fesa::Vector high(24), low(24);
|
|
const double strain = std::ldexp(1.0, -60);
|
|
for (std::size_t a = 0; a < 8; ++a) high[3 * a] = 1;
|
|
for (auto a : {1, 2, 5, 6}) low[3 * a] = strain;
|
|
const auto linear = brick.EvaluateLinearHighLow(high, low);
|
|
const auto nonlinear = brick.EvaluateNonlinearHighLow(high, low);
|
|
ASSERT_TRUE(linear.HasValue());
|
|
ASSERT_TRUE(nonlinear.HasValue());
|
|
const auto& l = linear.Value();
|
|
const auto& n = nonlinear.Value();
|
|
const auto increment = Subtract(
|
|
HighLow{n.high.internal_force[3], n.internal_force_low[3]},
|
|
HighLow{l.high.internal_force[3], l.internal_force_low[3]});
|
|
EXPECT_NEAR(increment.high, 4.5 * strain * strain,
|
|
1e-12 * strain * strain);
|
|
}
|
|
|
|
TEST(Hex8HighLow, VolumetricAndTransverseTermsRetainLowStrain) {
|
|
auto brick = UnitBrick(0, 0.25);
|
|
fesa::Vector high(24), low(24);
|
|
const double strain = std::ldexp(1.0, -60);
|
|
for (std::size_t a = 0; a < 8; ++a) high[3*a] = 1;
|
|
for (auto a : {1, 2, 5, 6}) low[3*a] = strain;
|
|
const auto linear = brick.EvaluateLinearHighLow(high, low);
|
|
const auto nonlinear = brick.EvaluateNonlinearHighLow(high, low);
|
|
ASSERT_TRUE(linear.HasValue()); ASSERT_TRUE(nonlinear.HasValue());
|
|
// Uniform axial strain: lambda=mu=4.8, each nodal face integral is 1/4.
|
|
EXPECT_NEAR(linear.Value().high.internal_force[3], 3.6*strain, 1e-13*strain);
|
|
EXPECT_NEAR(linear.Value().high.internal_force[7], 1.2*strain, 1e-13*strain);
|
|
EXPECT_NEAR(linear.Value().high.strain_energy, 7.2*strain*strain,
|
|
1e-13*strain*strain);
|
|
const auto quadratic = Subtract(
|
|
{nonlinear.Value().high.internal_force[3], nonlinear.Value().internal_force_low[3]},
|
|
{linear.Value().high.internal_force[3], linear.Value().internal_force_low[3]});
|
|
EXPECT_NEAR(quadratic.high, 5.4*strain*strain, 1e-12*strain*strain);
|
|
}
|
|
|
|
TEST(Hex8HighLow, RejectsInvalidLowShapeAndOverlappingComponents) {
|
|
auto brick = UnitBrick();
|
|
fesa::Vector high(24), low(24);
|
|
EXPECT_FALSE(brick.EvaluateLinearHighLow(high, fesa::Vector(23)).HasValue());
|
|
high[0] = 1;
|
|
low[0] = 1;
|
|
EXPECT_FALSE(brick.EvaluateNonlinearHighLow(high, low).HasValue());
|
|
}
|
|
|
|
TEST(Hex8HighLow, LinearAndNonlinearZeroStateHaveSameFullHessian) {
|
|
auto brick = UnitBrick();
|
|
fesa::Vector zero(24);
|
|
const auto linear = brick.EvaluateLinearHighLow(zero, zero);
|
|
const auto nonlinear = brick.EvaluateNonlinearHighLow(zero, zero);
|
|
ASSERT_TRUE(linear.HasValue());
|
|
ASSERT_TRUE(nonlinear.HasValue());
|
|
for (std::size_t i = 0; i < 24; ++i)
|
|
for (std::size_t j = 0; j < 24; ++j) {
|
|
EXPECT_EQ(linear.Value().high.tangent(i, j),
|
|
nonlinear.Value().high.tangent(i, j));
|
|
EXPECT_EQ(linear.Value().tangent_low(i, j),
|
|
nonlinear.Value().tangent_low(i, j));
|
|
}
|
|
}
|
|
|
|
TEST(Hex8HighLow, CachedLinearHessianIsIndependentOfTrialAndPriorFailure) {
|
|
auto brick = UnitBrick(0, 0.25);
|
|
fesa::Vector zero(24), high(24), low(24);
|
|
high[3] = 0.1;
|
|
low[3] = std::ldexp(1.0, -60);
|
|
const auto reference = brick.EvaluateLinearHighLow(zero, zero);
|
|
ASSERT_TRUE(reference.HasValue());
|
|
EXPECT_FALSE(brick.EvaluateLinearHighLow(high, fesa::Vector(23)).HasValue());
|
|
const auto strained = brick.EvaluateLinearHighLow(high, low);
|
|
ASSERT_TRUE(strained.HasValue());
|
|
for (std::size_t i = 0; i < 24; ++i)
|
|
for (std::size_t j = 0; j < 24; ++j) {
|
|
EXPECT_EQ(reference.Value().high.tangent(i,j), strained.Value().high.tangent(i,j));
|
|
EXPECT_EQ(reference.Value().tangent_low(i,j), strained.Value().tangent_low(i,j));
|
|
}
|
|
const auto nonlinear_zero = brick.EvaluateNonlinearHighLow(zero, zero);
|
|
ASSERT_TRUE(nonlinear_zero.HasValue());
|
|
for (std::size_t i = 0; i < 24; ++i)
|
|
for (std::size_t j = 0; j < 24; ++j) {
|
|
EXPECT_EQ(reference.Value().high.tangent(i,j), nonlinear_zero.Value().high.tangent(i,j));
|
|
EXPECT_EQ(reference.Value().tangent_low(i,j), nonlinear_zero.Value().tangent_low(i,j));
|
|
}
|
|
}
|
|
|
|
TEST(Hex8HighLow, CoupledBricksTransmitLowStrainAcrossSharedFace) {
|
|
const auto left = UnitBrick(), right = UnitBrick(1);
|
|
fesa::Vector high(24), left_low(24), right_low(24);
|
|
const double strain = std::ldexp(1.0, -60);
|
|
for (std::size_t a = 0; a < 8; ++a) {
|
|
high[3 * a] = 1;
|
|
const bool positive = a == 1 || a == 2 || a == 5 || a == 6;
|
|
left_low[3 * a] = positive ? strain : 0;
|
|
right_low[3 * a] = positive ? 2 * strain : strain;
|
|
}
|
|
const auto l = left.EvaluateLinearHighLow(high, left_low);
|
|
const auto r = right.EvaluateLinearHighLow(high, right_low);
|
|
ASSERT_TRUE(l.HasValue());
|
|
ASSERT_TRUE(r.HasValue());
|
|
const std::array<std::size_t, 4> face_left{1, 2, 5, 6};
|
|
const std::array<std::size_t, 4> face_right{0, 3, 4, 7};
|
|
for (std::size_t a = 0; a < 4; ++a) {
|
|
const auto i = 3 * face_left[a], j = 3 * face_right[a];
|
|
const auto assembled = fesa::math_internal::Add(
|
|
{l.Value().high.internal_force[i], l.Value().internal_force_low[i]},
|
|
{r.Value().high.internal_force[j], r.Value().internal_force_low[j]});
|
|
EXPECT_NEAR(assembled.high, 0, 1e-13 * strain);
|
|
}
|
|
EXPECT_NEAR(l.Value().high.strain_energy + r.Value().high.strain_energy,
|
|
12 * strain * strain, 1e-13 * strain * strain);
|
|
}
|
|
|
|
TEST(Hex8HighLow, NodeZeroSignedDirectionMatchesForceAndEnergyDerivatives) {
|
|
using namespace fesa::math_internal;
|
|
auto brick = UnitBrick();
|
|
fesa::Vector high(24), low(24);
|
|
for (std::size_t a = 0; a < 8; ++a) {
|
|
high[3 * a] = 1;
|
|
low[3 * a] = (a == 1 || a == 2 || a == 5 || a == 6)
|
|
? std::ldexp(1.0, -60) : 0;
|
|
}
|
|
const auto baseline = brick.EvaluateNonlinearHighLow(high, low);
|
|
ASSERT_TRUE(baseline.HasValue());
|
|
const auto& base = baseline.Value();
|
|
for (int exponent : {-65, -70, -75}) {
|
|
const double step = std::ldexp(1.0, exponent);
|
|
auto plus_high = high, minus_high = high;
|
|
auto plus_low = low, minus_low = low;
|
|
const auto plus = Add({high[0], low[0]}, HighLow{step});
|
|
const auto minus = Subtract({high[0], low[0]}, HighLow{step});
|
|
plus_high[0] = plus.high; plus_low[0] = plus.low;
|
|
minus_high[0] = minus.high; minus_low[0] = minus.low;
|
|
const auto positive = brick.EvaluateNonlinearHighLow(plus_high, plus_low);
|
|
const auto negative = brick.EvaluateNonlinearHighLow(minus_high, minus_low);
|
|
ASSERT_TRUE(positive.HasValue());
|
|
ASSERT_TRUE(negative.HasValue());
|
|
for (std::size_t i = 0; i < 24; ++i) {
|
|
const auto derivative = Divide(Subtract(
|
|
{positive.Value().high.internal_force[i], positive.Value().internal_force_low[i]},
|
|
{negative.Value().high.internal_force[i], negative.Value().internal_force_low[i]}),
|
|
HighLow{2 * step});
|
|
const auto error = Subtract(derivative,
|
|
{base.high.tangent(i, 0), base.tangent_low(i, 0)});
|
|
EXPECT_LE(std::abs(error.high), 1e-25);
|
|
}
|
|
const auto gradient = Divide(Subtract(
|
|
{positive.Value().high.strain_energy, positive.Value().strain_energy_low},
|
|
{negative.Value().high.strain_energy, negative.Value().strain_energy_low}),
|
|
HighLow{2 * step});
|
|
const auto energy_error = Subtract(gradient,
|
|
{base.high.internal_force[0], base.internal_force_low[0]});
|
|
// Centered energy differences retain the StVK cubic term: O(step^2).
|
|
// For this unit E=12 brick its directional coefficient is bounded by 32.
|
|
EXPECT_LE(std::abs(energy_error.high), 32 * step * step + 1e-44);
|
|
}
|
|
}
|
|
|
|
TEST(Hex8HighLow, GeometryCertificateIncludesLowOnlyCurrentCellWidth) {
|
|
fesa::Hex8Element::Coordinates coordinates{{{0, 0, 0}, {1, 0, 0},
|
|
{1, 1, 0}, {0, 1, 0},
|
|
{0, 0, 1}, {1, 0, 1},
|
|
{1, 1, 1}, {0, 1, 1}}};
|
|
fesa::Vector high(24), positive_low(24), negative_low(24);
|
|
for (std::size_t a = 0; a < 8; ++a) {
|
|
high[3 * a] = -coordinates[a][0];
|
|
positive_low[3 * a] = std::ldexp(coordinates[a][0], -60);
|
|
negative_low[3 * a] = -positive_low[3 * a];
|
|
}
|
|
using fesa::hex8_internal::Certificate;
|
|
EXPECT_EQ(fesa::hex8_internal::Certify(coordinates, &high, &positive_low),
|
|
Certificate::kPositive);
|
|
EXPECT_EQ(fesa::hex8_internal::Certify(coordinates, &high, &negative_low),
|
|
Certificate::kNonpositive);
|
|
EXPECT_NE(fesa::hex8_internal::Certify(coordinates, &high),
|
|
Certificate::kPositive);
|
|
}
|
|
|
|
TEST(Hex8HighLow, SignedZeroMaterialCoefficientHasIdenticalResponse) {
|
|
auto positive = UnitBrick(0, 0.0), negative = UnitBrick(0, -0.0);
|
|
fesa::Vector high(24), low(24);
|
|
high[3] = 0.01;
|
|
for (bool nonlinear : {false, true}) {
|
|
const auto p = nonlinear ? positive.EvaluateNonlinearHighLow(high, low)
|
|
: positive.EvaluateLinearHighLow(high, low);
|
|
const auto n = nonlinear ? negative.EvaluateNonlinearHighLow(high, low)
|
|
: negative.EvaluateLinearHighLow(high, low);
|
|
ASSERT_TRUE(p.HasValue());
|
|
ASSERT_TRUE(n.HasValue());
|
|
EXPECT_EQ(p.Value().high.strain_energy, n.Value().high.strain_energy);
|
|
EXPECT_EQ(p.Value().strain_energy_low, n.Value().strain_energy_low);
|
|
for (std::size_t i = 0; i < 24; ++i) {
|
|
EXPECT_EQ(p.Value().high.internal_force[i], n.Value().high.internal_force[i]);
|
|
EXPECT_EQ(p.Value().internal_force_low[i], n.Value().internal_force_low[i]);
|
|
for (std::size_t j = 0; j < 24; ++j) {
|
|
EXPECT_EQ(p.Value().high.tangent(i,j), n.Value().high.tangent(i,j));
|
|
EXPECT_EQ(p.Value().tangent_low(i,j), n.Value().tangent_low(i,j));
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
TEST(Hex8HighLow, FiniteRotationRetainsTinyShearForceCovariance) {
|
|
using namespace fesa::math_internal;
|
|
auto brick = UnitBrick();
|
|
fesa::Hex8Element::Coordinates x{{{0, 0, 0}, {1, 0, 0},
|
|
{1, 1, 0}, {0, 1, 0},
|
|
{0, 0, 1}, {1, 0, 1},
|
|
{1, 1, 1}, {0, 1, 1}}};
|
|
fesa::Vector zero(24), rotation(24), shear(24), rotated_shear(24);
|
|
const double gamma = std::ldexp(1.0, -60);
|
|
for (std::size_t a = 0; a < 8; ++a) {
|
|
// Q is an exact quarter turn; Q*(gamma*y,0,0)=(0,gamma*y,0).
|
|
rotation[3*a] = HighLow{-x[a][1] - x[a][0]}.high;
|
|
rotation[3*a+1] = x[a][0] - x[a][1];
|
|
shear[3*a] = gamma*x[a][1];
|
|
rotated_shear[3*a+1] = gamma*x[a][1];
|
|
}
|
|
fesa::Vector turned_high(24), turned_low(24);
|
|
for (std::size_t j = 0; j < 24; ++j) {
|
|
const auto full = Add(HighLow{rotation[j]}, HighLow{rotated_shear[j]});
|
|
turned_high[j] = full.high; turned_low[j] = full.low;
|
|
}
|
|
const auto origin = brick.EvaluateNonlinearHighLow(zero, zero);
|
|
const auto deformed = brick.EvaluateNonlinearHighLow(shear, zero);
|
|
const auto turned = brick.EvaluateNonlinearHighLow(rotation, zero);
|
|
const auto turned_deformed = brick.EvaluateNonlinearHighLow(turned_high, turned_low);
|
|
ASSERT_TRUE(origin.HasValue()); ASSERT_TRUE(deformed.HasValue());
|
|
ASSERT_TRUE(turned.HasValue()); ASSERT_TRUE(turned_deformed.HasValue());
|
|
// The fixed F64 reference gradients leave coefficient-level rotation error.
|
|
// Subtract the same rigid baseline; do not project that force to zero.
|
|
for (std::size_t a = 0; a < 8; ++a) {
|
|
std::array<HighLow, 3> baseline{}, rotated{};
|
|
for (std::size_t i = 0; i < 3; ++i) {
|
|
const auto j = 3*a+i;
|
|
baseline[i] = Subtract(
|
|
{deformed.Value().high.internal_force[j], deformed.Value().internal_force_low[j]},
|
|
{origin.Value().high.internal_force[j], origin.Value().internal_force_low[j]});
|
|
rotated[i] = Subtract(
|
|
{turned_deformed.Value().high.internal_force[j], turned_deformed.Value().internal_force_low[j]},
|
|
{turned.Value().high.internal_force[j], turned.Value().internal_force_low[j]});
|
|
}
|
|
EXPECT_LE(std::abs(Add(rotated[0], baseline[1]).high), 1e-13*gamma);
|
|
EXPECT_LE(std::abs(Subtract(rotated[1], baseline[0]).high), 1e-13*gamma);
|
|
EXPECT_LE(std::abs(Subtract(rotated[2], baseline[2]).high), 1e-13*gamma);
|
|
}
|
|
}
|
|
TEST(Hex8HighLow,
|
|
MeanVolumeLowOnlyNonuniformTraceRetainsMeanAndCrossPointHessian) {
|
|
auto brick = UnitBrick(0, .25);
|
|
fesa::Vector high(24), low(24), zero(24);
|
|
const double c = std::ldexp(1.0, -60);
|
|
for (std::size_t n = 0; n < 8; ++n) high[3 * n] = 1;
|
|
low[6] = c;
|
|
low[18] = c;
|
|
const double coefficient = 7 * 4.8 / 18 + 8.0 / 8;
|
|
const auto response = brick.EvaluateLinearHighLow(high, low);
|
|
const auto high_only = brick.EvaluateLinearHighLow(high, zero);
|
|
ASSERT_TRUE(response.HasValue());
|
|
ASSERT_TRUE(high_only.HasValue());
|
|
EXPECT_EQ(high_only.Value().high.strain_energy, 0);
|
|
EXPECT_NEAR(response.Value().high.strain_energy, coefficient * c * c,
|
|
1e-13 * c * c);
|
|
EXPECT_NEAR(response.Value().high.internal_force[6] +
|
|
response.Value().high.internal_force[18],
|
|
2 * coefficient * c, 1e-13 * c);
|
|
for (const auto& point : response.Value().high.points) {
|
|
const auto& s = point.cauchy_stress;
|
|
EXPECT_NEAR((s[0] + s[1] + s[2]) / 3, 4 * c, 1e-13 * c);
|
|
EXPECT_NEAR(point.strain[0], c * point.reference_coordinates[1], 1e-13 * c);
|
|
}
|
|
const auto& k = response.Value().high.tangent;
|
|
EXPECT_NEAR(k(0, 0), 41.0 / 18, 2e-14);
|
|
EXPECT_NEAR(k(0, 1), 19.0 / 30, 2e-14);
|
|
const auto nonlinear = brick.EvaluateNonlinearHighLow(high, low);
|
|
ASSERT_TRUE(nonlinear.HasValue());
|
|
const auto cubic_energy = Subtract({nonlinear.Value().high.strain_energy,
|
|
nonlinear.Value().strain_energy_low},
|
|
{response.Value().high.strain_energy,
|
|
response.Value().strain_energy_low});
|
|
EXPECT_NEAR(cubic_energy.high, (5 * 4.8 / 18 + 8.0 / 6) * c * c * c,
|
|
1e-12 * c * c * c);
|
|
}
|
|
} // namespace
|